From dd74c5bd529b58f5286edf2e17e63601db768116 Mon Sep 17 00:00:00 2001 From: Chris Sangwin Date: Tue, 19 Nov 2024 15:37:16 +0000 Subject: [PATCH] Update STACK sample materials. --- .../AlgMap-2-1.xml | 2 +- .../AlgMap-2-2.xml | 3 +- .../AlgMap-2-3.xml | 2 +- .../AlgMap-2-4.xml | 2 +- .../AlgMap-3-1.xml | 5 +- .../AlgMap-3-2.xml | 3 +- .../AlgMap-3-3.xml | 3 +- .../AlgMap-3-4.xml | 3 +- .../AlgMap-3-5.xml | 5 +- .../AlgMap-3-6.xml | 3 +- .../AlgMap-3-7.xml | 3 +- .../AlgMap-3-8.xml | 3 +- .../AlgMap-3-9.xml | 3 +- .../AlgMap-5-1.xml | 3 +- .../AlgMap-5-2.xml | 3 +- .../08-Algebraic-fractions/AlgMap-8-21.xml | 2 +- .../08-Algebraic-fractions/AlgMap-8-23.xml | 3 +- .../08-Algebraic-fractions/AlgMap-8-3.xml | 2 +- .../08-Algebraic-fractions/AlgMap-8-5.xml | 2 +- .../08-Algebraic-fractions/AlgMap-8-8.xml | 2 +- .../09-Linear-equations/AlgMap-9-1.xml | 2 +- .../09-Linear-equations/AlgMap-9-6.xml | 2 +- .../AlgMap-10-7.xml | 2 +- .../AlgMap-10-8.xml | 2 +- .../AlgMap-11-11.xml | 2 +- .../AlgMap-11-9.xml | 2 +- .../AlgMap-13-1-.xml | 2 +- .../AlgMap-13-13.xml | 2 +- .../AlgMap-13-16.xml | 2 +- .../AlgMap-13-17.xml | 2 +- .../AlgMap-13-20.xml | 2 +- .../AlgMap-13-4.xml | 2 +- .../AlgMap-13-7.xml | 2 +- .../AlgMap-13-8.xml | 2 +- .../AlgMap-14-6.xml | 3 +- .../15-Quadratic-equations/AlgMap-15-1.xml | 3 +- .../15-Quadratic-equations/AlgMap-15-3.xml | 3 +- .../15-Quadratic-equations/AlgMap-15-7.xml | 3 +- .../CR_Diff_04/CR-Diff-04-product-1-b.xml | 5 +- .../CR_Diff_04/CR-Diff-04-product-1-c.xml | 5 +- .../CR_Diff_04/CR-Diff-04-product-1-d.xml | 5 +- .../CR_Diff_04/CR-Diff-04-product-1-f.xml | 5 +- .../CR_Diff_04/CR-Diff-04-product-2-e.xml | 5 +- .../CR_Diff_04/CR-Diff-04-product-2-g.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-1-a.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-1-b.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-1-c.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-1-d.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-1-e.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-2-a.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-2-b.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-2-d.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-2-e.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-3-a.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-3-b.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-3-c.xml | 5 +- .../CR_Diff_05/CR-Diff-05-quotient-3-d.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-a.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-b.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-c.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-d.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-f.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-1-h.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-2-a.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-2-b.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-2-d.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-2-e.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-2-f.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-a.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-b.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-c.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-d.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-e.xml | 5 +- .../CR_Diff_06/CR-Diff-06-chain-3-f.xml | 5 +- .../CR_Diff_07/CR-Diff-07-implicit-1-a.xml | 3 +- .../CR_Diff_07/CR-Diff-07-implicit-1-b.xml | 5 +- .../CR_Diff_07/CR-Diff-07-implicit-1-c.xml | 3 +- .../CR_Diff_07/CR-Diff-07-implicit-2-a.xml | 3 +- .../CR_Diff_07/CR-Diff-07-implicit-2-b.xml | 3 +- .../CR_Diff_07/CR-Diff-07-implicit-2-e.xml | 5 +- .../CR-Diff-08-parametrical-1-d.xml | 3 +- .../CR-Diff-08-parametrical-2-b.xml | 3 +- .../CR_Diff_09/CR-Diff-09-misc-2-b.xml | 5 +- .../CR_Diff_09/CR-Diff-09-misc-2-c.xml | 3 +- .../CR_Diff_09/CR-Diff-09-misc-4-b.xml | 6 +- .../CR_Diff_09/CR-Diff-09-misc-5-b.xml | 7 +- .../CR_Int_11/CR-Int-11-linearity-1-b.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-1-c.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-1-d.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-1-e.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-1-h.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-1-k.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-2-a.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-2-d.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-2-f.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-2-l.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-3-e.xml | 5 +- .../CR_Int_11/CR-Int-11-linearity-3-f.xml | 5 +- .../CR_Int_12/CR-Int-12-definite-1-f.xml | 5 +- .../CR_Int_12/CR-Int-12-definite-1-g.xml | 5 +- .../CR_Int_12/CR-Int-12-definite-1-h.xml | 5 +- .../CR_Int_12/CR-Int-12-definite-3.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-1-a.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-1-e.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-2-a.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-2-b.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-2-c.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-2-d.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-4-a.xml | 3 +- .../CR_Int_13/CR-Int-13-parts-5.xml | 5 +- .../CR_Int_13/CR-Int-13-parts-6.xml | 6 +- .../CR_Int_13/CR-Int-13-parts-7.xml | 6 +- .../CR_Int_14/CR-Int-14-substitution-1-b.xml | 5 +- .../CR_Int_14/CR-Int-14-substitution-1-i.xml | 5 +- .../CR_Int_14/CR-Int-14-substitution-3-b.xml | 8 +- .../CR_Int_14/CR-Int-14-substitution-3-c.xml | 6 +- .../CR_Int_14/CR-Int-14-substitution-3-d.xml | 8 +- .../CR_Int_14/CR-Int-14-substitution-3-f.xml | 8 +- .../CR_Int_14/CR-Int-14-substitution-3-g.xml | 8 +- .../CR_Int_14/CR-Int-14-substitution-5-a.xml | 5 +- .../CR_Int_14/CR-Int-14-substitution-6-a.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-1-b.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-1-e.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-10.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-2-a.xml | 6 +- .../CR_Int_15/CR-Int-15-partialfrac-2-b.xml | 6 +- .../CR_Int_15/CR-Int-15-partialfrac-3-a.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-3-b.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-3-c.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-4-b.xml | 6 +- .../CR_Int_15/CR-Int-15-partialfrac-4-c.xml | 6 +- .../CR_Int_15/CR-Int-15-partialfrac-5.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-6.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-7.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-8.xml | 5 +- .../CR_Int_15/CR-Int-15-partialfrac-9.xml | 2 +- .../CR_Int_16/CR-Int-16-trigonometric-1-b.xml | 3 +- .../CR_Int_16/CR-Int-16-trigonometric-3.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-03.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-04.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-05.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-06.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-08.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-09.xml | 6 +- .../CR_Int_17/CR-Int-17-misc-10.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-12.xml | 3 +- .../CR_Int_17/CR-Int-17-misc-13.xml | 5 +- .../CR_Int_17/CR-Int-17-misc-14.xml | 5 +- .../Doc-Examples/D-L-distance.xml | 40 +- .../Doc-Examples/Drag_and_drop-1-grouping.xml | 32 +- .../Doc-Examples/Drag_and_drop-2-Grid.xml | 32 +- .../Drag_and_drop-3-Grid_with_index.xml | 30 +- .../Drag_and_drop-4-Using-images.xml | 34 +- .../stacklibrary/Doc-Examples/GeoGebra.xml | 38 +- .../Doc-Examples/Parsons-1-minimal.xml | 31 +- .../Parsons-2-Interchangable-order.xml | 28 +- .../Doc-Examples/Parsons-3-builder.xml | 208 +++++---- .../Features/MCQ-example-multiselqnalpha.xml | 36 +- .../stacklibrary/Features/MCQ-example.xml | 31 +- .../Features/Reveal_block_example.xml | 368 ++++++++-------- .../Features/Scientific-units.xml | 48 +- .../Differential_Equation_3.xml | 3 +- .../Topics/Complex_cube_roots.xml | 412 +++++++++--------- ...hs-Discrete_mathematics_graph-theory-2.xml | 34 +- .../Cross-product-non-cancellation.xml | 54 ++- .../Diagonalizable-proof-comprehension.xml | 221 +++++----- ...Eigenvalues-eigenvectors-give-examples.xml | 242 +++++----- .../LinearAlgebra/Eigenvalues-vectors-3-3.xml | 148 ++++--- .../LinearAlgebra/Eigenvalues-vectors-4-4.xml | 191 ++++---- .../Eigenvalues-vectors-PDPT.xml | 156 ++++--- .../Equation-plane-counter-example.xml | 107 +++-- .../LinearAlgebra/Linear-dependence.xml | 48 +- .../Topics/LinearAlgebra/Linear-system.xml | 132 +++--- .../Matrix-Algebra-give-examples.xml | 302 +++++++------ .../LinearAlgebra/Proof-dot-product.xml | 167 ++++--- .../Proof-gaps-linear-dependence.xml | 316 +++++++------- .../Show-Ax-forms-a-subspace-Parsons.xml | 27 +- .../Topics/ODE_2nd_order_linear.xml | 52 ++- .../Topics/Parsons-proof-template.xml | 118 +++-- .../Proof_comprehension_infinite_primes.xml | 166 ++++--- .../Proof/Proof_comprehension_roots_unity.xml | 106 +++-- .../Proof/Proof_gaps_induction_series.xml | 159 ++++--- .../Topics/Topics_units_basic.xml | 87 ++-- .../stacklibrary/Topics/Vector-Calculus.xml | 80 ++-- .../Topics/equivalence_reasoning_example.xml | 56 ++- ...ot-Discrete_mathematics_graph_theory-1.xml | 50 +-- 186 files changed, 2407 insertions(+), 2630 deletions(-) diff --git a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-1.xml b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-1.xml index 589de191957..624ecfdaf5e 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-1.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-1.xml @@ -25,7 +25,7 @@ ta:factor(n); [[feedback:prt1]]

]]> - {@n@} = {@ta@} + {@n@} = {@ta@} diff --git a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-2.xml b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-2.xml index be63a16d99e..838e5d2f99e 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-2.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-2.xml @@ -20,8 +20,7 @@ a:2^(rand(1)+1)*3^(rand(2))*5^(rand(2)); b:2^(rand(1)+1)*3^(rand(2))*5^(rand(2))*7; -ta:ratsimp(rootscontract(radcan(sqrt(a)*sqrt(b)))); - +ta:ratsimp(rootscontract(radcan(sqrt(a)*sqrt(b)))); [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-3.xml b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-3.xml index 1c6b76b70a0..8ac52386232 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-3.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-3.xml @@ -32,7 +32,7 @@ ta:gcd(a,b); [[feedback:prt1]]

]]> - (Hcf) of \({@a@}\) and \({@b@}\) is \({@ta@}\). + (Hcf) of \({@a@}\) and \({@b@}\) is \({@ta@}\). diff --git a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-4.xml b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-4.xml index f0d45114612..897bff0451c 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-4.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/02-Factorisation-of-whole-numbers/AlgMap-2-4.xml @@ -33,7 +33,7 @@ ta:lcm(a,b); [[feedback:prt1]]

]]> - (LCM) of \({@a@}\) and \({@b@}\) is \({@ta@}\). + (LCM) of \({@a@}\) and \({@b@}\) is \({@ta@}\). diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-1.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-1.xml index 61d1f54c1b4..b495b3d2661 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-1.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-1.xml @@ -26,14 +26,13 @@ d:b; c:d+1; ta:(a/b)+(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> - \[{@a/b@}+{@c/d@} = {@ta@}.\] + \[{@a/b@}+{@c/d@} = {@ta@}.\] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-2.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-2.xml index a7658e6a407..05167218dd2 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-2.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-2.xml @@ -26,8 +26,7 @@ d:b; c:d+rand(3)+1; ta:(a/b)-(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-3.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-3.xml index 04585208291..cfb6403034c 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-3.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-3.xml @@ -27,8 +27,7 @@ d:b+1+2*rand(3); c:d+rand(3)+1; ta:(a/b)+(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-4.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-4.xml index 2a7b98eef9b..c6daab90536 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-4.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-4.xml @@ -27,8 +27,7 @@ d:rand([3,7,11]); c:rand([2,5,13])^rand([0,1]); ta:(a/b)-(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-5.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-5.xml index 8f5d3e1c851..3e769bebe03 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-5.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-5.xml @@ -27,14 +27,13 @@ d:7; c:rand([1,2,3,4,5,6,8,9]); ta:(a/b)+(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> - \[{@a/b@}+{@c/d@} = {@ta@}.\] + \[{@a/b@}+{@c/d@} = {@ta@}.\] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-6.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-6.xml index 4285eeae5e1..47c21864c1f 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-6.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-6.xml @@ -27,8 +27,7 @@ d:3; c:rand([1,2,4,5,7,8,10]); ta:(a/b)-(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-7.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-7.xml index 7f9459ff7fe..ef3d182dce5 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-7.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-7.xml @@ -28,8 +28,7 @@ d:f*b; c:d-1; ta:(a/b)+(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-8.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-8.xml index 8262fc00d9f..28015759293 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-8.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-8.xml @@ -28,8 +28,7 @@ d:f*b; c:1; ta:(a/b)-(c/d); lcm:lcm(b,d); -simp:false - +simp:false [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-9.xml b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-9.xml index 0fdaa11f350..f7344c556e5 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-9.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/03-Addition-and-subtraction-of-fractions/AlgMap-3-9.xml @@ -28,8 +28,7 @@ d:f*rand([2,4]); c:d+1; ta:(a/b)+(c/d); lcm:lcm(b,d); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-1.xml b/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-1.xml index c2f32580f49..18849d72ec8 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-1.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-1.xml @@ -28,8 +28,7 @@ f:e+rand(4)+1; g:rand(5)+1; h:g+rand(4)+1; ta:((a/b)+(c/d))/((e/f)+(g/h)); -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-2.xml b/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-2.xml index 22c38de5e18..f36c8981501 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-2.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/05-Combinations-of-arithmetic-operations-on-fractions/AlgMap-5-2.xml @@ -28,8 +28,7 @@ t:c/d; ta1:(s^2+2*t^2); ta2:(3-s*t); ta:ta1/ta2; -simp:false; - +simp:false; [[feedback:prt1]]

]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-21.xml b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-21.xml index 9ff4c413023..2bea67bb350 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-21.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-21.xml @@ -157,7 +157,7 @@ fta:ev(factor(ta),simp); - 3 + 2 ans diff --git a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-23.xml b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-23.xml index 6f9ae072080..9705ed3a4f7 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-23.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-23.xml @@ -11,8 +11,7 @@ Give an equivalent expression without brackets.
= [[input:ans]] -[[validation:ans]] -]]> +[[validation:ans]]]]> diff --git a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-3.xml b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-3.xml index c4e14d57cf6..b63e2d3d82f 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-3.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-3.xml @@ -26,7 +26,7 @@ ta:ev(1/a,simp); [[feedback:prt1]]

]]> - \[ \frac{@v@}{@ev(a*v,simp)@} = {@ta@}. \] + \[ \frac{@v@}{@ev(a*v,simp)@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-5.xml b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-5.xml index 40b3a601fbe..dbe5162f51b 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-5.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-5.xml @@ -24,7 +24,7 @@ [[feedback:prt1]]

]]> - \[ \frac{@b-a@}{@a-b@} = {@ta@}. \] + \[ \frac{@b-a@}{@a-b@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-8.xml b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-8.xml index e43538bb278..0a42df4a482 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-8.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/08-Algebraic-fractions/AlgMap-8-8.xml @@ -29,7 +29,7 @@ ta:ev((a*f*(v-c))/(b*f*(v-c)^3),simp); [[feedback:prt1]]

]]> - \[ \frac{@ev(a*f*(v-c),simp)@}{@ev(b*f*(v-c)^3,simp)@} = {@ta@}. \] + \[ \frac{@ev(a*f*(v-c),simp)@}{@ev(b*f*(v-c)^3,simp)@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-1.xml b/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-1.xml index 549bfa00249..80fb543dea2 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-1.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-1.xml @@ -37,7 +37,7 @@ ta:(k2-k1)/cf1; [[feedback:prt1]]

]]> - \[ {@cf1*v+k1@} = {@k2@} \Rightarrow {@v@} = {@ta@}. \] + \[ {@cf1*v+k1@} = {@k2@} \Rightarrow {@v@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-6.xml b/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-6.xml index eafe2769158..6587262f42e 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-6.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/09-Linear-equations/AlgMap-9-6.xml @@ -37,7 +37,7 @@ ta:35/4; [[feedback:prt1]]

]]> - \[ {@(3-v)/5+3@} = {@(2*v+1)/10@} \Rightarrow {@v@} = {@ta@}. \] + \[ {@(3-v)/5+3@} = {@(2*v+1)/10@} \Rightarrow {@v@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-7.xml b/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-7.xml index 1ef7272c71e..3540ffeebe9 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-7.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-7.xml @@ -12,7 +12,7 @@ Simply remove all common factors from the expression. In this example: \[ {@v^p1+v^p2@} = {@ta@}. \] -The important thing is to remember the 1 after factoring. +The important thing is to remember the 1 after factoring. 1 0.1 diff --git a/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-8.xml b/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-8.xml index 786d89c56c8..7406b65c192 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-8.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/10-Expressions-single-term-common-factors/AlgMap-10-8.xml @@ -12,7 +12,7 @@ Simply remove all common factors from the expression. In this example: \[ {@v^p1-v^p2@} = {@ta@}. \] -The important thing is to remember the 1 after factoring. +The important thing is to remember the 1 after factoring. 1 0.1 diff --git a/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-11.xml b/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-11.xml index bbce064231a..c5a6449ef7a 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-11.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-11.xml @@ -36,7 +36,7 @@ Now you have an equation for \(x\). [[feedback:prt1]]

]]> - \[ {@y@} = {@sqrt(x^2+4)@} \Rightarrow x = {@ta@} . \] + \[ {@y@} = {@sqrt(x^2+4)@} \Rightarrow x = {@ta@} . \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-9.xml b/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-9.xml index f3be7bb74c7..1d69b2d14e7 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-9.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/11-Rearranging-algebraic-formulae/AlgMap-11-9.xml @@ -33,7 +33,7 @@ Now you have an equation for \(x\). [[feedback:prt1]]

]]> - \[{@a@} = {@sqrt(b+x)@} \Rightarrow x = {@ta@}.\] + \[{@a@} = {@sqrt(b+x)@} \Rightarrow x = {@ta@}.\] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-1-.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-1-.xml index 65b64827210..79dd07fdd8a 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-1-.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-1-.xml @@ -2,7 +2,7 @@ - AlgMap-13.1 + AlgMap-13.1 +Therefore \((a+b)^2 = (x+4y)^2. \) 1 0.1 diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-16.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-16.xml index 57af19ee6f3..3b33f6b1c91 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-16.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-16.xml @@ -13,7 +13,7 @@ The trick to factorising this expression is to carry out a substitution, \(u=xy\). Then we obtain the quadratic: \[ u^2-2u+1, \] which is easily solved by normal methods: -\[ u^2-2u+1 = \left(u-1\right)^2 = \left(xy-1\right)^2. \] +\[ u^2-2u+1 = \left(u-1\right)^2 = \left(xy-1\right)^2. \] 1 0.1 diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-17.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-17.xml index 343ead37684..8368496bb12 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-17.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-17.xml @@ -32,7 +32,7 @@ which is now clearly a difference of two squares. So factorising gives: [[feedback:prt1]]

]]> - \[ {@(a+b)^2-(a+c)^2@} = {@ta@}. \] + \[ {@(a+b)^2-(a+c)^2@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-20.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-20.xml index da7272cd230..ff25eab1320 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-20.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-20.xml @@ -36,7 +36,7 @@ Then factor out \(x+y\) to give: [[feedback:prt1]]

]]> - \[ {@(a*x+a*y-b*x-b*y)@} = {@ta@}. \] + \[ {@(a*x+a*y-b*x-b*y)@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-4.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-4.xml index 3e41d0ca0c5..90f83b48c22 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-4.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-4.xml @@ -38,7 +38,7 @@ ta:factor((cf1*v+a)*(cf2*v+b)); [[feedback:prt1]]

]]> - \[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@ta@}. \] + \[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-7.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-7.xml index eab28d2bd5d..a5e17aa422e 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-7.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-7.xml @@ -43,7 +43,7 @@ ta:factor((cf1*v+a)*(cf2*v+b)); [[feedback:prt1]]

]]> - \[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@ta@}. \] + \[ {@expand((cf1*v+a)*(cf2*v+b))@} = {@ta@}. \] diff --git a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-8.xml b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-8.xml index 218cf00cefa..d5b67e265b6 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-8.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/13-Factorising-algebraic-expressions/AlgMap-13-8.xml @@ -148,7 +148,7 @@ ta:factor((cf1*v+a)*(cf2*v+b)); - 3 + 2 ans diff --git a/samplequestions/stacklibrary/Algebra-Refresher/14-Algebraic-fractions-involving-factorising/AlgMap-14-6.xml b/samplequestions/stacklibrary/Algebra-Refresher/14-Algebraic-fractions-involving-factorising/AlgMap-14-6.xml index f9bebeeabd0..c8212ad5e7b 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/14-Algebraic-fractions-involving-factorising/AlgMap-14-6.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/14-Algebraic-fractions-involving-factorising/AlgMap-14-6.xml @@ -14,8 +14,7 @@ By factorisng the numerator and the denominator we obtain: \[\frac{@factor(n)@}{@factor(d)@}.\] Then we can cancel the \({@x@}\)'s and constants from the numerator -and denominator to obtain: \[ {@ta@}. \] - +and denominator to obtain: \[ {@ta@}. \] 1 0.1 diff --git a/samplequestions/stacklibrary/Algebra-Refresher/15-Quadratic-equations/AlgMap-15-1.xml b/samplequestions/stacklibrary/Algebra-Refresher/15-Quadratic-equations/AlgMap-15-1.xml index a7ee1c7972f..63bcf804230 100644 --- a/samplequestions/stacklibrary/Algebra-Refresher/15-Quadratic-equations/AlgMap-15-1.xml +++ b/samplequestions/stacklibrary/Algebra-Refresher/15-Quadratic-equations/AlgMap-15-1.xml @@ -14,8 +14,7 @@ Write this quadratic in factored form: [[input:ansf]]\(=0\). [[validation:ansf]]
Solve this equation, giving your answer as a set \(\left(\mbox{e.g. }\left\{x_1 , x_2\right\}\right)\):

-\({@v@} \in \) [[input:ans]] [[validation:ans]][[feedback:prt1]] -]]> +\({@v@} \in \) [[input:ans]] [[validation:ans]][[feedback:prt1]]]]> [[input:ans2]] [[validation:ans2]] -[[feedback:prt1]] -]]> +[[feedback:prt1]]]]> -(i.e. the form \(\left({@v@}+a\right)^2+b\)). -]]> +(i.e. the form \(\left({@v@}+a\right)^2+b\)).]]> Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -17,7 +16,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}({@pp1@})\right]\cdot {@pp2@} + ({@pp1@})\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle ({@diff(pp1,v)@})\cdot {@pp2@} + ({@pp1@})\cdot {@diff(pp2,v)@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-c.xml index 1d27af40a33..3f6501c657e 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-c.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -17,7 +16,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}({@pp1@})\right]\cdot {@pp2@} + ({@pp1@})\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle ({@diff(pp1,v)@})\cdot {@pp2@} + ({@pp1@})\cdot {@diff(pp2,v)@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-d.xml index 665720ec0da..2366b21bc63 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-d.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -17,7 +16,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}({@pp1@})\right]\cdot {@pp2@} + ({@pp1@})\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle ({@diff(pp1,v)@})\cdot {@pp2@} + ({@pp1@})\cdot {@diff(pp2,v)@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-f.xml index 6e9a4f44966..8e5b4c36f78 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-1-f.xml @@ -7,8 +7,7 @@ Differentiate \[\left({@pp1@}\right)\left({@pp2@}\right)\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -17,7 +16,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}({@pp1@})\right]\cdot {@pp2@} + ({@pp1@})\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle \left({@diff(pp1,v)@}\right)\cdot {@pp2@} + \left({@pp1@}\right)\cdot {@diff(pp2,v)@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-e.xml index f0c9056fc7b..b3fff060b60 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-e.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}[{@p@}]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -18,7 +17,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}[{@pp1@}]\right]\cdot {@pp2@} + {@pp1@}\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle {@diff(pp1,v)@}\cdot {@pp2@} + {@pp1@}\cdot [{@diff(pp2,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-g.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-g.xml index 460a1ac9cab..4da2a22d284 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-g.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_04/CR-Diff-04-product-2-g.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}[{@p@}]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule as follows: @@ -18,7 +17,7 @@ \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle \left[\frac{d}{d{@v@}}[{@pp1@}]\right]\cdot {@pp2@} + {@pp1@}\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right] \\ &\displaystyle =&\displaystyle {@diff(pp1,v)@}\cdot {@pp2@} + {@pp1@}\cdot [{@diff(pp2,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-a.xml index acbd4060a88..9266d4da4e1 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-a.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{{@diff(pp1,v)*pp2@} - {@pp1*diff(pp2,v)@}}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle \frac{@diff(pp1,v)*pp2-pp1*diff(pp2,v)@}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-b.xml index da2be8cce2a..6f71fd2b79b 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-b.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{{@diff(pp1,v)*pp2@} - {@pp1*diff(pp2,v)@}}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle \frac{@diff(pp1,v)*pp2-pp1*diff(pp2,v)@}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-c.xml index 38eaa5f6495..d7de93b43c2 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-c.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{{@diff(pp1,v)*pp2@} - {@pp1*diff(pp2,v)@}}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle \frac{@diff(pp1,v)*pp2-pp1*diff(pp2,v)@}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-d.xml index a800c67171e..56cdf4ffcf7 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-d.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{{@diff(pp1,v)*pp2@} - {@pp1*diff(pp2,v)@}}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle \frac{@diff(pp1,v)*pp2-pp1*diff(pp2,v)@}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-e.xml index 30a09709633..dd4b46c432f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-1-e.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{{@diff(pp1,v)*pp2@} - {@pp1*diff(pp2,v)@}}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle \frac{@diff(pp1,v)*pp2-pp1*diff(pp2,v)@}{({@pp2@})^2} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-a.xml index f8d3e11621b..48dfc1644ec 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-a.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -18,7 +17,7 @@ \frac{d}{d{@v@}}\left[{@p@}\right] &\displaystyle =&\displaystyle \frac{\left[\frac{d}{d{@v@}}({@pp1@})\right]\cdot {@pp2@} - {@pp1@}\cdot \left[\frac{d}{d{@v@}}[{@pp2@}]\right]}{[{@pp2@}]^2} \\ &\displaystyle =&\displaystyle \frac{[{@diff(pp1,v)@}]\cdot {@pp2@} - {@pp1@}\cdot [{@diff(pp2,v)@}]}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-b.xml index 6ac12771a6f..ed54942b0b6 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-b.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-d.xml index 24b800fdd99..804d4debfc4 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-d.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -19,7 +18,7 @@ &\displaystyle =&\displaystyle \frac{[{@diff(pp1,v)@}]\cdot {@pp2@} - {@pp1@}\cdot [{@diff(pp2,v)@}]}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@}\\ &\displaystyle =&\displaystyle {@ratsimp(diff(p,v))@}. - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-e.xml index 6b8985c21ae..329136fe394 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-2-e.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-a.xml index 152956b1a7c..790ae0fbde9 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-a.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-b.xml index 24d2bf06113..cfc3ba0be19 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-b.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-c.xml index fcf4dc4c09c..78a53541498 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-c.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-d.xml index f0e345de818..41b4fbd0343 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_05/CR-Diff-05-quotient-3-d.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left[{@p@}\right]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_quotient_rule as follows: @@ -20,7 +19,7 @@ &\displaystyle =&\displaystyle \frac{{@factor(diff(pp1,v))*pp2@} - {@pp1*factor(diff(pp2,v))@}}{@pp2^2@} \\ &\displaystyle =&\displaystyle \frac{@factor(factor(diff(pp1,v))*pp2-pp1*factor(diff(pp2,v)))@}{@pp2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-a.xml index 49c7f468648..d6e695d452b 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-a.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@rdm2@} \\ &\displaystyle =&\displaystyle {@rdm3*rdm2@}({@pp@})^{@rdm3-1@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-b.xml index 366395b6cd3..8da5b12abcd 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-b.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm2@}\). So, &\displaystyle =&\displaystyle {@rdm2@}g^{{@rdm2@}-1}\cdot (-{@rdm1@}){@v@}^{{@rdm1@}-1} \\ &\displaystyle =&\displaystyle -{@rdm1*rdm2@}{@v@}^{@rdm1-1@}({@pp@})^{@rdm2-1@} \\ &\displaystyle =&\displaystyle -{@rdm1*rdm2*v^(rdm1-1)*pp^(rdm2-1)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-c.xml index f1f7c9df7a2..43b6d9768a1 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-c.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@rdm2@} \\ &\displaystyle =&\displaystyle {@rdm3*rdm2@}({@pp@})^{@rdm3-1@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-d.xml index 2a19aeb4daa..00594b58b4c 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-d.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@rdm2@} \\ &\displaystyle =&\displaystyle {@rdm3*rdm2@}({@pp@})^{@rdm3-1@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-f.xml index 60408867e1d..947a430847d 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-f.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle {@rdm3@}({@pp@})^{@rdm3-1@}[{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-h.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-h.xml index c0e0bb2c9cd..a83aca2f8af 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-h.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-1-h.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle {@rdm3@}({@pp@})^{@rdm3-1@}[{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-a.xml index d478c5da664..45af7f1ff0d 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-a.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=g({@v@})^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@rdm3@}g^{{@rdm3@}-1}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle {@rdm3@}({@pp@})^{@rdm3-1@}[{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-b.xml index 12f9cde808a..b867e181b25 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-b.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=sin(g({@v@}))\). So, &\displaystyle =&\displaystyle {@diff(sin(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle [{@subst(pp,g,diff(sin(g),g))@}][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-d.xml index cbf3ebc5228..1d3d903b3b4 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-d.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=(g({@v@}))^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@diff(tan(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle [{@subst(pp,g,diff(tan(g),g))@}][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-e.xml index be277becbe3..2264b488031 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-e.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=(g({@v@}))^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@diff((g)^rdm3,g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle [{@subst(pp,g,diff((g)^rdm3,g))@}][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-f.xml index f2e51b1bf4f..998d4b483df 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-2-f.xml @@ -7,8 +7,7 @@ Differentiate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=(g({@v@}))^{@rdm3@}\). So, &\displaystyle =&\displaystyle {@diff((g)^rdm3,g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle \left[{@subst(pp,g,diff((g)^rdm3,g))@}\right][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-a.xml index 000abe1db4d..af84b26cdf0 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-a.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \[f({@v@})=e^{g({@v@})}\]. So, &\displaystyle =&\displaystyle {@diff(exp(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle \left[{@subst(pp,g,diff(exp(g),g))@}\right][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-b.xml index 90d08d0d723..8b10db9cd47 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-b.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \[f({@v@})=e^{(g({@v@}))}\]. So, &\displaystyle =&\displaystyle {@diff(exp(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle [{@subst(pp,g,diff(exp(g),g))@}][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-c.xml index c4cedece3b3..50bee807cde 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-c.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=cos(g({@v@}))\). So, &\displaystyle =&\displaystyle {@diff(cos(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle [{@subst(pp,g,diff(cos(g),g))@}][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-d.xml index 47b5365c485..a4a463870c6 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-d.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=ln(g({@v@}))\). So, &\displaystyle =&\displaystyle {@diff(log(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle \left[{@subst(pp,g,diff(log(g),g))@}\right][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-e.xml index 4ecab020944..2c4290d30e2 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-e.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}[{@p@}]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ Then \(f({@v@})=sin[g({@v@})]\). So, &\displaystyle =&\displaystyle \frac{d}{dg}[sin(g)]\cdot \frac{d}{d{@v@}}[{@pp@}] \\ &\displaystyle =&\displaystyle {@diff(sin(g),g)@}\cdot \frac{@rdm@}{{@rdm@} {@v@}} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-f.xml index 2b830006f49..99df3331d86 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_06/CR-Diff-06-chain-3-f.xml @@ -7,8 +7,7 @@ Differentiate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule as follows: @@ -23,7 +22,7 @@ So \(f({@v@})=ln(g({@v@}))\). So, &\displaystyle =&\displaystyle {@diff(log(g),g)@}\cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle \left[{@subst(pp,g,diff(log(g),g))@}\right][{@diff(pp,v)@}] \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-a.xml index 70bc474ff6c..8f9d5c89704 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-a.xml @@ -9,8 +9,7 @@ \[x = {@p@}\] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-b.xml index 78247f5181b..d449631ce83 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-b.xml @@ -9,8 +9,7 @@ \[x = {@p@}\] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-c.xml index 2e7b4a821f8..a8f46c831db 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-1-c.xml @@ -9,8 +9,7 @@ \[x = {@p@}\] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-a.xml index 8c4a02fb820..14bdce3773e 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-a.xml @@ -7,8 +7,7 @@ Find \(\frac{dy}{dx}\) where \({@p@}=0\) using implicit differentiation. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] Differentiating implicitly we obtain: diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-b.xml index 3f478656d48..f5a44b887bc 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-b.xml @@ -7,8 +7,7 @@ Find \(\frac{dy}{dx}\) where \({@p@}=0\) using implicit differentiation. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] \[y^2-y+x^2+x=0\] So, diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-e.xml index 32653f62832..1996f2a5b23 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_07/CR-Diff-07-implicit-2-e.xml @@ -7,8 +7,7 @@ Find \(\frac{dy}{dx}\) where \({@p@}=0\) using implicit differentiation. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] Differentiating implicity with respect to x we obtain: @@ -16,7 +15,7 @@ \[ \frac{dy}{dx}\left({@exp(y)-1/y@}\right) = {@1/x-1@}. \] \[\frac{dy}{dx} = {@(1/x-1)/(exp(y)-1/y)@}. \] Rationalising and factorising gives: -\[\frac{dy}{dx} = {@ans@}.\] +\[\frac{dy}{dx} = {@ans@}.\] 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-1-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-1-d.xml index a33c632fc90..8d102444f33 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-1-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-1-d.xml @@ -20,8 +20,7 @@ v:t; x:log(t)+t; -y:t-log(t); - +y:t-log(t); [[feedback:Result]]

]]> diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-2-b.xml index 47c68c5e996..a68bed2e27d 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_08/CR-Diff-08-parametrical-2-b.xml @@ -22,8 +22,7 @@ rdm1:2+rand(4); rdm2:2+rand(4); x:cos(rdm1*v); -y:tan(rdm2*v); - +y:tan(rdm2*v); [[feedback:Result]]

]]> diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-b.xml index 4e3398b24b1..24f2e6ac54e 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-b.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}\left( {@p@}\right). \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_product_rule and the quotient rulecalc_quotient_rule. @@ -35,7 +34,7 @@ Hence, &\displaystyle =&\displaystyle \frac{[{@diff(p1,v)@}]{@p2@} - {@p1@}[{@diff(p2,v)@}]}{[{@p2@}]^2} \\ &\displaystyle =&\displaystyle \frac{{@diff(p1,v)*p2@} - {@p1*diff(p2,v)@}}{@p2^2@} \\ &\displaystyle =&\displaystyle {@factor(diff(p,v))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-c.xml index 025ea864695..d950989d049 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-2-c.xml @@ -27,8 +27,7 @@ pp1:ppp1*ppp2; pp2:tan(rdm1*v); p:pp1/pp2; p2:cos(rdm1*v)*cos(rdm2*v) -ta:diff(p2,v); - +ta:diff(p2,v); [[feedback:Result]]

]]> diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-4-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-4-b.xml index ad4fa3b1888..3fe28faf433 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-4-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-4-b.xml @@ -8,8 +8,7 @@ Find the following derivative: \[ \frac{d}{d{@v@}}[{@p@}]. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_chain_rule more than once. @@ -37,8 +36,7 @@ So, &\displaystyle =&\displaystyle e^g \cdot {@diff(pp,v)@} \\ &\displaystyle =&\displaystyle e^{@pp@}{@diff(pp,v)@} \\ &\displaystyle =&\displaystyle {@diff(p,v)@} - \end{array}\] -]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-5-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-5-b.xml index 58d9fb13018..09423a8207f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-5-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Diff_09/CR-Diff-09-misc-5-b.xml @@ -8,8 +8,7 @@ Find the following second derivative: \[ \frac{d^2}{d{@v@}^2}({@p@}). \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-b.xml index dafcfc62c31..60a60feed1f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-b.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -17,7 +16,7 @@ \int \left({@p@}\right) d{@v@} &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}[{@int(ppp1,v)@}] \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-c.xml index 11cb41354f0..3906378289f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-c.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -17,7 +16,7 @@ \int \left({@p@}\right) d{@v@} &\displaystyle =&\displaystyle \int {@pp1@} d{@v@} - \int {@pp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(ppp1,v)@} - {@int(ppp2,v)@} + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-d.xml index 6ba42910344..f27c59ed6a0 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-d.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -17,7 +16,7 @@ \int \left({@p@}\right) d{@v@} &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}[{@int(ppp1,v)@}] \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-e.xml index b3c1ae67721..697dcd09ee6 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-e.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -17,7 +16,7 @@ \int \left({@p@}\right) d{@v@} &\displaystyle =&\displaystyle \int {@pp1@} d{@v@} - \int {@pp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(ppp1,v)@} - {@int(ppp2,v)@} + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-h.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-h.xml index 3ad855d9878..f3428979eb8 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-h.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-h.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -17,7 +16,7 @@ \int \left({@p@}\right) d{@v@} &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}[{@int(ppp1,v)@}] \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-k.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-k.xml index c86ef19bd2d..492469bc191 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-k.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-1-k.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -18,7 +17,7 @@ &\displaystyle =&\displaystyle {@rdm@}\int {@ppp1@} d{@v@} - {@rdm@}\int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm@}{@int(ppp1,v)@} - {@rdm@}{@int(ppp2,v)@} + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-a.xml index c0b97596bb5..1bd6cfd054c 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-a.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -18,7 +17,7 @@ &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} + \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}\left[{@int(ppp1,v)@}\right] + \left[{@int(ppp2,v)@}\right] + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-d.xml index da8e126a2da..ed2b3e551eb 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-d.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -18,7 +17,7 @@ &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} + \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}\left[{@int(ppp1,v)@}\right] + \left[{@int(ppp2,v)@}\right] + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-f.xml index e3d46e12a49..620a9557656 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-f.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -18,7 +17,7 @@ &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} + {@rdm2@}\int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}\left[{@int(ppp1,v)@}\right] + {@rdm2@}\left[{@int(ppp2,v)@}\right] + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-l.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-l.xml index a90ac0a8492..dbcc98802cd 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-l.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-2-l.xml @@ -7,8 +7,7 @@ Integrate \[{@p@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule as follows: @@ -18,7 +17,7 @@ &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} + \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@}\left[{@int(ppp1,v)@}\right] + \left[{@int(ppp2,v)@}\right] + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-e.xml index 4cb92a53908..29b5fba5def 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-e.xml @@ -7,8 +7,7 @@ Simplify and integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_indices we get that @@ -24,7 +23,7 @@ So, using linearity in integration calc_int_linearity_rule, &\displaystyle =&\displaystyle \int {@pp2*ppp1@} d{@v@} - \int {@pp2*ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(pp2*ppp1,v)@} - {@int(pp2*ppp2,v)@} + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-f.xml index 21a27ef0463..6be5efdd748 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_11/CR-Int-11-linearity-3-f.xml @@ -7,8 +7,7 @@ Simplify and integrate \[\frac{@pp1@}{@pp2@}\] with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_indices we get that @@ -24,7 +23,7 @@ So, using linearity in integration calc_int_linearity_rule, &\displaystyle =&\displaystyle \int {@ppp1/pp2@} d{@v@} - \int {@ppp2/pp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(ppp1/pp2,v)@} - {@int(ppp2/pp2,v)@} + c \\ &\displaystyle =&\displaystyle {@int(p,v)@} + c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-f.xml index 2357a689573..a86eacb1805 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-f.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm2@}{@p@}d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-g.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-g.xml index f84c99c498a..3474c3b1069 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-g.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-g.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm2@}{@p@}d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-h.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-h.xml index 96782ef06c1..f8b11e4cc7d 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-h.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-1-h.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm2@}{@p@}d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-3.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-3.xml index 5fa078ea8f7..a6bba5a021a 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-3.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_12/CR-Int-12-definite-3.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm4@}{@p@}d{@v@}.\] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-a.xml index 21bfbdca534..55b935ecb98 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-a.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-e.xml index 1a120888043..ee8378c0695 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-1-e.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@}. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-a.xml index 4e802a8d608..bf271ed9f80 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-a.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm4@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-b.xml index 1dd95a05e95..9d6e366e457 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-b.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm4@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-c.xml index c8210257cc9..20c9a71da71 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-c.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm4@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-d.xml index b855904dff4..cef9cfa0e82 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-2-d.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm3@}_{@rdm4@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-4-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-4-a.xml index c977706d276..670d2701c75 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-4-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-4-a.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[ \int^{@rdm2@}_{@rdm3@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] Integrate {@p@} with respect to {@v@} using the method of integration by parts, and taking \({@p@}=1\cdot \ {@p@}\). -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-6.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-6.xml index 11d0b4f9d20..20b9f413ee6 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-6.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-6.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@} using the method of integration by parts. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_parts as follows: @@ -32,8 +31,7 @@ So, \[\begin{array}{rcl}\displaystyle 2\int {@p@} d{@v@} &\displaystyle =&\displaystyle {@pp1*pp1@} + c \\ \int {@p@} d{@v@} &\displaystyle =&\displaystyle {@int(p,v)@} + k - \end{array}\] -]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-7.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-7.xml index 1b31f0cacbe..fe0b3616f23 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-7.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_13/CR-Int-13-parts-7.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to \(t\) using the method of integration by parts. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] +\end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-b.xml index 11ed1048096..56cf54e7251 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-b.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@} using the substitution \(u={@ppp@}\). -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -22,7 +21,7 @@ Hence, &\displaystyle =&\displaystyle \int {@subst(u,ppp,p)/diff(ppp,v)@} d{@u@} \\ &\displaystyle =&\displaystyle {@int(subst(u,ppp,p)/diff(ppp,v),u)+c@} \\ &\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-i.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-i.xml index cb08b5c66f7..73265af0919 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-i.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-1-i.xml @@ -7,8 +7,7 @@ Integrate {@p@} with respect to {@v@} using the substitution \(u={@ppp@}\). -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -22,7 +21,7 @@ Hence, &\displaystyle =&\displaystyle \int {@subst(u,ppp,p)/diff(ppp,v)@} d{@u@} \\ &\displaystyle =&\displaystyle {@int(subst(u,ppp,p)/diff(ppp,v),u)+c@} \\ &\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-b.xml index eb782aeeca4..c8846916414 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-b.xml @@ -10,8 +10,7 @@ Hint: Use the substitution \(u = {@pp2@}\)
[[input:ans1]] -[[validation:ans1]] -]]> +[[validation:ans1]]]]> calc_int_methods_substitution. @@ -38,7 +37,7 @@ Then, \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm1@}) - F({@rdm2@}) \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,subst(pp2,u,int(expand(subst(q,v,p)*diff(q,u)),u)))@}-{@subst(rdm2,v,subst(pp2,u,int(expand(subst(q,v,p)*diff(q,u)),u)))@} \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,subst(pp2,u,int(expand(subst(q,v,p)*diff(q,u)),u)))-subst(rdm2,v,subst(pp2,u,int(expand(subst(q,v,p)*diff(q,u)),u)))@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 @@ -66,8 +65,7 @@ q1:(int(p,v));]]> [[feedback:Result]]

]]> - \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] - + \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-c.xml index 472a0580ac0..60a489fd874 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-c.xml @@ -53,15 +53,13 @@ pp2:(v+rdm3)^(1/2); p:v*pp2; dumvar7:u; q:rhs(solve(u=pp2,v)[1]); -q1:int(p,v); -]]> +q1:int(p,v);]]> [[feedback:Result]]

]]> - \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] - + \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-d.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-d.xml index ff02a9a22dd..1f486857128 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-d.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-d.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@}\] Hint: Use the substitution \(u = {@pp2@}\) -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -36,7 +35,7 @@ Then, \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm1@}) - F({@rdm2@}) \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)@}-{@subst(rdm2,v,q1)@} \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)-subst(rdm2,v,q1)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 @@ -61,8 +60,7 @@ q1:factor(int(p,v)); [[feedback:Result]]

]]> - \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] - + \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-f.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-f.xml index f1f82a9934b..add8e3d0ebb 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-f.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-f.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@}\] Hint: Use the substitution \(u = {@pp2@}\) -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -36,7 +35,7 @@ Then, \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm1@}) - F({@rdm2@}) \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)@}-{@subst(rdm2,v,q1)@} \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)-subst(rdm2,v,q1)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 @@ -59,8 +58,7 @@ q1:int(p,v); [[feedback:Result]]

]]> - \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] - + \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-g.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-g.xml index 8a2aa58f758..d5298df168d 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-g.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-3-g.xml @@ -8,8 +8,7 @@ Evaluate the following definite integral: \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@}\] Hint: Use the substitution \(u = {@pp2@}\) -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -36,7 +35,7 @@ Then, \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm1@}) - F({@rdm2@}) \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)@}-{@subst(rdm2,v,q1)@} \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q1)-subst(rdm2,v,q1)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 @@ -61,8 +60,7 @@ q1:int(p,v);]]> [[feedback:Result]]

]]> - \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] - + \[\int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} = {@int(p,v,rdm2,rdm1)@}\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-5-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-5-a.xml index 59ff813505e..246b1d89a3a 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-5-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-5-a.xml @@ -7,8 +7,7 @@ Find the following integral:\[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -19,7 +18,7 @@ Hence, \[\begin{array}{rcl}\displaystyle \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@pp2/u@} \frac{d{@u@}}{@diff(pp1,v)@} \\&\displaystyle =&\displaystyle \int {@1/u@} d{@u@} \\&\displaystyle =&\displaystyle {@int(1/u,u)+c@} \\&\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-6-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-6-a.xml index 18ce062ca5f..83587aea12c 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-6-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_14/CR-Int-14-substitution-6-a.xml @@ -7,8 +7,7 @@ Using the method of integration by substitution, find the following integral:\[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_substitution. @@ -19,7 +18,7 @@ Hence, \[\begin{array}{rcl}\displaystyle \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@pp2/u@} \frac{d{@u@}}{@diff(pp1,v)@} \\&\displaystyle =&\displaystyle \int {@pp2/u/diff(pp1,v)@} d{@u@} \\&\displaystyle =&\displaystyle {@pp2/diff(pp1,v)@} \int {@1/u@} d{@u@} \\&\displaystyle =&\displaystyle {@pp2/diff(pp1,v)@}{@int(1/u,u)+c@} \\&\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-b.xml index af57ed740d2..d5a741533c2 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-b.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following integral: \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -36,7 +35,7 @@ Hence, \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@q@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@} \int {@ppp1@} d{@v@} + {@rdm2@} \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-e.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-e.xml index e729f173056..ab6e4d31858 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-e.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-1-e.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following integral: \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -36,7 +35,7 @@ Hence, \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@q@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1@} \int {@ppp1@} d{@v@} + {@rdm2@} \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-10.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-10.xml index 3a72682cdb6..c3d793c6f02 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-10.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-10.xml @@ -9,8 +9,7 @@ \[ \int {@p@} d{@v@} \] by expressing the integrand in partial fractions. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions @@ -39,7 +38,7 @@ So, &\displaystyle =&\displaystyle {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm3@} \int {@ppp2@} d{@v@} + \int ({@pp3@}) d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm3*int(ppp2,v)@} + {@int(pp3,v)@}+c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm3*int(ppp2,v)+int(pp3,v)@}+c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-a.xml index 9e9a6da3439..981c517b6cd 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-a.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following definite integral: \[ \int^{@rdm5@}_{@rdm6@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-b.xml index 42c2630ebf0..86459866675 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-2-b.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following definite integral: \[ \int^{@rdm5@}_{@rdm6@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-a.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-a.xml index c14b3798330..4995931db7a 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-a.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-a.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following integral: \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -37,7 +36,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm2@} \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm2*int(ppp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-b.xml index 56e4ddccfa4..7353bd4af44 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-b.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following integral: \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -37,7 +36,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm2@} \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm2*int(ppp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-c.xml index 031ad63da75..95c8adf554f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-3-c.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following integral: \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -37,7 +36,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm2@} \int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm2*int(ppp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-b.xml index dc5178d7036..54bd8df22c9 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-b.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following definite integral: \[ \int^{@rdm4@}_{@rdm5@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -39,8 +38,7 @@ Then, \int^{@rdm4@}_{@rdm5@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm4@}) - F({@rdm5@}) \\ &\displaystyle =&\displaystyle {@subst(rdm4,v,pq)@} - \left[{@subst(rdm5,v,pq)@}\right] \\ &\displaystyle =&\displaystyle {@subst(rdm4,v,pq)-subst(rdm5,v,pq)@} - \end{array}\] -]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-c.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-c.xml index 12b988010db..5278442fd2f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-c.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-4-c.xml @@ -8,8 +8,7 @@ By expressing the integrand as the sum of its partial fractions, find the following definite integral: \[ \int^{@rdm4@}_{@rdm5@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -33,8 +32,7 @@ Then, \int^{@rdm4@}_{@rdm5@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm4@}) - F({@rdm5@}) \\ &\displaystyle =&\displaystyle {@subst(rdm4,v,pq)@} - \left[{@subst(rdm5,v,pq)@}\right] \\ &\displaystyle =&\displaystyle {@subst(rdm4,v,pq)-subst(rdm5,v,pq)@} - \end{array}\] -]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-5.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-5.xml index fecbce3fe79..a1a23503c73 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-5.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-5.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -36,7 +35,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm3@} \int {@ppp1@} d{@v@} + {@rdm3@} \int {@ppp2@} d{@v@} + {@rdm3@} \int {@ppp3@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm2*int(ppp2,v)@} + {@rdm3*int(ppp3,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm2*int(ppp2,v)+rdm3*int(ppp3,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-6.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-6.xml index d26937caa13..ede775a561b 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-6.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-6.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -36,7 +35,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm4@} \int {@ppp1@} d{@v@} + {@rdm5@} \int {@ppp2@} d{@v@} + {@rdm6@} \int {@ppp3@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)@} + {@rdm5*int(ppp2,v)@} + {@rdm6*int(ppp3,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)+rdm5*int(ppp2,v)+rdm6*int(ppp3,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-7.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-7.xml index a2cc4dcb6c1..82d83cabe1f 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-7.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-7.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -36,7 +35,7 @@ Hence, &\displaystyle =&\displaystyle {@rdm4@} \int {@ppp1@} d{@v@} + {@rdm5@} \int {@ppp2@} d{@v@} + {@rdm6@} \int {@ppp3@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)@} + {@rdm5*int(ppp2,v)@} + {@rdm6*int(ppp3,v)@} +c \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)+rdm5*int(ppp2,v)+rdm6*int(ppp3,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-8.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-8.xml index 641ce4f5c50..e69158fe494 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-8.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-8.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] Note that the degree of the numerator is greater then the degree of the denominator. -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions @@ -37,7 +36,7 @@ So, &\displaystyle =&\displaystyle {@rdm4@} \int {@ppp1@} d{@v@} + {@rdm5@} \int {@ppp2@} d{@v@} + \int ({@pp3@}) d{@v@} \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)@} + {@rdm5*int(ppp2,v)@} + {@int(pp3,v)@}+c \\ &\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)+rdm5*int(ppp2,v)+int(pp3,v)@}+c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-9.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-9.xml index 3e73fd6fc40..866cdc7bad3 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-9.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_15/CR-Int-15-partialfrac-9.xml @@ -28,7 +28,7 @@ So, &\displaystyle =&\displaystyle {@rdm2@} \int {@ppp1@} d{@v@} + {@rdm4@} \int {@ppp2@} d{@v@} + {@rdm3@} \int \left({@ppp3@}\right) d{@v@} + \int {@pp4@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)@} + {@rdm4*int(ppp2,v)@} + {@rdm3*int(ppp3,v)@}+ {@int(pp4,v)@} + c \\ &\displaystyle =&\displaystyle {@rdm2*int(ppp1,v)+rdm4*int(ppp2,v)+rdm3*int(ppp3,v)+int(pp4,v)@}+c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-1-b.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-1-b.xml index b44076e1e8e..0d559ea4768 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-1-b.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-1-b.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] \[ \int {@p@} d{@v@} = {@int(p,v)@}+c\] diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-3.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-3.xml index ee0728028ce..07f73d2f676 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-3.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_16/CR-Int-16-trigonometric-3.xml @@ -7,8 +7,7 @@ Use the identity \[\sin(A)\cos(A)=\frac{\sin(2A)}{2}\] to find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-03.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-03.xml index fb082988f8e..bd86bcc84c9 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-03.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-03.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-04.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-04.xml index 2ba8a92c5cb..9085e307f3e 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-04.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-04.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule: @@ -17,7 +16,7 @@ &\displaystyle =&\displaystyle {@rdm1@}\int {@ppp1@} d{@v@} + {@rdm3@}\int {@ppp2@} d{@v@} + \int {@pp3@} d{@v@} \\ &\displaystyle =&\displaystyle {@rdm1*int(ppp1,v)@} + {@rdm3*int(ppp2,v)@} + {@int(pp3,v)@} +c \\ &\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-05.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-05.xml index 8489a5ccf82..72cd99a92fb 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-05.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-05.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_linearity_rule: @@ -17,7 +16,7 @@ &\displaystyle =&\displaystyle \int {@pp1@} d{@v@} + {@rdm2@}\int {@ppp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(pp1,v)@} + {@rdm2*int(ppp2,v)@} +c \\ &\displaystyle =&\displaystyle {@int(p,v)+c@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-06.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-06.xml index 4dd6439c637..40378dd87e0 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-06.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-06.xml @@ -7,8 +7,7 @@ By taking logarithms to the base \(e\) establish that \(a^x\) can be written as \(e^{xlna}\). Hence find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-08.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-08.xml index 6cba78325b8..31d92e3cf6a 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-08.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-08.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -33,7 +32,7 @@ Hence, \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@q@} d{@v@} \\ &\displaystyle =&\displaystyle \int {@pp1@} d{@v@} + \int {@pp2@} d{@v@} \\ &\displaystyle =&\displaystyle {@int(pp1,v)+int(pp2,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-09.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-09.xml index 511b4146830..7dac9b5de22 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-09.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-09.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] +\[\int {@p@} d{@v@} = \frac{@pp1*int(pp2,v)@}{2}+ \frac{c}{2}.\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-10.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-10.xml index e32e6925f6f..97f9f4156be 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-10.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-10.xml @@ -7,8 +7,7 @@ Find \[ \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] trig_standard_identities @@ -46,7 +45,7 @@ Then \int^{@rdm1@}_{@rdm2@} {@p@} d{@v@} &\displaystyle =&\displaystyle F({@rdm1@}) - F({@rdm2@}) \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q)@} - \left[{@subst(rdm2,v,q)@}\right] \\ &\displaystyle =&\displaystyle {@subst(rdm1,v,q)-subst(rdm2,v,q)@} - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-12.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-12.xml index e9ba630a07b..001fd4e90d2 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-12.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-12.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] calc_int_methods_parts as follows: diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-13.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-13.xml index f93abfd689c..ee810718ec9 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-13.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-13.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions. @@ -31,7 +30,7 @@ Hence, \[\begin{array}{rcl}\displaystyle \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@q@} d{@v@} \\&\displaystyle =&\displaystyle {@rdm4@} \int {@ppp1@} d{@v@} + {@rdm5@} \int {@ppp2@} d{@v@} + {@rdm6@} \int {@ppp3@} d{@v@} \\&\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)@} + {@rdm5*int(ppp2,v)@} + {@rdm6*int(ppp3,v)@} +c \\&\displaystyle =&\displaystyle {@rdm4*int(ppp1,v)+rdm5*int(ppp2,v)+rdm6*int(ppp3,v)@} +c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-14.xml b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-14.xml index fa35afaf541..7960254c8a2 100644 --- a/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-14.xml +++ b/samplequestions/stacklibrary/Calculus-Refresher/CR_Int_17/CR-Int-17-misc-14.xml @@ -7,8 +7,7 @@ Find \[ \int {@p@} d{@v@}. \] -[[input:ans1]] [[validation:ans1]] - +[[input:ans1]] [[validation:ans1]] alg_partial_fractions @@ -34,7 +33,7 @@ So, \[\begin{array}{rcl}\displaystyle \int {@p@} d{@v@} &\displaystyle =&\displaystyle \int {@q@} d{@v@} \\&\displaystyle =&\displaystyle {@rdm3@} \int {@ppp1@} d{@v@} + {@rdm4@} \int {@ppp2@} d{@v@} + \int ({@pp3@}) d{@v@} \\&\displaystyle =&\displaystyle {@rdm3*int(ppp1,v)@} + {@rdm4*int(ppp2,v)@} + {@int(pp3,v)@}+c \\&\displaystyle =&\displaystyle {@rdm3*int(ppp1,v)+rdm4*int(ppp2,v)+int(pp3,v)@}+c - \end{array}\] ]]> + \end{array}\]]]> 1 0.1 diff --git a/samplequestions/stacklibrary/Doc-Examples/D-L-distance.xml b/samplequestions/stacklibrary/Doc-Examples/D-L-distance.xml index 81ed888254e..e2f3ad5dd65 100644 --- a/samplequestions/stacklibrary/Doc-Examples/D-L-distance.xml +++ b/samplequestions/stacklibrary/Doc-Examples/D-L-distance.xml @@ -1,6 +1,5 @@ - D-L distance @@ -10,12 +9,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -32,7 +31,7 @@ ta:first(allow1);]]> [[feedback:prt1]] - + The purpose of this question is to illustrate using string match and the Levenshtein distance. This is the question outlined in the `Levenshtein distance` page of mathematical topics in the documentation. This can be found on your server at `[YOUR SERVER ADDRESS]/question/type/stack/doc/doc.php/Topics/Levenshtein_distance.md` . @@ -57,7 +56,7 @@ ta:first(allow1);]]> cos-1 lang [ - + ans1 string @@ -65,16 +64,16 @@ ta:first(allow1);]]> 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -82,7 +81,7 @@ ta:first(allow1);]]> 1 1 - + 0 @@ -94,19 +93,19 @@ ta:first(allow1);]]> 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -126,7 +125,7 @@ ta:first(allow1);]]> 2 - + ans1 @@ -140,7 +139,7 @@ ta:first(allow1);]]> 3 - + ans1 @@ -154,7 +153,7 @@ ta:first(allow1);]]> 4 - + ans1 @@ -168,7 +167,7 @@ ta:first(allow1);]]> 5 - + ans1 @@ -176,10 +175,9 @@ ta:first(allow1);]]> prt1 0.0000000 - + prt1-1-F - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-1-grouping.xml b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-1-grouping.xml index 1d6e1acd541..352fd9a125b 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-1-grouping.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-1-grouping.xml @@ -1,6 +1,5 @@ - Drag and drop - 1 - grouping example @@ -18,12 +17,12 @@ Drag the functions to their appropriate category.

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -93,7 +92,7 @@ wa: [ cos-1 lang [ - + ans1 parsons @@ -101,16 +100,16 @@ wa: [ 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -124,27 +123,27 @@ tans: match_column_set(ta); 0 - + AlgEquiv sans tans - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -168,7 +167,7 @@ tans: match_column_set(ta); 2 - + ans1 apply(group_answer,[wa, steps]) @@ -181,5 +180,4 @@ tans: match_column_set(ta); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-2-Grid.xml b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-2-Grid.xml index d7626c76f42..03652736d08 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-2-Grid.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-2-Grid.xml @@ -1,6 +1,5 @@ - Drag and drop -2- Grid @@ -16,12 +15,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -96,7 +95,7 @@ wa: [ cos-1 lang [ - + ans1 parsons @@ -104,16 +103,16 @@ wa: [ 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -127,27 +126,27 @@ tans: match_set_row(ta); 0 - + AlgEquiv sans tans - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -186,7 +185,7 @@ tans: match_set_row(ta); 3 - + ans1 apply(match_answer,[ta2, steps, 3]) @@ -199,5 +198,4 @@ tans: match_set_row(ta); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-3-Grid_with_index.xml b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-3-Grid_with_index.xml index 25a53e39c50..6a8429892f5 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-3-Grid_with_index.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-3-Grid_with_index.xml @@ -1,6 +1,5 @@ - Drag and drop - 3 - Grid with index @@ -17,12 +16,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -95,7 +94,7 @@ wa: [ cos-1 lang [ - + ans1 parsons @@ -103,16 +102,16 @@ wa: [ 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -124,27 +123,27 @@ wa: [ 0 - + AlgEquiv sans ta - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -182,5 +181,4 @@ wa: [ - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-4-Using-images.xml b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-4-Using-images.xml index 218de6c846e..ab533783e34 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-4-Using-images.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Drag_and_drop-4-Using-images.xml @@ -1,6 +1,5 @@ - Drag and drop - 4 - Using images @@ -16,12 +15,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -57,9 +56,7 @@ ta: [ ["f", "g"], ["dfdx", "dgdx"], ["df2d2x", "dg2d2x"] -]; - -]]> +];]]> [[feedback:prt1]] @@ -90,7 +87,7 @@ ta: [ cos-1 lang [ - + ans1 parsons @@ -98,10 +95,10 @@ ta: [ 15 1 0 - + 0 - - + + 1 0 0 @@ -121,27 +118,27 @@ tans: match_set_row(ta); 0 - + AlgEquiv sans tans - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -166,7 +163,7 @@ tans: match_set_row(ta); 2 - + ans1 apply(match_answer,[wa, steps, 3]) @@ -179,5 +176,4 @@ tans: match_set_row(ta); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/GeoGebra.xml b/samplequestions/stacklibrary/Doc-Examples/GeoGebra.xml index 91df6a159a8..ed94b65c1a7 100644 --- a/samplequestions/stacklibrary/Doc-Examples/GeoGebra.xml +++ b/samplequestions/stacklibrary/Doc-Examples/GeoGebra.xml @@ -1,6 +1,5 @@ - GeoGebra - 1 - minimal question @@ -14,12 +13,12 @@ ]]> - + 1 0.1 0 - + 2024092500 @@ -59,7 +58,7 @@ ta:-1/m; cos-1 lang [ - + ans1 algebraic @@ -67,10 +66,10 @@ ta:-1/m; 15 1 0 - + 0 - - + + 0 0 0 @@ -85,10 +84,10 @@ ta:-1/m; 15 1 0 - + 0 - - + + 1 0 0 @@ -102,11 +101,11 @@ ta:-1/m; 1 1 - + 0 - + NumAbsolute ans1*m -1 @@ -114,19 +113,19 @@ ta:-1/m; 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -156,14 +155,14 @@ ta:-1/m; 2 - + ans1 1/m remember - + prt1 @@ -173,5 +172,4 @@ ta:-1/m; - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Parsons-1-minimal.xml b/samplequestions/stacklibrary/Doc-Examples/Parsons-1-minimal.xml index b2b33f9a3ec..85299882e35 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Parsons-1-minimal.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Parsons-1-minimal.xml @@ -1,6 +1,5 @@ - Parsons proofs 1- Minimal @@ -13,12 +12,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -43,8 +42,7 @@ proof_steps: [ proof_steps: random_permutation(proof_steps); /*a correct order, edit if changing question*/ -ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "alg_int", "contra", "conc"); -]]> +ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "alg_int", "contra", "conc");]]> [[feedback:prt1]] @@ -75,7 +73,7 @@ ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "al cos-1 lang [ - + ans1 parsons @@ -83,16 +81,16 @@ ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "al 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -109,19 +107,19 @@ ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "al AlgEquiv pd 0 - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -158,10 +156,9 @@ ta: proof("assume", "defn_rat", "defn_rat2", "defn_log", "defn_log2", "alg", "al prt1 0.0000000 - + prt1-1-F - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Parsons-2-Interchangable-order.xml b/samplequestions/stacklibrary/Doc-Examples/Parsons-2-Interchangable-order.xml index 24ac3986375..f4d35523ab4 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Parsons-2-Interchangable-order.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Parsons-2-Interchangable-order.xml @@ -1,6 +1,5 @@ - parsons proof 2-Interchangable order @@ -25,7 +24,7 @@ Can you see the differences between these proofs?]]> 1 0.1 0 - + 2024092500 @@ -94,7 +93,7 @@ tas: setify(map(proof_flatten, tal));]]> cos-1 lang [ - + ans1 parsons @@ -102,16 +101,16 @@ tas: setify(map(proof_flatten, tal));]]> 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -124,23 +123,23 @@ tas: setify(map(proof_flatten, tal));]]> 0 - + AlgEquiv pd 0 - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -170,7 +169,7 @@ tas: setify(map(proof_flatten, tal));]]> 2 - + ans1 apply(parsons_answer,[wa, proof_steps]) @@ -183,5 +182,4 @@ tas: setify(map(proof_flatten, tal));]]> - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Doc-Examples/Parsons-3-builder.xml b/samplequestions/stacklibrary/Doc-Examples/Parsons-3-builder.xml index e9d535d954b..f067345b4da 100644 --- a/samplequestions/stacklibrary/Doc-Examples/Parsons-3-builder.xml +++ b/samplequestions/stacklibrary/Doc-Examples/Parsons-3-builder.xml @@ -1,107 +1,106 @@ - Parsons-feedback-builder - [[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 - @@ -111,10 +110,10 @@ ps:map(lambda([ex],[first(ex),second(ex)]),proof_steps);]]> {#map(first,proof_steps)#} - This question illustrates a general framework for questions that ask the student to construct a proof by selecting phrases from a given list and arranging them in order. - -The question author can specify various kinds of rules for generating feedback if the proof is invalid. Most of the logic is in a Maxima file `builder.mac` in the contrib directory, - + This question illustrates a general framework for questions that ask the student to construct a proof by selecting phrases from a given list and arranging them in order. + +The question author can specify various kinds of rules for generating feedback if the proof is invalid. Most of the logic is in a Maxima file `builder.mac` in the contrib directory, + The advantage is that teachers can mange meaningful feedback for individual steps, but of course that is more work than using the auto-generated feedback. As illustrated in this question, the auto-generated feedback can sit alongside the bespoke feedback generated by the builder library. 1 @@ -137,7 +136,7 @@ The advantage is that teachers can mange meaningful feedback for individual step cos-1 lang [ - + ans1 parsons @@ -145,16 +144,16 @@ The advantage is that teachers can mange meaningful feedback for individual step 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -162,33 +161,33 @@ The advantage is that teachers can mange meaningful feedback for individual step 1 1 - sa: parsons_decode(ans1); -[pd, saa]:proof_assessment(sa, proof_alternatives(ta)); + sa: parsons_decode(ans1); +[pd, saa]:proof_assessment(sa, proof_alternatives(ta)); [sc,an,fb]:builder_check_rules(sa,proof_steps,prules); 0 - + AlgEquiv pd 0 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - {@fb@} + {@fb@} {@proof_assessment_display(saa, proof_steps)@} @@ -227,5 +226,4 @@ The advantage is that teachers can mange meaningful feedback for individual step - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Features/MCQ-example-multiselqnalpha.xml b/samplequestions/stacklibrary/Features/MCQ-example-multiselqnalpha.xml index c664cb2dd12..b7ebeb7e8fa 100644 --- a/samplequestions/stacklibrary/Features/MCQ-example-multiselqnalpha.xml +++ b/samplequestions/stacklibrary/Features/MCQ-example-multiselqnalpha.xml @@ -1,6 +1,5 @@ - MCQ_example_multiselqnalpha @@ -10,12 +9,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -58,7 +57,7 @@ corr1:mcq_correct(ta1); cos-1 lang [ - + ans1 checkbox @@ -66,16 +65,16 @@ corr1:mcq_correct(ta1); 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -83,31 +82,31 @@ corr1:mcq_correct(ta1); 1 1 - + 0 - + Sets setify(ans1) setify(corr1) - + 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -133,7 +132,7 @@ corr1:mcq_correct(ta1); 357901509 1 - + ans1 corr1 @@ -147,7 +146,7 @@ corr1:mcq_correct(ta1); 2 - + ans1 [corr1[1]] @@ -160,5 +159,4 @@ corr1:mcq_correct(ta1); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Features/MCQ-example.xml b/samplequestions/stacklibrary/Features/MCQ-example.xml index cd4105a90d0..45faa81c9ed 100644 --- a/samplequestions/stacklibrary/Features/MCQ-example.xml +++ b/samplequestions/stacklibrary/Features/MCQ-example.xml @@ -1,6 +1,5 @@ - MCQ_example_Remainder Theorem T/F @@ -10,12 +9,12 @@ [[input:ans1]] [[validation:ans1]]]]> - + 1 0.1 0 - + 2024092500 @@ -43,9 +42,7 @@ statements:makelist([sconcat("(",ascii(96+i),")"),statements[i][1],statements[i] statements:maplist(lambda([ex],[ex[1],ex[2],sconcat("",ex[1]," ",ex[3])]),statements); /* Produce lists of correct and incorrect statements: */ tans:mcq_correct(statements); -incorr:maplist(first, sublist(statements, lambda([ex], not(second(ex))))); - -]]> +incorr:maplist(first, sublist(statements, lambda([ex], not(second(ex)))));]]> [[feedback:prt1]] @@ -77,7 +74,7 @@ The marking counts the number correct and the number incorrect. You are then ab cos-1 lang [ - + ans1 checkbox @@ -85,16 +82,16 @@ The marking counts the number correct and the number incorrect. You are then ab 15 1 0 - + 0 - - + + 1 1 0 0 0 - + prt1 @@ -108,8 +105,7 @@ The marking counts the number correct and the number incorrect. You are then ab PRT score fields can be variables so, should you choose to, and use that value to assign a score. */ -nocorrect:cardinality(intersection(setify(tans),setify(ans1))); -]]> +nocorrect:cardinality(intersection(setify(tans),setify(ans1)));]]> 0 @@ -117,7 +113,7 @@ nocorrect:cardinality(intersection(setify(tans),setify(ans1))); Sets setify(ans1) setify(tans) - + 0 = 1 @@ -125,7 +121,7 @@ nocorrect:cardinality(intersection(setify(tans),setify(ans1))); -1 prt1-0-T - + = 0 @@ -171,10 +167,9 @@ nocorrect:cardinality(intersection(setify(tans),setify(ans1))); prt1 0.0000000 - + prt1-0-F - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Features/Reveal_block_example.xml b/samplequestions/stacklibrary/Features/Reveal_block_example.xml index 7b8a37d784e..5ea9bd0a09d 100644 --- a/samplequestions/stacklibrary/Features/Reveal_block_example.xml +++ b/samplequestions/stacklibrary/Features/Reveal_block_example.xml @@ -1,6 +1,5 @@ - Subspace (reveal example) @@ -38,7 +37,7 @@ For example, \(w_1 = \) [[input:answ1]] [[validation:answ1]] is in \(W\) and 3 0.1 0 - + 2023051500 @@ -67,13 +66,13 @@ taw1:transpose(matrix([null,null,null])); taw2:null; - + - + {@Ws@} - + 1 0 @@ -87,13 +86,15 @@ taw2:null; Incorrect answer.]]> + . + *10 none 1 i cos-1 lang [ - + ans0 boolean @@ -101,16 +102,16 @@ taw2:null; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ans1 @@ -119,16 +120,16 @@ taw2:null; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ans2 @@ -137,16 +138,16 @@ taw2:null; 5 1 5 - + 0 - - + + 1 0 0 1 1 - + ans3 @@ -157,14 +158,14 @@ taw2:null; 5 [?, ...] 0 - - + + 1 0 1 0 0 - + ansv1 @@ -173,16 +174,16 @@ taw2:null; 2 1 5 - + 0 - - + + 1 0 0 0 0 - + ansv2 @@ -191,16 +192,16 @@ taw2:null; 2 1 5 - + 0 - - + + 1 0 0 0 0 - + answ1 @@ -209,16 +210,16 @@ taw2:null; 3 1 5 - + 0 - - + + 1 0 0 0 0 - + answ2 @@ -227,16 +228,16 @@ taw2:null; 3 1 5 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -244,7 +245,7 @@ taw2:null; 1 1 - + 0 @@ -252,11 +253,11 @@ taw2:null; AlgEquiv ans1 issubspace - + 0 = 1 - + -1 prt1-1-T @@ -264,7 +265,7 @@ taw2:null; = 0 - + -1 prt1-1-F @@ -283,19 +284,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 0 - + AlgEquiv ans1 true - + 0 = 0 - + 1 prt2-1-T - + = 0 @@ -308,23 +309,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 - + AlgEquiv deg 1 - + 1 + 0 - + 2 prt2-2-T - + - 0 - + -1 prt2-2-F @@ -333,23 +334,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 2 - + AlgEquiv point_in_space(ans2, matrix([0],[0],[0])) true - + 1 + 0 - + 3 prt2-3-T - + - 0 - + -1 prt2-3-F @@ -358,27 +359,27 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 3 - + AlgEquiv cspace(ans2) cspace(Ws) - + 1 = 1 - + -1 prt2-4-T - + - 0 - + -1 prt2-4-F - + @@ -388,23 +389,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 1 - + 0 - + AlgEquiv ans1 false - + 0 = 0 - + 1 prt3-1-T - + = 0 @@ -417,15 +418,15 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 - + AlgEquiv ans0 not(point_in_space(Ws,matrix([0],[0],[0]))) - + 0 = 0 - + -1 prt3-2-T @@ -433,7 +434,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); = 0 - + -1 prt3-2-F @@ -447,27 +448,27 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 1 - + 0 - + AlgEquiv ans1 false - + 0 = 0 - + 1 prt4-1-T - + = 0 - + -1 prt4-1-F @@ -476,23 +477,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 - + AlgEquiv point_in_space(Ws,ansv1) true - + 0 + 0 - + 2 prt4-2-T - + - 0 - + -1 prt4-2-F @@ -501,23 +502,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 2 - + AlgEquiv point_in_space(Ws,ansv2) true - + 0 = 0 - + 3 prt4-3-T - + - 0 - + -1 prt4-3-F @@ -526,15 +527,15 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 3 - + AlgEquiv point_in_space(Ws,ansv1+ansv2) false - + 0 = 1 - + -1 prt4-4-T @@ -542,7 +543,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); - 0 - + -1 prt4-4-F @@ -556,27 +557,27 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 1 - + 0 - + AlgEquiv ans1 false - + 0 = 0 - + 1 prt5-1-T - + = 0 - + -1 prt5-1-F @@ -585,23 +586,23 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 - + AlgEquiv point_in_space(Ws,answ1) true - + 0 + 0 - + 2 prt5-2-T - + - 0 - + -1 prt5-2-F @@ -610,15 +611,15 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 2 - + AlgEquiv point_in_space(Ws,answ2*answ1) false - + 0 = 1 - + -1 prt5-3-T @@ -626,7 +627,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); - 0 - + -1 prt5-3-F @@ -636,10 +637,10 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 1 - + ans0 - + ans1 @@ -655,19 +656,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 @@ -683,29 +684,29 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt3 - - + + NULL prt4 - - + + NULL prt5 - - + + NULL 2 - + ans0 - + ans1 @@ -721,19 +722,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 @@ -749,29 +750,29 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt3 - - + + NULL prt4 - - + + NULL prt5 - - + + NULL 3 - + ans0 - + ans1 @@ -787,19 +788,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 @@ -810,31 +811,31 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt2 0.0000000 - + prt2-4-F prt3 - - + + NULL prt4 - - + + NULL prt5 - - + + NULL 4 - + ans0 true @@ -845,7 +846,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ans2 - + ans3 @@ -853,19 +854,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 @@ -875,8 +876,8 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt2 - - + + NULL @@ -887,20 +888,20 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt4 - - + + NULL prt5 - - + + NULL 5 - + ans0 false @@ -911,7 +912,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ans2 - + ans3 @@ -919,19 +920,19 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 @@ -941,8 +942,8 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt2 - - + + NULL @@ -954,10 +955,10 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); 6 - + ans0 - + ans1 @@ -965,7 +966,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ans2 - + ans3 @@ -995,14 +996,14 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); prt2 - - + + NULL prt3 - - + + NULL @@ -1031,7 +1032,7 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ans2 - + ans3 @@ -1039,51 +1040,50 @@ deg:apply(max, maplist(lambda([ex], hipow(ans2, ex)), lv)); ansv1 - + ansv2 - + answ1 - + answ2 - + prt1 0.0000000 - + prt1-1-F prt2 - - + + NULL prt3 0.0000000 - + prt3-2-F prt4 - - + + NULL prt5 - - + + NULL - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Features/Scientific-units.xml b/samplequestions/stacklibrary/Features/Scientific-units.xml index 5bd188f9b9a..e1822ef0e2c 100644 --- a/samplequestions/stacklibrary/Features/Scientific-units.xml +++ b/samplequestions/stacklibrary/Features/Scientific-units.xml @@ -1,6 +1,5 @@ - Scientific units @@ -10,12 +9,12 @@

[[input:ans1]] [[validation:ans1]]

]]> - + 1 0.1 0 - + 2024092500 @@ -62,7 +61,7 @@ uw2: stackunits((len*width)/100,m^2); cos-1 lang [ - + ans1 units @@ -70,10 +69,10 @@ uw2: stackunits((len*width)/100,m^2); 15 1 0 - + 0 - - + + 0 0 0 @@ -87,11 +86,11 @@ uw2: stackunits((len*width)/100,m^2); 1 1 - + 0 - + UnitsStrictAbsolute ans1 ta1 @@ -99,24 +98,24 @@ uw2: stackunits((len*width)/100,m^2); 0 = 1 - + -1 prt1-1-T - + = 0 - + 1 prt1-1-F - + 1 - + UnitsAbsolute ans1 ta1 @@ -124,7 +123,7 @@ uw2: stackunits((len*width)/100,m^2); 1 + 0.5 - + -1 prt1-2-T @@ -132,16 +131,16 @@ uw2: stackunits((len*width)/100,m^2); - 0 - + 2 prt1-2-F - + 2 - + UnitsAbsolute ans1 uw2 @@ -149,7 +148,7 @@ uw2: stackunits((len*width)/100,m^2); 0 + 0 - + -1 prt1-3-T @@ -157,11 +156,11 @@ uw2: stackunits((len*width)/100,m^2); - 0 - + -1 prt1-3-F - + @@ -189,7 +188,7 @@ uw2: stackunits((len*width)/100,m^2); 2 - + ans1 uw2 @@ -203,7 +202,7 @@ uw2: stackunits((len*width)/100,m^2); 3 - + ans1 uw1 @@ -216,5 +215,4 @@ uw2: stackunits((len*width)/100,m^2); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/General-maths-questions/First-Order-ODE/Differential_Equation_3.xml b/samplequestions/stacklibrary/General-maths-questions/First-Order-ODE/Differential_Equation_3.xml index 2bd9aae267b..db49466b86e 100644 --- a/samplequestions/stacklibrary/General-maths-questions/First-Order-ODE/Differential_Equation_3.xml +++ b/samplequestions/stacklibrary/General-maths-questions/First-Order-ODE/Differential_Equation_3.xml @@ -25,8 +25,7 @@ correctanswer2:sqrt(n1)*tanh(sqrt(n1)*(n2*x+x^3/3)+c); wronganswer1:sqrt(n1)*tanh(sqrt(n1)*(n2*x+x^3/3+p)); wronganswer2:sqrt(n1)*tanh(sqrt(n1)*(n2*x+x^3/3)); wronganswer3:rat(exponentialize(correctanswer)); -wronganswer4:sqrt(n1)*tanh(sqrt(n1)*(n2*x+x^3/3)+p); - +wronganswer4:sqrt(n1)*tanh(sqrt(n1)*(n2*x+x^3/3)+p); [[feedback:Result]]

]]> diff --git a/samplequestions/stacklibrary/Topics/Complex_cube_roots.xml b/samplequestions/stacklibrary/Topics/Complex_cube_roots.xml index c101d787304..30b0e6c2d09 100644 --- a/samplequestions/stacklibrary/Topics/Complex_cube_roots.xml +++ b/samplequestions/stacklibrary/Topics/Complex_cube_roots.xml @@ -1,158 +1,157 @@ - Complex roots/unsorted multi-input answers - -a) Convert the number \(z={@z@}\) to polar coordinates, i.e. write the number as \(z = r\, e^{\mathrm i\, \theta} = r\, \exp(\mathrm i\, \theta)\). The argument \(\theta\) should be given in radians and as the principal value, i.e. \(-\pi < \theta \le \pi\). -

-

-b) Find the three different roots \(u_1\), \(u_2\) or \(u_3\) of \(z\), where. \(u_1^3 = u_2^3 = u_3^3 = z\), but \(u_1 \neq u_2\), \(u_2 \neq u_3\), \(u_3 \neq u_1\). -

-

-Answers: Give all answers exactly! The answers in b) must also be given in polar form. - The easiest way to enter the exponential function is as exp(). -

-

-Example: \(\dfrac{6}{5}\, \exp\left(\dfrac{\mathrm i\, \pi}{7}\right) = \dfrac{6}{5}\, e^{\frac{\mathrm i\, \pi}{7}}\) is entered as (6/5)*exp(%i*%pi/7). -

- - - - - - - - - - - - - -
a)\(z =~\)[[input:SAns1]]\(\, \exp(\)[[input:SAns2]]\(\, \mathrm{i})\)
[[validation:SAns1]][[validation:SAns2]]
- - - - - - - - - - - - - - - - - - - + +a) Convert the number \(z={@z@}\) to polar coordinates, i.e. write the number as \(z = r\, e^{\mathrm i\, \theta} = r\, \exp(\mathrm i\, \theta)\). The argument \(\theta\) should be given in radians and as the principal value, i.e. \(-\pi < \theta \le \pi\). +

+

+b) Find the three different roots \(u_1\), \(u_2\) or \(u_3\) of \(z\), where. \(u_1^3 = u_2^3 = u_3^3 = z\), but \(u_1 \neq u_2\), \(u_2 \neq u_3\), \(u_3 \neq u_1\). +

+

+Answers: Give all answers exactly! The answers in b) must also be given in polar form. + The easiest way to enter the exponential function is as exp(). +

+

+Example: \(\dfrac{6}{5}\, \exp\left(\dfrac{\mathrm i\, \pi}{7}\right) = \dfrac{6}{5}\, e^{\frac{\mathrm i\, \pi}{7}}\) is entered as (6/5)*exp(%i*%pi/7). +

+ +
b)\(u_1 =~\)[[input:SAns3]][[validation:SAns3]] [[feedback:prt3]]
\(u_2 =~\)[[input:SAns4]][[validation:SAns4]] [[feedback:prt4]]
\(u_3 =~\)[[input:SAns5]][[validation:SAns5]][[feedback:prt5]]
+ + + + + + + + + + + +
a)\(z =~\)[[input:SAns1]]\(\, \exp(\)[[input:SAns2]]\(\, \mathrm{i})\)
[[validation:SAns1]][[validation:SAns2]]
+ + + + + + + + + + + + + + + + + + +
b)\(u_1 =~\)[[input:SAns3]][[validation:SAns3]] [[feedback:prt3]]
\(u_2 =~\)[[input:SAns4]][[validation:SAns4]] [[feedback:prt4]]
\(u_3 =~\)[[input:SAns5]][[validation:SAns5]][[feedback:prt5]]
]]> - a) When a complex number is expressed in polar form, \(r\) is the distance from the origin, which is the same as -\[\lvert z \rvert=\sqrt{0^2+\left({@radius@}\right)^2}={@radius@}.\] -

- -

The argument \(\theta\) is given by the angle between the positive real axis and the vector from the origin to \(z\), with the requirement \(-\pi < \theta \leq \pi\). -We can immediately see from the sign of \(z\) that \(\theta = \displaystyle {@arg_z@}\), since the real part is \(0\).

-

Now we can write \(z\) in polar form: \[z = {@radius@} \, e^{ {@arg_z@} \, \mathrm i }\]

- -

b) Using the following formula, we can then calculate the complex \(n\):th roots:

-

\[\sqrt[n]{z} = \sqrt[n]{r} \,\exp\left( \mathrm i\,\frac{\theta + 2k\pi}{n}\right), \quad k = 0, 1, \dots , n-1.\]

- -

With \(k=0\) we get -\[\begin{split} u_1 &= \sqrt[3]{{@radius@}} \exp\left( \mathrm i\, \frac{{@arg_z@}}{3} \right) \\ -&= {@polarform_simp(u1)@}. -\end{split}\]

- -

Similarly with \(k=1\) we get -\[\begin{split} u_2 &= \sqrt[3]{{@radius@}} \exp \left( \mathrm i\, \frac{{@arg_z@} + 2\pi}{3}\right) \\ -&= {@polarform_simp(u2)@}, -\end{split}\] -

-

and with \(k=2\): -\[\begin{split} u_3 &= \sqrt[3]{{@radius@}}\exp \left( \mathrm i \, \frac{{@arg_z@} + 4\pi}{3}\right) \\ -&= {@polarform_simp(u3)@}. + a) When a complex number is expressed in polar form, \(r\) is the distance from the origin, which is the same as +\[\lvert z \rvert=\sqrt{0^2+\left({@radius@}\right)^2}={@radius@}.\] +

+ +

The argument \(\theta\) is given by the angle between the positive real axis and the vector from the origin to \(z\), with the requirement \(-\pi < \theta \leq \pi\). +We can immediately see from the sign of \(z\) that \(\theta = \displaystyle {@arg_z@}\), since the real part is \(0\).

+

Now we can write \(z\) in polar form: \[z = {@radius@} \, e^{ {@arg_z@} \, \mathrm i }\]

+ +

b) Using the following formula, we can then calculate the complex \(n\):th roots:

+

\[\sqrt[n]{z} = \sqrt[n]{r} \,\exp\left( \mathrm i\,\frac{\theta + 2k\pi}{n}\right), \quad k = 0, 1, \dots , n-1.\]

+ +

With \(k=0\) we get +\[\begin{split} u_1 &= \sqrt[3]{{@radius@}} \exp\left( \mathrm i\, \frac{{@arg_z@}}{3} \right) \\ +&= {@polarform_simp(u1)@}. +\end{split}\]

+ +

Similarly with \(k=1\) we get +\[\begin{split} u_2 &= \sqrt[3]{{@radius@}} \exp \left( \mathrm i\, \frac{{@arg_z@} + 2\pi}{3}\right) \\ +&= {@polarform_simp(u2)@}, +\end{split}\] +

+

and with \(k=2\): +\[\begin{split} u_3 &= \sqrt[3]{{@radius@}}\exp \left( \mathrm i \, \frac{{@arg_z@} + 4\pi}{3}\right) \\ +&= {@polarform_simp(u3)@}. \end{split}\]

]]> 1 0.1 0 - + 2024092500 - numerator : rand([2,3,5,7,11,13]); -denominator : rand_with_prohib(2,13, [numerator, numerator*2, numerator*3]); -radius: ev((numerator/denominator)^3,simp); -arg_z: rand([-pi/2, pi/2]); -zPar: radius*exp(arg_z*%i); -polar_z: polarform(zPar); -z:ev(zPar,simp); - -arg1: arg_z/3; -arg2: arg1+(1*2*pi/3); -arg3: arg1+(2*2*pi/3); - -u1: ev(radius^(1/3)*exp(arg1*%i),simp); -u2: ev(radius^(1/3)*exp(arg2*%i),simp); -u3: ev(radius^(1/3)*exp(arg3*%i),simp); - -/* Kuvaa varten muuttujia: */ -xmin: -radius*1.5; -ymin: xmin; -xmax: radius*1.5; -ymax: xmax; -r:radius; -xangle_startp: ev(r/2,simp); -yangle_endp: ev(imagpart(z)/2,simp); - -startx : if (arg_z = pi/2) then radius/2 else 0; -starty : if (arg_z = pi/2) then 0 else imagpart(zPar)/2; -endx : if (arg_z = pi/2) then 0 else radius/2; -endy : if (arg_z = pi/2) then imagpart(zPar)/2 else 0; - -Tans1 : radius; -Tans2 : arg_z; -Tans3 : polarform_simp(u1); -Tans4 : polarform_simp(u2); -Tans5 : polarform_simp(u3); - -Twrong1 : ev(radius/3,simp); -Twrong2 : ev(arg_z*2,simp); -/* Not a root. */ -Twrong3 : polarform_simp(Tans3*2); -/* A root, but not the right form. */ -Twrong4 : ev(ratsimp(Tans4),simp); -/* Both properties wrong! */ + numerator : rand([2,3,5,7,11,13]); +denominator : rand_with_prohib(2,13, [numerator, numerator*2, numerator*3]); +radius: ev((numerator/denominator)^3,simp); +arg_z: rand([-pi/2, pi/2]); +zPar: radius*exp(arg_z*%i); +polar_z: polarform(zPar); +z:ev(zPar,simp); + +arg1: arg_z/3; +arg2: arg1+(1*2*pi/3); +arg3: arg1+(2*2*pi/3); + +u1: ev(radius^(1/3)*exp(arg1*%i),simp); +u2: ev(radius^(1/3)*exp(arg2*%i),simp); +u3: ev(radius^(1/3)*exp(arg3*%i),simp); + +/* Kuvaa varten muuttujia: */ +xmin: -radius*1.5; +ymin: xmin; +xmax: radius*1.5; +ymax: xmax; +r:radius; +xangle_startp: ev(r/2,simp); +yangle_endp: ev(imagpart(z)/2,simp); + +startx : if (arg_z = pi/2) then radius/2 else 0; +starty : if (arg_z = pi/2) then 0 else imagpart(zPar)/2; +endx : if (arg_z = pi/2) then 0 else radius/2; +endy : if (arg_z = pi/2) then imagpart(zPar)/2 else 0; + +Tans1 : radius; +Tans2 : arg_z; +Tans3 : polarform_simp(u1); +Tans4 : polarform_simp(u2); +Tans5 : polarform_simp(u3); + +Twrong1 : ev(radius/3,simp); +Twrong2 : ev(arg_z*2,simp); +/* Not a root. */ +Twrong3 : polarform_simp(Tans3*2); +/* A root, but not the right form. */ +Twrong4 : ev(ratsimp(Tans4),simp); +/* Both properties wrong! */ Twrong5 : Tans5*4; - a)

-

[[feedback:prt1]]

-

b)

+ a)

+

[[feedback:prt1]]

+

b)

[[feedback:prt2]]

]]> - -Determine the three roots \(\sqrt[3]{z}\).
+ +Determine the three roots \(\sqrt[3]{z}\).
Answer: \(u_1 = {@polarform_simp(u1)@}\), \(u_2 = {@polarform_simp(u2)@}\) and \(u_3 = {@polarform_simp(u3)@}\).]]> - 0 @@ -175,7 +174,7 @@ We then have one PRT which checks the _set_ of answers is correct.]]> cos-1 lang [ - + SAns1 numerical @@ -183,16 +182,16 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 4 1 0 - + 0 - - + + 1 0 0 1 3 - + SAns2 @@ -201,16 +200,16 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 5 1 0 - + 0 - - + + 1 0 1 1 3 - + SAns3 @@ -219,16 +218,16 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 15 1 0 - + 0 - - + + 1 0 0 1 3 - + SAns4 @@ -237,16 +236,16 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 15 1 0 - + 0 - - + + 1 0 0 1 3 - + SAns5 @@ -255,16 +254,16 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 15 1 0 - + 0 - - + + 1 0 0 1 3 - + prt1 @@ -272,19 +271,19 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 1 1 - + 0 - + AlgEquiv SAns1 Tans1 - + 0 = 0.5 - + 1 prt2-1-T @@ -292,25 +291,25 @@ We then have one PRT which checks the _set_ of answers is correct.]]> = 0 - + 1 prt2-1-F - The radius \(r\) is unfortunately wrong.

+ The radius \(r\) is unfortunately wrong.

If \(z = {@zPar@}\), then what must the distance to the origin be? That distance is the same as the radius! (As usual, use the Pythagorean theorem to calculate the distance.)

]]> 1 - + AlgEquiv SAns2 Tans2 - + 1 + 0.5 - + -1 prt1-2-T @@ -318,11 +317,11 @@ We then have one PRT which checks the _set_ of answers is correct.]]> - 0 - + -1 prt1-2-F - The argument \(\theta\) is unfortunately wrong.

+ The argument \(\theta\) is unfortunately wrong.

Use the figure! You know that the real part of \(z\) is \(0\), so what must the angle be? Remember the requirement \(-\pi < \theta \leq \pi\).

]]> @@ -333,10 +332,10 @@ We then have one PRT which checks the _set_ of answers is correct.]]> 0 1 - SAnss: {polarform_simp(SAns3), polarform_simp(SAns4), polarform_simp(SAns5)}; -TAnss: {polarform_simp(Tans3), polarform_simp(Tans4), polarform_simp(Tans5)}; - -/* Make sure all answers are solutions. */ + SAnss: {polarform_simp(SAns3), polarform_simp(SAns4), polarform_simp(SAns5)}; +TAnss: {polarform_simp(Tans3), polarform_simp(Tans4), polarform_simp(Tans5)}; + +/* Make sure all answers are solutions. */ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); @@ -345,23 +344,23 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); AlgEquiv SAnssc {z} - + 1 + 0 - + 1 prt2-1-T - + - 0 - + -1 prt2-1-F - + @@ -370,19 +369,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); Sets SAnss TAnss - + 0 = 1 - + -1 prt3-1-T - + = 0 - + -1 prt3-1-F @@ -396,7 +395,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 0 2 - + 0 @@ -404,19 +403,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); AlgEquiv SAns3^3 z - + 1 = 1 - + 1 prt3-1-T - + = 0 - + 1 prt3-1-F @@ -429,19 +428,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); CasEqual complex_exponentialp(SAns3) true - + 1 + 0 - + -1 prt3-2-T - + = 0 - + -1 prt3-2-F @@ -455,7 +454,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 1 2 - + 0 @@ -463,19 +462,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); AlgEquiv SAns4^3 z - + 1 = 1 - + 1 prt4-1-T - + = 0 - + 1 prt4-1-F @@ -488,19 +487,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); CasEqual complex_exponentialp(SAns4) true - + 1 + 0 - + -1 prt4-2-T - + = 0 - + -1 prt4-2-F @@ -514,7 +513,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 0 2 - + 0 @@ -522,19 +521,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); AlgEquiv SAns5^3 z - + 1 = 1 - + 1 prt5-1-T - + = 0 - + 1 prt5-1-F @@ -547,19 +546,19 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); CasEqual complex_exponentialp(SAns5) true - + 1 + 0 - + -1 prt5-2-T - + = 0 - + -1 prt5-2-F @@ -576,7 +575,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 1940161873 1 - + SAns1 Tans1 @@ -630,7 +629,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 2 - + SAns1 Twrong1 @@ -684,7 +683,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 3 - + SAns1 Tans1 @@ -738,7 +737,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 4 - + SAns1 Tans1 @@ -768,7 +767,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); prt2 0.0000000 - + prt3-1-F @@ -792,7 +791,7 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); 5 - + SAns1 Tans1 @@ -881,5 +880,4 @@ SAnssc:map(lambda([ex],ev(ratsimp(ex^3),simp)),SAnss); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/JSXGraphs-Discrete_mathematics_graph-theory-2.xml b/samplequestions/stacklibrary/Topics/JSXGraphs-Discrete_mathematics_graph-theory-2.xml index 5fc2935275a..f24e1b1a014 100644 --- a/samplequestions/stacklibrary/Topics/JSXGraphs-Discrete_mathematics_graph-theory-2.xml +++ b/samplequestions/stacklibrary/Topics/JSXGraphs-Discrete_mathematics_graph-theory-2.xml @@ -1,6 +1,5 @@ - @@ -43,7 +42,7 @@ 1 0.1 0 - + 2024092500 @@ -61,10 +60,10 @@ ta1:2; [[feedback:prt1]] - + - + 1 0 @@ -86,7 +85,7 @@ ta1:2; cos-1 lang [ - + ans1 algebraic @@ -94,16 +93,16 @@ ta1:2; 15 1 0 - + 0 - - + + 1 0 0 1 1 - + prt1 @@ -111,27 +110,27 @@ ta1:2; 1 1 - + 0 - + AlgEquiv ans1 ta1 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -155,7 +154,7 @@ ta1:2; 2 - + ans1 3 @@ -168,5 +167,4 @@ ta1:2; - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Cross-product-non-cancellation.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Cross-product-non-cancellation.xml index a24f786db32..d1526268268 100644 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Cross-product-non-cancellation.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Cross-product-non-cancellation.xml @@ -1,6 +1,5 @@ - Cross-product-non-cancellation. @@ -18,7 +17,7 @@ 1 0.1 0 - + 2024092500 @@ -62,7 +61,7 @@ incorr1:mcq_incorrect(ta1);]]> cos-1 lang [ - + ans1 checkbox @@ -70,16 +69,16 @@ incorr1:mcq_incorrect(ta1);]]> 15 1 0 - + 0 - - + + 1 1 0 0 0 - + prt1 @@ -87,15 +86,15 @@ incorr1:mcq_incorrect(ta1);]]> 0 1 - + 0 - + AlgEquiv setify(ans1) setify(corr1) - + 1 = 1 @@ -103,7 +102,7 @@ incorr1:mcq_incorrect(ta1);]]> -1 prt1-0-T - + = 0 @@ -111,20 +110,20 @@ incorr1:mcq_incorrect(ta1);]]> 1 prt1-0-F - + 1 - + AlgEquiv subsetp(setify(ans1),setify(corr1)) true - + 0 + 0.5 - + -1 prt1-2-T @@ -132,32 +131,32 @@ incorr1:mcq_incorrect(ta1);]]> - 0 - + 2 prt1-2-F - + 2 - + CasEqual cardinality(ev(intersection(setify(incorr1),setify(ans1)),simp)) 0 - + 0 + 0 - + -1 prt1-3-T - + - 0 - + -1 prt1-3-F @@ -177,7 +176,7 @@ incorr1:mcq_incorrect(ta1);]]> 1201499788 1 - + ans1 [incorr1[1]] @@ -191,7 +190,7 @@ incorr1:mcq_incorrect(ta1);]]> 2 - + ans1 corr1 @@ -205,7 +204,7 @@ incorr1:mcq_incorrect(ta1);]]> 3 - + ans1 [corr1[1],incorr1[1]] @@ -219,7 +218,7 @@ incorr1:mcq_incorrect(ta1);]]> 4 - + ans1 [corr1[1]] @@ -227,7 +226,7 @@ incorr1:mcq_incorrect(ta1);]]> prt1 0.5000000 - + prt1-2-T @@ -236,5 +235,4 @@ incorr1:mcq_incorrect(ta1);]]> - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Diagonalizable-proof-comprehension.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Diagonalizable-proof-comprehension.xml index a7f5cb4a67a..992c30ebb45 100644 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Diagonalizable-proof-comprehension.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Diagonalizable-proof-comprehension.xml @@ -1,6 +1,5 @@ - Diagonalizable proof comprehension @@ -53,7 +52,7 @@ This proof is not correct because [[input:an2]] [[validation:an2]] 10 0.1 0 - + 2023010400 @@ -86,9 +85,7 @@ tb1:false; tballow2:["the converse is missing","missing converse", "half the proof is missing", "the reverse direction is missing", "you must prove the converse as well", "only proved one way", "the converse has not been proved","it doesn't prove the double implication","they have only proved it in one direction","show the converse","The proof should be and if and only if proof","there is no converse in the proof", "there is no converse", "it only proves one direction of the if and only if statement", "did not proof the converse of the theorem"]; tballow2:append(tballow2, ["didn't prove that A having n linearly independent eigenvectors means that A is diagonalizable"]); tbforbid2:["the converse is not true"]; -tb3:true; - -]]> +tb3:true;]]> @@ -100,7 +97,7 @@ tb3:true; ]]> - + This question is distributed as part of the STACK source code as an example. This is licenced as Creative Commons Attribution-ShareAlike 4.0 International License. @@ -125,7 +122,7 @@ tb3:true; cos-1 lang [ - + an1 boolean @@ -133,16 +130,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + an2 @@ -151,10 +148,10 @@ tb3:true; 50 1 0 - + 0 - - + + 1 0 0 @@ -169,16 +166,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ans1 @@ -187,16 +184,16 @@ tb3:true; 15 1 5 - + 0 - - + + 1 0 0 1 3 - + ans2 @@ -205,16 +202,16 @@ tb3:true; 15 1 5 - + 0 - - + + 1 0 0 1 3 - + ans3 @@ -223,9 +220,9 @@ tb3:true; 15 1 4 - + 0 - + lambdak 1 0 @@ -241,16 +238,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + answ2 @@ -259,16 +256,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + answ3 @@ -277,16 +274,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + answ4 @@ -295,16 +292,16 @@ tb3:true; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -312,44 +309,44 @@ tb3:true; 0 1 - + 0 - + CasEqual ans1 ta1 - + 0 = 0.5 - + 2 prt1-1-T - + = 0 - + 1 prt1-1-F - + 1 - + CasEqual ans1 P*A*P^(-1) - + 0 = 0.25 - + 2 prt1-2-T @@ -357,49 +354,49 @@ tb3:true; - 0 - + 2 prt1-2-F - + 2 - + CasEqual ans2 ta2 - + 0 + 0.5 - + -1 prt1-3-T - + - 0 - + 3 prt1-3-F - + 3 - + CasEqual ans2 D*P - + 0 + 0.25 - + -1 prt1-4-T @@ -407,11 +404,11 @@ tb3:true; - 0 - + -1 prt1-4-F - + @@ -421,32 +418,31 @@ tb3:true; 1 3 - sa3:at(ans3,[p_k=pk,lambda_k=lambdak]); - + sa3:at(ans3,[p_k=pk,lambda_k=lambdak]); 0 - + AlgEquiv sa3 ta3 - + 0 = 1 - + -1 prt2-1-T - + = 0 - + -1 prt2-1-F - + @@ -461,23 +457,23 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 0 - + AlgEquiv sa1 sa2 - + 0 = 1 - + -1 prt3-1-T - + = 0 - + -1 prt3-1-F @@ -492,27 +488,27 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 1 2 - + 0 - + AlgEquiv an1 tb1 - + 0 = 0.33 - + 1 prt4-1-T - + = 0 - + -1 prt4-1-F @@ -521,32 +517,32 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 1 - + StringSloppy an2 - + 0 = 0 - + -1 prt4-2-T - + + 0 - + 2 prt4-2-F - + 2 - + Levenshtein an2 [tballow2,tbforbid2] @@ -554,19 +550,19 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 0 + 0.67 - + -1 prt4-3-T - + - 0 - + -1 prt4-3-F - + @@ -576,37 +572,37 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 1 2 - + 0 - + AlgEquiv an3 tb3 - + 0 = 1 - + -1 prt5-1-T - + = 0 - + -1 prt5-1-F - + 1 - + an1 tb1 @@ -680,7 +676,7 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; 2 - + an1 false @@ -707,19 +703,19 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; answ1 - + answ2 - + answ3 - + answ4 - + prt1 @@ -735,8 +731,8 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; prt3 - - + + NULL @@ -753,5 +749,4 @@ sa2:[wsa1,wsa2,wsa3,wsa4]; - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-eigenvectors-give-examples.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-eigenvectors-give-examples.xml index 0f5733f2662..0a19ad10dc6 100644 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-eigenvectors-give-examples.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-eigenvectors-give-examples.xml @@ -1,6 +1,5 @@ - Eigenvalues and eigenvectors - give examples @@ -64,7 +63,7 @@ In this question, we have eigenvalues \(\lambda_1 = 1\) and \(\lambda_2 = {@a2@} 1 0.1 0 - + 2022082900 @@ -110,10 +109,10 @@ D:D1 . P1; testa6:D; - + - \(\lambda_1 = 1\) (fixed), \(\lambda_2 = {@a2@}\): {@ta6@} + \(\lambda_1 = 1\) (fixed), \(\lambda_2 = {@a2@}\): {@ta6@} This question is distributed as part of the STACK source code as an example. This is licenced as Creative Commons Attribution-ShareAlike 4.0 International License. @@ -138,7 +137,7 @@ testa6:D; cos-1 lang [ - + ans1 algebraic @@ -146,16 +145,16 @@ testa6:D; 15 1 0 - + 0 - - + + 1 0 0 1 3 - + ans2 @@ -164,16 +163,16 @@ testa6:D; 2 1 0 - + 0 - - + + 1 0 0 1 3 - + ans3 @@ -182,16 +181,16 @@ testa6:D; 2 1 0 - + 0 - - + + 1 0 0 1 3 - + ans4 @@ -200,16 +199,16 @@ testa6:D; 2 1 0 - + 0 - - + + 1 0 0 1 3 - + ans5 @@ -218,16 +217,16 @@ testa6:D; 2 1 0 - + 0 - - + + 1 0 0 0 0 - + ans6 @@ -236,16 +235,16 @@ testa6:D; 2 1 0 - + 0 - - + + 1 0 0 1 3 - + ans7 @@ -254,16 +253,16 @@ testa6:D; 70 1 0 - + 0 - - + + 1 0 0 1 2 - + prt1 @@ -271,56 +270,56 @@ testa6:D; 1 1 - + 0 - + AlgEquiv ans1 ta1 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + 1 prt1-1-F - + 1 - + SubstEquiv ans1 ta1 - + 0 = 0.5 - + -1 prt1-2-T - + - 0 - + -1 prt1-2-F - + @@ -337,7 +336,7 @@ node1:is(sa2evrank=ta2evrank) 0 - + AlgEquiv node1 true @@ -345,15 +344,15 @@ node1:is(sa2evrank=ta2evrank) 0 = 1 - + -1 prt2-1-T - + = 0 - + -1 prt2-1-F @@ -367,19 +366,19 @@ node1:is(sa2evrank=ta2evrank) 1 1 - + 0 - + AlgEquiv ans2 matrix([0],[0]) - + 1 = 0 - + -1 prt3-1-T @@ -387,32 +386,32 @@ node1:is(sa2evrank=ta2evrank) = 0 - + 1 prt3-1-F - + 1 - + AlgEquiv ans2.ans3 a1*ans3 - + 1 = 1 - + -1 prt3-2-T - + - 0 - + -1 prt3-2-F @@ -427,11 +426,11 @@ node1:is(sa2evrank=ta2evrank) 1 1 - + 0 - + AlgEquiv ans4 matrix([0],[0]) @@ -439,7 +438,7 @@ node1:is(sa2evrank=ta2evrank) 1 = 0 - + -1 prt4-1-T @@ -447,32 +446,32 @@ node1:is(sa2evrank=ta2evrank) = 0 - + 1 prt4-1-F - + 1 - + AlgEquiv ans2.ans4 a2*ans4 - + 1 = 1 - + -1 prt4-2-T - + - 0 - + -1 prt4-2-F @@ -487,27 +486,27 @@ node1:is(sa2evrank=ta2evrank) 1 1 - + 0 - + AlgEquiv ans5 ta5 - + 0 = 1 - + -1 prt5-1-T - + = 0 - + -1 prt5-1-F @@ -540,19 +539,19 @@ node1:is(sa6evrank=[a2,a1]); 0 - + AlgEquiv sa6evrank [a2,a1] - + 0 = 1 - + -1 prt6-1-T - + = 0 @@ -565,7 +564,7 @@ node1:is(sa6evrank=[a2,a1]); 1 - + AlgEquiv node2 true @@ -573,11 +572,11 @@ node1:is(sa6evrank=[a2,a1]); 0 = 0 - + 5 prt6-2-T - + - 0 @@ -590,19 +589,19 @@ node1:is(sa6evrank=[a2,a1]); 2 - + AlgEquiv determinant(ans6) determinant(ans2) - + 0 + 0 - + 3 prt6-3-T - + - 0 @@ -615,7 +614,7 @@ node1:is(sa6evrank=[a2,a1]); 3 - + AlgEquiv node4 true @@ -623,11 +622,11 @@ node1:is(sa6evrank=[a2,a1]); 0 + 0 - + 4 prt6-4-T - + - 0 @@ -640,19 +639,19 @@ node1:is(sa6evrank=[a2,a1]); 4 - + AlgEquiv sa2tr sa6tr - + 0 + 0 - + 0 prt6-5-T - + = 0 @@ -665,7 +664,7 @@ node1:is(sa6evrank=[a2,a1]); 5 - + AlgEquiv node6 true @@ -673,15 +672,15 @@ node1:is(sa6evrank=[a2,a1]); 0 + 0 - + 2 prt6-6-T - + - 0 - + -1 prt6-6-F @@ -694,7 +693,7 @@ node1:is(sa6evrank=[a2,a1]); 873158876 1 - + ans1 ta1 @@ -758,7 +757,7 @@ node1:is(sa6evrank=[a2,a1]); 2 - + ans1 testa1 @@ -822,7 +821,7 @@ node1:is(sa6evrank=[a2,a1]); 3 - + ans1 (x-10)*(x-2) @@ -849,7 +848,7 @@ node1:is(sa6evrank=[a2,a1]); ans7 - + prt1 @@ -890,7 +889,7 @@ node1:is(sa6evrank=[a2,a1]); 4 - + ans1 testa1 @@ -954,34 +953,34 @@ node1:is(sa6evrank=[a2,a1]); 5 - + ans1 ev(ta1,x=lambda) ans2 - + ans3 - + ans4 - + ans5 - + ans6 - + ans7 - + prt1 @@ -991,35 +990,34 @@ node1:is(sa6evrank=[a2,a1]); prt2 - - + + NULL prt3 - - + + NULL prt4 - - + + NULL prt5 - - + + NULL prt6 - - + + NULL - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-3-3.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-3-3.xml index 52b2598d1cd..4e956cb2088 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-3-3.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-3-3.xml @@ -1,6 +1,5 @@ - Eigenvalues and vectors of 3*3 matrices. @@ -25,7 +24,7 @@ This gives 6 0.1 0 - + 2023010400 @@ -76,7 +75,7 @@ cp:expand(determinant(LI-M)); cos-1 lang [ - + l1 algebraic @@ -84,16 +83,16 @@ cp:expand(determinant(LI-M)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + l2 @@ -102,16 +101,16 @@ cp:expand(determinant(LI-M)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + l3 @@ -120,16 +119,16 @@ cp:expand(determinant(LI-M)); 5 1 0 - + 0 - - + + 1 0 1 1 3 - + sev1 @@ -138,16 +137,16 @@ cp:expand(determinant(LI-M)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + sev2 @@ -156,16 +155,16 @@ cp:expand(determinant(LI-M)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + sev3 @@ -174,16 +173,16 @@ cp:expand(determinant(LI-M)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + ev1 @@ -191,27 +190,27 @@ cp:expand(determinant(LI-M)); 1 2 - + 0 - + AlgEquiv M.sev1 l1*sev1 - + 1 = 1 - + 1 ev1-1-T - + = 0 - + -1 ev1-1-F @@ -220,15 +219,15 @@ cp:expand(determinant(LI-M)); 1 - + AlgEquiv sev1 matrix([0],[0],[0]) - + 1 = 0 - + -1 ev1-2-T @@ -236,11 +235,11 @@ cp:expand(determinant(LI-M)); - 0 - + -1 ev1-2-F - + @@ -250,27 +249,27 @@ cp:expand(determinant(LI-M)); 1 2 - + 0 - + AlgEquiv M.sev2 l2*sev2 - + 1 = 1 - + 1 ev2-1-T - + = 0 - + -1 ev2-1-F @@ -279,15 +278,15 @@ cp:expand(determinant(LI-M)); 1 - + AlgEquiv sev2 matrix([0],[0],[0]) - + 1 = 0 - + -1 ev2-2-T @@ -295,11 +294,11 @@ cp:expand(determinant(LI-M)); - 0 - + -1 ev2-2-F - + @@ -309,27 +308,27 @@ cp:expand(determinant(LI-M)); 1 2 - + 0 - + AlgEquiv M.sev3 l3*sev3 - + 1 = 1 - + 1 ev3-1-T - + = 0 - + -1 ev3-1-F @@ -338,15 +337,15 @@ cp:expand(determinant(LI-M)); 1 - + AlgEquiv sev3 matrix([0],[0],[0]) - + 1 = 0 - + -1 ev3-2-T @@ -354,11 +353,11 @@ cp:expand(determinant(LI-M)); - 0 - + -1 ev3-2-F - + @@ -368,27 +367,27 @@ cp:expand(determinant(LI-M)); 1 1 - + 0 - + AlgEquiv {l1,l2,l3} {e1,e2,e3} - + 0 = 0.75 - + 4 prt1-1-T - + = 0 - + 4 prt1-1-F @@ -397,23 +396,23 @@ cp:expand(determinant(LI-M)); 4 - + AlgEquiv length({l1,l2,l3}) 3 - + 0 + 0.25 - + -1 prt1-5-T - + - 0 - + -1 prt1-5-F @@ -430,7 +429,7 @@ cp:expand(determinant(LI-M)); 1510782468 1 - + l1 e1 @@ -482,7 +481,7 @@ cp:expand(determinant(LI-M)); 2 - + l1 e1 @@ -534,7 +533,7 @@ cp:expand(determinant(LI-M)); 3 - + l1 e3 @@ -585,5 +584,4 @@ cp:expand(determinant(LI-M)); - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-4-4.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-4-4.xml index 78edc28b2ed..ff0d865941b 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-4-4.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-4-4.xml @@ -1,6 +1,5 @@ - Eigenvalues and vectors of of structured 4*4 matrices. @@ -33,7 +32,7 @@ This gives 2 0.1 0 - + 2023121100 @@ -57,8 +56,7 @@ cp:expand(determinant(LI-M)); S1:submatrix(3,4,M,3,4); cp1:matrix([lambda,0],[0,lambda])-S1; cp2:expand(determinant(cp1)); -cp3:factor(expand(cp/cp2)); - +cp3:factor(expand(cp/cp2)); \( PDP^{-1} = {@P@}{@D@}{@PI@} = {@M@}.\) - + 1 0 @@ -93,7 +91,7 @@ cp3:factor(expand(cp/cp2)); cos-1 lang [ - + l1 algebraic @@ -101,16 +99,16 @@ cp3:factor(expand(cp/cp2)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + l2 @@ -119,16 +117,16 @@ cp3:factor(expand(cp/cp2)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + l3 @@ -137,16 +135,16 @@ cp3:factor(expand(cp/cp2)); 5 1 0 - + 0 - - + + 1 0 1 1 3 - + l4 @@ -155,16 +153,16 @@ cp3:factor(expand(cp/cp2)); 5 1 0 - + 0 - - + + 1 0 0 1 3 - + sev1 @@ -173,16 +171,16 @@ cp3:factor(expand(cp/cp2)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + sev2 @@ -191,16 +189,16 @@ cp3:factor(expand(cp/cp2)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + sev3 @@ -209,16 +207,16 @@ cp3:factor(expand(cp/cp2)); 5 1 1 - + 0 - - + + 1 0 1 1 3 - + sev4 @@ -227,16 +225,16 @@ cp3:factor(expand(cp/cp2)); 5 1 0 - + 0 - - + + 1 0 0 1 3 - + ev1 @@ -244,27 +242,27 @@ cp3:factor(expand(cp/cp2)); 1 2 - + 0 - + AlgEquiv M.sev1 l1*sev1 - + 1 = 1 - + 1 ev1-1-T - + = 0 - + -1 ev1-1-F @@ -273,15 +271,15 @@ cp3:factor(expand(cp/cp2)); 1 - + AlgEquiv sev1 matrix([0],[0],[0],[0]) - + 1 = 0 - + -1 ev1-2-T @@ -289,11 +287,11 @@ cp3:factor(expand(cp/cp2)); - 0 - + -1 ev1-2-F - + @@ -303,27 +301,27 @@ cp3:factor(expand(cp/cp2)); 1 2 - + 0 - + AlgEquiv M.sev2 l2*sev2 - + 1 = 1 - + 1 ev2-1-T - + = 0 - + -1 ev2-1-F @@ -332,15 +330,15 @@ cp3:factor(expand(cp/cp2)); 1 - + AlgEquiv sev2 matrix([0],[0],[0],[0]) - + 1 = 0 - + -1 ev2-2-T @@ -348,11 +346,11 @@ cp3:factor(expand(cp/cp2)); - 0 - + -1 ev2-2-F - + @@ -362,27 +360,27 @@ cp3:factor(expand(cp/cp2)); 1 2 - + 0 - + AlgEquiv M.sev3 l3*sev3 - + 1 = 1 - + 1 ev3-1-T - + = 0 - + -1 ev3-1-F @@ -391,15 +389,15 @@ cp3:factor(expand(cp/cp2)); 1 - + AlgEquiv sev3 matrix([0],[0],[0],[0]) - + 1 = 0 - + -1 ev3-2-T @@ -407,11 +405,11 @@ cp3:factor(expand(cp/cp2)); - 0 - + -1 ev3-2-F - + @@ -421,27 +419,27 @@ cp3:factor(expand(cp/cp2)); 1 2 - + 0 - + AlgEquiv M.sev4 l4*sev4 - + 1 = 1 - + 1 ev4-1-T - + = 0 - + -1 ev4-1-F @@ -450,15 +448,15 @@ cp3:factor(expand(cp/cp2)); 1 - + AlgEquiv sev4 matrix([0],[0],[0],[0]) - + 1 = 0 - + -1 ev4-2-T @@ -466,11 +464,11 @@ cp3:factor(expand(cp/cp2)); - 0 - + -1 ev4-2-F - + @@ -480,27 +478,27 @@ cp3:factor(expand(cp/cp2)); 1 1 - + 0 - + AlgEquiv {l1,l2,l3,l4} {e1,e2,e3,e4} - + 0 = 0.75 - + 4 prt1-1-T - + = 0 - + 4 prt1-1-F @@ -509,23 +507,23 @@ cp3:factor(expand(cp/cp2)); 4 - + AlgEquiv length({l1,l2,l3,l4}) 4 - + 0 + 0.25 - + -1 prt1-5-T - + - 0 - + -1 prt1-5-F @@ -542,7 +540,7 @@ cp3:factor(expand(cp/cp2)); 1510782468 1 - + l1 e1 @@ -608,7 +606,7 @@ cp3:factor(expand(cp/cp2)); 2 - + l1 e1 @@ -674,7 +672,7 @@ cp3:factor(expand(cp/cp2)); 3 - + l1 e3 @@ -739,5 +737,4 @@ cp3:factor(expand(cp/cp2)); - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-PDPT.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-PDPT.xml index a05e5f1a875..77f6e064d90 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-PDPT.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Eigenvalues-vectors-PDPT.xml @@ -1,6 +1,5 @@ - Find eigenvalues 3*3 +PDP^-1 @@ -24,7 +23,7 @@ 10 0.1 0 - + 2021120900 @@ -84,7 +83,7 @@ B: U_P.(D^2012).U_PT cos-1 lang [ - + ans1 algebraic @@ -92,16 +91,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans2 @@ -110,16 +109,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans3 @@ -128,16 +127,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans4 @@ -146,16 +145,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans5 @@ -164,16 +163,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans6 @@ -182,16 +181,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans7 @@ -200,16 +199,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans8 @@ -218,16 +217,16 @@ B: U_P.(D^2012).U_PT 5 1 0 - + 0 - - + + 1 0 0 1 1 - + prt1 @@ -235,27 +234,27 @@ B: U_P.(D^2012).U_PT 1 1 - + 0 - + AlgEquiv A.ans2 ans1*ans2 - + 1 = 0.3400000 - + 1 prt1-1-T - + = 0.0000000 - + 1 prt1-1-F @@ -264,23 +263,23 @@ B: U_P.(D^2012).U_PT 1 - + AlgEquiv A.ans4 ans3*ans4 - + 1 + 0.3300000 - + 2 prt1-2-T - + - 0.0000000 - + 2 prt1-2-F @@ -289,23 +288,23 @@ B: U_P.(D^2012).U_PT 2 - + AlgEquiv A.ans6 ans5*ans6 - + 1 + 0.3300000 - + 3 prt1-3-T - + - 0.0000000 - + 3 prt1-3-F @@ -314,23 +313,23 @@ B: U_P.(D^2012).U_PT 3 - + AlgEquiv {ans1,ans3,ans5} {lambda1,lambda2,lambda3} - + 0 + 0.0000000 - + 4 prt1-4-T - + - 0.5000000 - + 4 prt1-4-F @@ -339,15 +338,15 @@ B: U_P.(D^2012).U_PT 4 - + AlgEquiv elementp(transpose(matrix([0,0,0])), {ans2,ans4,ans6}) true - + 1 - 0.4000000 - + -1 prt1-5-T @@ -355,11 +354,11 @@ B: U_P.(D^2012).U_PT - 0.0000000 - + -1 prt1-5-F - + @@ -374,23 +373,23 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} 0 - + AlgEquiv transpose(ans7).A.ans7 ans8 - + 1 = 0.8000000 - + 1 prt2-1-T - + = 0.0000000 - + 1 prt2-1-F @@ -399,23 +398,23 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} 1 - + AlgEquiv sde {0} - + 1 + 0.2000000 - + -1 prt2-2-T - + - 0.0000000 - + -1 prt2-2-F @@ -425,7 +424,7 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} 1 - + ans1 lambda1 @@ -473,7 +472,7 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} 2 - + ans1 lambda2 @@ -521,7 +520,7 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} 3 - + ans1 lambda1 @@ -548,11 +547,11 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} ans7 - + ans8 - + prt1 @@ -562,11 +561,10 @@ sde:{ans8[1,2],ans8[1,3],ans8[2,1],ans8[2,3],ans8[3,1],ans8[3,1]} prt2 - - + + NULL - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Equation-plane-counter-example.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Equation-plane-counter-example.xml index 6f8c5a5460a..159b28d1b6b 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Equation-plane-counter-example.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Equation-plane-counter-example.xml @@ -1,6 +1,5 @@ - Subspace and planes in R3 @@ -26,7 +25,7 @@ Since the right hand side is \(0\) we immediately see that the zero vector belon 3 0.1 0 - + 2023010400 @@ -67,7 +66,7 @@ tac:transpose(tan).tap; cos-1 lang [ - + ans1 boolean @@ -75,16 +74,16 @@ tac:transpose(tan).tap; 15 1 0 - + 0 - - + + 1 0 0 1 3 - + ansp @@ -93,10 +92,10 @@ tac:transpose(tan).tap; 3 1 0 - + 0 - - + + 1 0 0 @@ -111,10 +110,10 @@ tac:transpose(tan).tap; 3 1 0 - + 0 - - + + 1 0 0 @@ -129,10 +128,10 @@ tac:transpose(tan).tap; 3 1 0 - + 0 - - + + 1 0 0 @@ -148,28 +147,27 @@ tac:transpose(tan).tap; sanse:elementp(matrix([null],[null],[null]),{ansp,ansu,ansv}); sansn:crossproduct(ansu,ansv); -sansc:transpose(sansn).ansp; - +sansc:transpose(sansn).ansp; 0 - + AlgEquiv ans1 ta1 - + 0 + 0.33 - + 4 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -178,15 +176,15 @@ sansc:transpose(sansn).ansp; 1 - + AlgEquiv sansn matrix([0],[0],[0]) - + 1 - 0 - + -1 prt1-2-T @@ -194,24 +192,24 @@ sansc:transpose(sansn).ansp; - 0 - + 2 prt1-2-F - + 2 - + AlgEquiv ansp matrix([0],[0],[0]) - + 1 + 0 - + -1 prt1-3-T @@ -219,24 +217,24 @@ sansc:transpose(sansn).ansp; - 0 - + 3 prt1-3-F - + 3 - + AlgEquiv sansc 0 - + 1 + 0.67 - + -1 prt1-4-T @@ -244,24 +242,24 @@ sansc:transpose(sansn).ansp; - 0 - + -1 prt1-4-F - + 4 - + AlgEquiv sanse true - + 0 + 0 - + -1 prt1-5-T @@ -269,17 +267,17 @@ sansc:transpose(sansn).ansp; - 0 - + 1 prt1-5-F - + 1 - + ans1 ta1 @@ -305,22 +303,22 @@ sansc:transpose(sansn).ansp; 2 - + ans1 true ansp - + ansu - + ansv - + prt1 @@ -331,22 +329,22 @@ sansc:transpose(sansn).ansp; 3 - + ans1 ta1 ansp - + ansu - + ansv - + prt1 @@ -357,7 +355,7 @@ sansc:transpose(sansn).ansp; 4 - + ans1 ta1 @@ -383,7 +381,7 @@ sansc:transpose(sansn).ansp; 5 - + ans1 ta1 @@ -408,5 +406,4 @@ sansc:transpose(sansn).ansp; - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-dependence.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-dependence.xml index a01d75ebfa1..efa1f91331a 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-dependence.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-dependence.xml @@ -1,6 +1,5 @@ - Linear dependence @@ -20,7 +19,7 @@ If such values do not exist, enter null for all entries.

1 0 0 - + 2023010400 @@ -71,7 +70,7 @@ detmatrix:determinant(matrixv312); cos-1 lang [ - + ans1 algebraic @@ -79,16 +78,16 @@ detmatrix:determinant(matrixv312); 5 1 0 - + 0 determinant - + 1 1 1 1 3 - + ans2 @@ -97,16 +96,16 @@ detmatrix:determinant(matrixv312); 5 1 0 - + 0 determinant - + 1 1 1 1 3 - + Result @@ -114,56 +113,56 @@ detmatrix:determinant(matrixv312); 1 1 - + 0 - + AlgEquiv ans1 correctanswer[1] - + 0 = 0.5 - + 1 Result-0-T - + = 0 - + 1 Result-0-F - + 1 - + AlgEquiv ans2 correctanswer[2] - + 0 + 0.5 - + -1 Result-1-T - + - 0 - + -1 Result-1-F - + @@ -187,7 +186,7 @@ detmatrix:determinant(matrixv312); 1988758674 1 - + ans1 correctanswer[1] @@ -205,7 +204,7 @@ detmatrix:determinant(matrixv312); 2 - + ans1 correctanswer[1]-1 @@ -222,5 +221,4 @@ detmatrix:determinant(matrixv312); - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-system.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-system.xml index 626ab07014b..197abee1308 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-system.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Linear-system.xml @@ -1,6 +1,5 @@ - Linear systems @@ -66,7 +65,7 @@ Evaluating this at \(k={@k2@}\) gives 6 0.1 0 - + 2023121100 @@ -123,8 +122,7 @@ WS:solve(flatten(args(submatrix(WTAM2,5).transpose([v1,v2,v3,v4])-submatrix(WTAM WS:stack_strip_percent(first(WS),[t]); taw1: maplist(lambda([ex2], rhs(first(sublist(WS,lambda([ex],lhs(ex)=ex2))))),[v1,v2,v3,v4]); -taw1: transpose(apply(matrix,[taw1])); - +taw1: transpose(apply(matrix,[taw1])); [[feedback:prt1]] @@ -133,7 +131,7 @@ taw1: transpose(apply(matrix,[taw1])); [[feedback:prt4]] - \( {@QAM@} \rightarrow {@TAM1@} \) Inconsistent: \(k={@k1@}\). Infinite solutions: \(k={@k2@}\). \(\mathbf{x} = {@ta4@} \). + \( {@QAM@} \rightarrow {@TAM1@} \) Inconsistent: \(k={@k1@}\). Infinite solutions: \(k={@k2@}\). \(\mathbf{x} = {@ta4@} \). This question is distributed as part of the STACK source code as an example. This is licenced as Creative Commons Attribution-ShareAlike 4.0 International License. @@ -158,7 +156,7 @@ taw1: transpose(apply(matrix,[taw1])); cos-1 lang [ - + ans1 matrix @@ -166,16 +164,16 @@ taw1: transpose(apply(matrix,[taw1])); 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans2 @@ -186,14 +184,14 @@ taw1: transpose(apply(matrix,[taw1])); 0 {?,?} 0 - - + + 1 0 1 1 3 - + ans3 @@ -202,16 +200,16 @@ taw1: transpose(apply(matrix,[taw1])); 15 1 0 - + 0 - - + + 1 0 1 1 3 - + ans4 @@ -220,16 +218,16 @@ taw1: transpose(apply(matrix,[taw1])); 5 1 0 - + 0 - - + + 1 0 0 1 3 - + prt1 @@ -238,29 +236,27 @@ taw1: transpose(apply(matrix,[taw1])); 1 /* Pick our the entries which need to be zero. */ -sa1:setify(flatten(makelist(makelist(ans1[l1,l2],l2,1,l1-1),l1,2,first(matrix_size(ans1))))); - - +sa1:setify(flatten(makelist(makelist(ans1[l1,l2],l2,1,l1-1),l1,2,first(matrix_size(ans1))))); 0 - + Sets sa1 {0} - + 0 = 0.2 - + 1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -269,23 +265,23 @@ sa1:setify(flatten(makelist(makelist(ans1[l1,l2],l2,1,l1-1),l1,2,first(matrix_si 1 - + AlgEquiv rref(ans1) rref(TAM1) - + 1 = 1 - + -1 prt1-2-T - + = 0 - + -1 prt1-2-F @@ -299,31 +295,31 @@ sa1:setify(flatten(makelist(makelist(ans1[l1,l2],l2,1,l1-1),l1,2,first(matrix_si 1 1 - + 0 - + Sets ans2 ta2 - + 0 = 1 - + -1 prt2-1-T - + = 0 - + -1 prt2-1-F - + @@ -338,40 +334,40 @@ sd1:determinant(at(SM2,k=ans3)) 0 - + AlgEquiv ans3 ta3 - + 0 = 1 - + -1 prt3-1-T - + = 0 - + 1 prt3-1-F - + 1 - + AlgEquiv sd1 0 - + 0 = 1 - + -1 prt3-2-T @@ -379,7 +375,7 @@ sd1:determinant(at(SM2,k=ans3)) - 0 - + -1 prt3-2-F @@ -394,20 +390,19 @@ sd1:determinant(at(SM2,k=ans3)) 1 v4:listofvars(ans4); -SM2:submatrix(ans1,5); - +SM2:submatrix(ans1,5); 0 - + AlgEquiv length(v4) 1 - + 1 = 0.3 - + 1 prt4-1-T @@ -415,7 +410,7 @@ SM2:submatrix(ans1,5); = 0 - + 1 prt4-1-F @@ -424,23 +419,23 @@ SM2:submatrix(ans1,5); 1 - + AlgEquiv at(QA,k=ans3).ans4 Qb - + 1 + 0.7 - + -1 prt4-2-T - + - 0 - + 2 prt4-2-F @@ -452,15 +447,15 @@ In fact 2 - + AlgEquiv at(SM2,k=ans3).ans4 submatrix(ans1,1,2,3,4) - + 1 + 0.7 - + -1 prt4-3-T @@ -471,7 +466,7 @@ So, although your row reductions contain a mistake you have correctly solved the - 0 - + -1 prt4-3-F @@ -490,7 +485,7 @@ So, no follow-through marking applies here either. 1814590374 1 - + ans1 TAM1 @@ -534,7 +529,7 @@ So, no follow-through marking applies here either. 2 - + ans1 WTAM1 @@ -577,5 +572,4 @@ So, no follow-through marking applies here either. - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Matrix-Algebra-give-examples.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Matrix-Algebra-give-examples.xml index 3ea731c855d..8b20b138cc9 100644 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Matrix-Algebra-give-examples.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Matrix-Algebra-give-examples.xml @@ -1,70 +1,69 @@ - Matrix Algebra - give an example - -
  • Give an example of matrices \(A\), \(B\) such that \(A\cdot B =\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \) and both \(A , \, B \neq \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \) - -
    \(A=\)[[input:a1A]][[validation:a1A]] , \(B=\)[[input:a1B]][[validation:a1B]][[feedback:prt1]]
    • -
  • Give a different pair of nonzero matrices \(C\), \(D\) such that \(C\cdot D =\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \). -
    \(C=\)[[input:a2A]][[validation:a2A]] , \(D=\)[[input:a2B]][[validation:a2B]][[feedback:prt2]]
    • -
  • Consider the following statement: -

    There do not exist \(2 \times 2 \) matrices \(E, \, F\) with rank\((E)\)\(=\)rank\((F)\)\(=2\) such that \(E\cdot F = \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \).

    -

    Select whether it is true or false, and give either a proof or counterexample as appropriate.

    -
    This statement is [[input:a4]][[validation:a4]] [[feedback:prt4]]
    - [[reveal input="a4" value="true"]] -

    Proof:

    [[input:a4_true]][[validation:a4_true]] - [[/reveal]] - [[reveal input="a4" value="false"]] -

    Counterexample:

    -
    \(E=\)[[input:a3A]][[validation:a3A]] , \(F=\)[[input:a3B]] [[validation:a3B]] [[feedback:prt3]]
    - [[/reveal]] -
    • + +
  • Give an example of matrices \(A\), \(B\) such that \(A\cdot B =\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \) and both \(A , \, B \neq \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \) + +
    \(A=\)[[input:a1A]][[validation:a1A]] , \(B=\)[[input:a1B]][[validation:a1B]][[feedback:prt1]]
    • +
  • Give a different pair of nonzero matrices \(C\), \(D\) such that \(C\cdot D =\left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \). +
    \(C=\)[[input:a2A]][[validation:a2A]] , \(D=\)[[input:a2B]][[validation:a2B]][[feedback:prt2]]
    • +
  • Consider the following statement: +

    There do not exist \(2 \times 2 \) matrices \(E, \, F\) with rank\((E)\)\(=\)rank\((F)\)\(=2\) such that \(E\cdot F = \left( \begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array} \right) \).

    +

    Select whether it is true or false, and give either a proof or counterexample as appropriate.

    +
    This statement is [[input:a4]][[validation:a4]] [[feedback:prt4]]
    + [[reveal input="a4" value="true"]] +

    Proof:

    [[input:a4_true]][[validation:a4_true]] + [[/reveal]] + [[reveal input="a4" value="false"]] +

    Counterexample:

    +
    \(E=\)[[input:a3A]][[validation:a3A]] , \(F=\)[[input:a3B]] [[validation:a3B]] [[feedback:prt3]]
    + [[/reveal]] +
    • ]]>         - Worked Solution -

    We denote the row of matrix \(A\) by \(A_i\), columns of matrix \(B\) by \(b_j\) and columns of matrix \(AB\) by \((ab)_j\). Then the matrix \(AB={@zmatrix@}\) are made up of two column vectors, namely \((ab)_1={@cvec@}\) and \((ab)_2={@cvec@}\).

    -Thus, we break this problem down into two parts which are \((ab)_1=A \cdot b_1={@cvec@}\) and \((ab)_2=A \cdot b_2={@cvec@}\).

    -Note that this is a linear transformation from \(\mathbb{R}^2\) to \(\mathbb{R}^2\) as \(A\) maps \(b_1\) to \({@cvec@}\) and \(b_2\) to \({@cvec@}\). -

    -

    By the dimension theorem, \(\text{dim}(\mathbb{R}^2)= \text{nullity}(A)+\text{rank}(A)\). -As \(A\neq{@zmatrix@}\), \(\text{nullity}(A)<2\). On the other hand, \(b_1\neq{@cvec@}\) and \(b_2\neq{@cvec@}\) is in the null space of \(A\) so, \(\text{nullity}(A)\neq0\) which implies that \(\text{nullity}(A)=1\). This means that the rows or columns of the matrix \(A\) are linearly dependent. -

    -

    -Again, from the dimension theorem, we know that \(\text{rank}(B)\neq2\) since if \(\text{rank}(B)=2\) then \(\text{nullity}(A)=2\) which contradicts our assumption that \(A\) cannot be the zero matrix. From our assumption, we also know that \(\text{rank}(B)\neq0\) as \(B\) cannot be the zero matrix. Hence, similar to \(A\), \(B\) has \(\text{rank}=1\).

    -

    -To find an example of matrices \(A,B\) which satisfies the condition, we set \(A\) to be any matrix with linearly dependent columns or rows. Then solve for \(B\). -For example, \(A\) can be of the form \(\left( \begin{array}{cc} a & a \\ ca & ca \end{array} \right)\) for any \(c,a \in \mathbb{R}\).

    + Worked Solution +

    We denote the row of matrix \(A\) by \(A_i\), columns of matrix \(B\) by \(b_j\) and columns of matrix \(AB\) by \((ab)_j\). Then the matrix \(AB={@zmatrix@}\) are made up of two column vectors, namely \((ab)_1={@cvec@}\) and \((ab)_2={@cvec@}\).

    +Thus, we break this problem down into two parts which are \((ab)_1=A \cdot b_1={@cvec@}\) and \((ab)_2=A \cdot b_2={@cvec@}\).

    +Note that this is a linear transformation from \(\mathbb{R}^2\) to \(\mathbb{R}^2\) as \(A\) maps \(b_1\) to \({@cvec@}\) and \(b_2\) to \({@cvec@}\). +

    +

    By the dimension theorem, \(\text{dim}(\mathbb{R}^2)= \text{nullity}(A)+\text{rank}(A)\). +As \(A\neq{@zmatrix@}\), \(\text{nullity}(A)<2\). On the other hand, \(b_1\neq{@cvec@}\) and \(b_2\neq{@cvec@}\) is in the null space of \(A\) so, \(\text{nullity}(A)\neq0\) which implies that \(\text{nullity}(A)=1\). This means that the rows or columns of the matrix \(A\) are linearly dependent. +

    +

    +Again, from the dimension theorem, we know that \(\text{rank}(B)\neq2\) since if \(\text{rank}(B)=2\) then \(\text{nullity}(A)=2\) which contradicts our assumption that \(A\) cannot be the zero matrix. From our assumption, we also know that \(\text{rank}(B)\neq0\) as \(B\) cannot be the zero matrix. Hence, similar to \(A\), \(B\) has \(\text{rank}=1\).

    +

    +To find an example of matrices \(A,B\) which satisfies the condition, we set \(A\) to be any matrix with linearly dependent columns or rows. Then solve for \(B\). +For example, \(A\) can be of the form \(\left( \begin{array}{cc} a & a \\ ca & ca \end{array} \right)\) for any \(c,a \in \mathbb{R}\).

    One such example is \(A={@ta1A@}\). An example for \(B\) which satisfies the condition would be \(B={@ta1B@}\).

    ]]>         1 0.1 0 - + 2024111500 - ta1A:matrix([1,1],[2,2]); -ta1B:matrix([2,2],[-2,-2]); -ta2A:matrix([1,1],[-1,-1]); -ta2B:matrix([1,1],[-1,-1]); -ta3A:matrix([null,null],[null,null]); -ta3B:matrix([null,null],[null,null]); -ta4:true; -zmatrix:matrix([0,0],[0,0]); + ta1A:matrix([1,1],[2,2]); +ta1B:matrix([2,2],[-2,-2]); +ta2A:matrix([1,1],[-1,-1]); +ta2B:matrix([1,1],[-1,-1]); +ta3A:matrix([null,null],[null,null]); +ta3B:matrix([null,null],[null,null]); +ta4:true; +zmatrix:matrix([0,0],[0,0]); cvec:matrix([0],[0]); - + - + This question is distributed as part of the STACK source code as an example. This is licenced as Creative Commons Attribution-ShareAlike 4.0 International License. @@ -89,7 +88,7 @@ cvec:matrix([0],[0]); cos-1 lang [ - + a1A matrix @@ -97,16 +96,16 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 1 3 - + a1B @@ -115,16 +114,16 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 1 3 - + a2A @@ -133,16 +132,16 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 1 3 - + a2B @@ -151,16 +150,16 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 1 3 - + a3A @@ -169,10 +168,10 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 @@ -187,10 +186,10 @@ cvec:matrix([0],[0]); 1 1 0 - + 0 - - + + 1 0 0 @@ -205,16 +204,16 @@ cvec:matrix([0],[0]); 3 1 0 - + 0 - - + + 1 0 0 0 0 - + a4_true @@ -223,16 +222,16 @@ cvec:matrix([0],[0]); 70 1 0 - + 0 - - + + 1 0 0 1 1 - + prt1 @@ -240,47 +239,47 @@ cvec:matrix([0],[0]); 1 1 - a: a1A; -b:a1B; -if notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elseif rank(a)=0 or rank(b)=0 or (rank(a)=0 and rank(b)=1) then Mark:-1 elseif notequal(rank(a.b),0) then Mark:0; + a: a1A; +b:a1B; +if notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elseif rank(a)=0 or rank(b)=0 or (rank(a)=0 and rank(b)=1) then Mark:-1 elseif notequal(rank(a.b),0) then Mark:0; /*Mark=1 when correct, Mark=0 when A multiplied by B does not give the zero matrix, Mark=-1 when A or B or both = the zero matrix.*/ 0 - + AlgEquiv Mark 1 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + 1 prt1-1-F - + 1 - + AlgEquiv Mark 0 - + 0 + 0 - + -1 prt1-2-T @@ -288,24 +287,24 @@ if notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elsei - 0 - + 2 prt1-2-F - + 2 - + AlgEquiv Mark -1 - + 0 + 0 - + -1 prt1-3-T @@ -313,11 +312,11 @@ if notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elsei - 0 - + -1 prt1-3-F - + @@ -327,49 +326,49 @@ if notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elsei 1 1 - a: a2A; -b:a2B; -c:a1A; -d:a1B; -if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 elseif notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elseif rank(a)=0 or rank(b)=0 or (rank(a)=0 and rank(b)=1) then Mark:-1 elseif notequal(rank(a.b),0) then Mark:0; + a: a2A; +b:a2B; +c:a1A; +d:a1B; +if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 elseif notequal(rank(a),0) and notequal(rank(b),0) and rank(a.b)=0 then Mark:1 elseif rank(a)=0 or rank(b)=0 or (rank(a)=0 and rank(b)=1) then Mark:-1 elseif notequal(rank(a.b),0) then Mark:0; /*Mark=1 when correct, Mark=0 when A multiplied by B does not give the zero matrix, Mark=-1 when A or B or both = the zero matrix, Mark=-2 if A and B have been given as the answer in part(a) of the question*/ 0 - + AlgEquiv Mark 1 - + 0 = 1 - + -1 prt2-1-T - + = 0 - + 1 prt2-1-F - + 1 - + AlgEquiv Mark 0 - + 0 + 0 - + -1 prt2-2-T @@ -377,24 +376,24 @@ if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 el - 0 - + 2 prt2-2-F - + 2 - + AlgEquiv Mark -1 - + 0 + 0 - + -1 prt2-3-T @@ -402,24 +401,24 @@ if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 el - 0 - + 3 prt2-3-F - + 3 - + AlgEquiv Mark -2 - + 0 + 0 - + -1 prt2-4-T @@ -427,11 +426,11 @@ if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 el - 0 - + -1 prt2-4-F - + @@ -441,48 +440,48 @@ if (a=d and b=c) then Mark:-2 elseif (a=c and b=d) or a=c or b=d then Mark:-2 el 1 1 - 0 - + AlgEquiv Mark 1 - + 0 = 1 - + -1 prt3-1-T - + = 0 - + 1 prt3-1-F - + 1 - + AlgEquiv Mark 0 - + 0 + 0 - + -1 prt3-2-T @@ -490,24 +489,24 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else - 0 - + 2 prt3-2-F - + 2 - + AlgEquiv Mark -1 - + 0 + 0 - + -1 prt3-3-T @@ -515,11 +514,11 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else - 0 - + -1 prt3-3-F - + @@ -529,37 +528,37 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else 1 1 - + 0 - + AlgEquiv a4 ta4 - + 0 = 1 - + -1 prt4-1-T - + = 0 - + -1 prt4-1-F - + 1 - + a1A ta1A @@ -605,7 +604,7 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else 2 - + a1A ta1A @@ -651,7 +650,7 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else 3 - + a1A ta1A @@ -697,7 +696,7 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else 4 - + a1A ta1A @@ -756,5 +755,4 @@ if (a=ta3A and b=ta3B) then Mark:1 elseif notequal(rank(a.b),0) then Mark:0 else     - -     \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-dot-product.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-dot-product.xml index 3e00c3f413d..11bb69fc3b8 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-dot-product.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-dot-product.xml @@ -1,6 +1,5 @@ - Dot product formula proof comprehension @@ -87,7 +86,7 @@ 3 0.1 0 - + 2023010400 @@ -99,8 +98,7 @@ ta32:2; ta33:1; ta34:2; ta35:1; -ta36:5; -]]> +ta36:5;]]> @@ -160,7 +158,7 @@ ta36:5; ]]> - + This question is distributed as part of the STACK source code as an example. This is licenced as Creative Commons Attribution-ShareAlike 4.0 International License. @@ -185,7 +183,7 @@ ta36:5; cos-1 lang [ - + ans1 dropdown @@ -193,16 +191,16 @@ ta36:5; 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ans31 @@ -211,16 +209,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans32 @@ -229,16 +227,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans33 @@ -247,16 +245,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans34 @@ -265,16 +263,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans35 @@ -283,16 +281,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + ans36 @@ -301,16 +299,16 @@ ta36:5; 3 1 0 - + 0 - - + + 1 0 0 1 3 - + prt1 @@ -318,31 +316,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans1 ta1 - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -352,31 +350,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans31 ta31 - + 1 = 1 - + -1 prt31-1-T - + = 0 - + -1 prt31-1-F - + @@ -386,31 +384,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans32 ta32 - + 1 = 1 - + -1 prt32-1-T - + = 0 - + -1 prt32-1-F - + @@ -420,31 +418,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans33 ta33 - + 1 = 1 - + -1 prt33-1-T - + = 0 - + -1 prt33-1-F - + @@ -454,31 +452,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans34 ta34 - + 1 = 1 - + -1 prt34-1-T - + = 0 - + -1 prt34-1-F - + @@ -488,31 +486,31 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans35 ta35 - + 1 = 1 - + -1 prt35-1-T - + = 0 - + -1 prt35-1-F - + @@ -522,37 +520,37 @@ ta36:5; 1 2 - + 0 - + AlgEquiv ans36 ta36 - + 1 = 1 - + -1 prt36-1-T - + = 0 - + -1 prt36-1-F - + 1 - + ans1 ta1 @@ -625,5 +623,4 @@ ta36:5; - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-gaps-linear-dependence.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-gaps-linear-dependence.xml index 7a6d32534db..2f0aba6e851 100755 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-gaps-linear-dependence.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Proof-gaps-linear-dependence.xml @@ -1,6 +1,5 @@ - Span proof @@ -57,12 +56,12 @@ May we assume that \(a,b,c\) are not all zero? ]]> - + 6 0.1 0 - + 2023010400 @@ -139,7 +138,7 @@ For the direction \(U \subseteq W\). cos-1 lang [ - + ans1 dropdown @@ -147,10 +146,10 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 @@ -165,10 +164,10 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 @@ -183,10 +182,10 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 @@ -201,10 +200,10 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 @@ -219,10 +218,10 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 @@ -237,16 +236,16 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv11 @@ -255,16 +254,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv12 @@ -273,16 +272,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv13 @@ -291,16 +290,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv21 @@ -309,16 +308,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv22 @@ -327,16 +326,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansv23 @@ -345,16 +344,16 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 0 0 - + ansxd @@ -363,16 +362,16 @@ For the direction \(U \subseteq W\). 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ansxd2 @@ -381,10 +380,10 @@ For the direction \(U \subseteq W\). 5 1 0 - + 0 - - + + 1 0 0 @@ -398,31 +397,31 @@ For the direction \(U \subseteq W\). 1 3 - + 0 - + AlgEquiv ans1 taa1 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -432,31 +431,31 @@ For the direction \(U \subseteq W\). 1 3 - + 0 - + AlgEquiv ans2 taa2 - + 0 = 1 - + -1 prt2-1-T - + = 0 - + -1 prt2-1-F - + @@ -466,31 +465,31 @@ For the direction \(U \subseteq W\). 1 3 - + 0 - + AlgEquiv ans3 taa3 - + 0 = 1 - + -1 prt3-1-T - + = 0 - + -1 prt3-1-F - + @@ -500,31 +499,31 @@ For the direction \(U \subseteq W\). 1 3 - + 0 - + AlgEquiv ans4 taa4 - + 0 = 1 - + -1 prt4-1-T - + = 0 - + -1 prt4-1-F - + @@ -534,31 +533,31 @@ For the direction \(U \subseteq W\). 1 3 - + 0 - + AlgEquiv ans5 taa5 - + 0 = 1 - + -1 prt5-1-T - + = 0 - + -1 prt5-1-F - + @@ -568,27 +567,27 @@ For the direction \(U \subseteq W\). 1 2 - + 0 - + AlgEquiv ansf1 false - + 0 = 1 - + -1 prtf1-1-T - + = 0 - + -1 prtf1-1-F @@ -606,27 +605,27 @@ For the direction \(U \subseteq W\). 0 - + AlgEquiv sa tav1 - + 0 = 1 - + -1 prtv1-1-T - + = 0 - + -1 prtv1-1-F - + @@ -640,54 +639,52 @@ For the direction \(U \subseteq W\). sa2:ev(expand(ansv21*(x+y)+ansv22*(y+z)+ansv23*(z+x)), simp); scx:ev(ratsimp(ansv21+ansv23),simp); scy:ev(ratsimp(ansv21+ansv22),simp); -scz:ev(ratsimp(ansv22+ansv23),simp); - - +scz:ev(ratsimp(ansv22+ansv23),simp); 0 - + AlgEquiv sa tav2 - + 0 = 1 - + -1 prtv2-1-T - + = 0 - + 1 prtv2-1-F - + 1 - + AlgEquiv sa2 a*x+b*y+c*z - + 0 = 1 - + -1 prtv2-2-T - + - 0 - + -1 prtv2-2-F @@ -706,62 +703,62 @@ so you must have done something wrong! 1 2 - + 0 - + AlgEquiv ansxd taaxd - + 0 = 0.5 - + 1 prtxd-1-T - + = 0 - + -1 prtxd-1-F - + 1 - + AlgEquiv ansxd2 3 - + 0 + 0.5 - + -1 prtxd-2-T - + - 0 - + -1 prtxd-2-F - + 1 - + ans1 first(mcq_correct(ta1)) @@ -875,54 +872,54 @@ so you must have done something wrong! 2 - + ans1 - + ans2 - + ans3 - + ans4 - + ans5 - + ansf1 - + ansv11 - + ansv12 - + ansv13 - + ansv21 - + ansv22 - + ansv23 - + ansxd @@ -930,54 +927,54 @@ so you must have done something wrong! ansxd2 - + prt1 - - + + NULL prt2 - - + + NULL prt3 - - + + NULL prt4 - - + + NULL prt5 - - + + NULL prtf1 - - + + NULL prtv1 - - + + NULL prtv2 - - + + NULL @@ -988,5 +985,4 @@ so you must have done something wrong! - diff --git a/samplequestions/stacklibrary/Topics/LinearAlgebra/Show-Ax-forms-a-subspace-Parsons.xml b/samplequestions/stacklibrary/Topics/LinearAlgebra/Show-Ax-forms-a-subspace-Parsons.xml index 28497df70df..a63a96cd714 100644 --- a/samplequestions/stacklibrary/Topics/LinearAlgebra/Show-Ax-forms-a-subspace-Parsons.xml +++ b/samplequestions/stacklibrary/Topics/LinearAlgebra/Show-Ax-forms-a-subspace-Parsons.xml @@ -1,6 +1,5 @@ - Drag/drop: forms a subspace @@ -20,7 +19,7 @@ 1 0.1 0 - + 2024072400 @@ -51,8 +50,7 @@ ta2:proof(proof_c("ass1","cs1"),proof_c(proof("ca1","ca2","ca3","ca4"), proof("c /* Generate the alternative proofs. */ tal:append(proof_alternatives(ta),proof_alternatives(ta2)); /* Create a set of flattened proofs. */ -tas:setify(map(proof_flatten, tal)); -]]> +tas:setify(map(proof_flatten, tal));]]> [[feedback:prt1]] @@ -83,7 +81,7 @@ tas:setify(map(proof_flatten, tal)); cos-1 lang [ - + ans1 string @@ -91,16 +89,16 @@ tas:setify(map(proof_flatten, tal)); 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -113,23 +111,23 @@ tas:setify(map(proof_flatten, tal)); 0 - + AlgEquiv pd 0 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -157,5 +155,4 @@ tas:setify(map(proof_flatten, tal)); - diff --git a/samplequestions/stacklibrary/Topics/ODE_2nd_order_linear.xml b/samplequestions/stacklibrary/Topics/ODE_2nd_order_linear.xml index bc47ef6bbcb..4cc71b95946 100644 --- a/samplequestions/stacklibrary/Topics/ODE_2nd_order_linear.xml +++ b/samplequestions/stacklibrary/Topics/ODE_2nd_order_linear.xml @@ -1,6 +1,5 @@ - ODE_2nd_order_linear_1 @@ -9,12 +8,12 @@ Find the general solution to \[ {@q@} =0 \] \(y(t) =\; \)[[input:ans1]] [[validation:ans1]]

    ]]>     - + 1 0.1 0 - + 2024092500 @@ -58,7 +57,7 @@ ta:A*%e^(l1*t)+B*%e^(l2*t); cos-1 lang [ - + ans1 algebraic @@ -66,16 +65,16 @@ ta:A*%e^(l1*t)+B*%e^(l2*t); 15 1 0 - + 0 - - + + 1 1 1 1 1 - + Result @@ -104,19 +103,19 @@ m:float(m); AlgEquiv p 0 - + 0 = 1 - + 1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -129,19 +128,19 @@ m:float(m); AlgEquiv lv 2 - + 0 = 1 - + 2 prt1-2-T - + = 0.75 - + -1 prt1-2-F @@ -154,11 +153,11 @@ m:float(m); AlgEquiv numberp(m) true - + 0 = 0 - + -1 prt1-3-T @@ -166,11 +165,11 @@ m:float(m); = 1 - + -1 prt1-3-F - +     @@ -186,7 +185,7 @@ m:float(m); 511077327 1 - + ans1 ta @@ -200,7 +199,7 @@ m:float(m); 2 - + ans1 %e^(l1*t)+%e^(l2*t) @@ -214,7 +213,7 @@ m:float(m); 3 - + ans1 sin(t) @@ -228,7 +227,7 @@ m:float(m); 4 - + ans1 A*B*%e^(l1*t) @@ -242,7 +241,7 @@ m:float(m); 5 - + ans1 D*%e^(l1*t)+C*%e^(l2*t); @@ -255,5 +254,4 @@ m:float(m); - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Parsons-proof-template.xml b/samplequestions/stacklibrary/Topics/Parsons-proof-template.xml index 61b1c56f8bb..5e1969761b0 100644 --- a/samplequestions/stacklibrary/Topics/Parsons-proof-template.xml +++ b/samplequestions/stacklibrary/Topics/Parsons-proof-template.xml @@ -1,66 +1,65 @@ - Parsons' proof template - {@thm@}

    -[[parsons input="ans1"]] -{# parsons_encode(proof_steps) #} -[[/parsons ]] + {@thm@}

    +[[parsons input="ans1"]] +{# parsons_encode(proof_steps) #} +[[/parsons ]]

    [[input:ans1]] [[validation:ans1]]

    ]]>         - -
    {@proof_display_para(tal[1], proof_steps)@} -
    {@proof_display_para(tal[2], proof_steps)@} - -Can you see the differences between these proofs? -[[/if]] -[[if test='len1>2' ]] -{@proof_display_para(tal[1], proof_steps)@} -[[/if]] -[[if test='len1<2' ]] -{@proof_display_para(tal[1], proof_steps)@} + +
    {@proof_display_para(tal[1], proof_steps)@} +
    {@proof_display_para(tal[2], proof_steps)@} + +Can you see the differences between these proofs? +[[/if]] +[[if test='len1>2' ]] +{@proof_display_para(tal[1], proof_steps)@} +[[/if]] +[[if test='len1<2' ]] +{@proof_display_para(tal[1], proof_steps)@} [[/if]]]]> 1 0.1 0 - + 2024092500 - @@ -70,9 +69,9 @@ tas: setify(map(proof_flatten, tal));]]> {@ map(first, proof_steps) @} - This question is a template for importing proofs from the STACK contrib directory. See -https://github.com/maths/moodle-qtype_stack/tree/master/stack/maxima/contrib/proofsamples - + This question is a template for importing proofs from the STACK contrib directory. See +https://github.com/maths/moodle-qtype_stack/tree/master/stack/maxima/contrib/proofsamples + It also demonstrates how to create sample Parsons problems. In particular, how to use the Parsons function to give tailored feedback about what stages are incorrect. 1 @@ -95,7 +94,7 @@ It also demonstrates how to create sample Parsons problems. In particular, how cos-1 lang [ - + ans1 parsons @@ -103,16 +102,16 @@ It also demonstrates how to create sample Parsons problems. In particular, how 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt1 @@ -120,28 +119,28 @@ It also demonstrates how to create sample Parsons problems. In particular, how 1 1 - sa: parsons_decode(ans1); + sa: parsons_decode(ans1); [pd, saa]:proof_assessment(sa, proof_alternatives(proof_ans)); 0 - + AlgEquiv pd 0 - + 1 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F @@ -184,5 +183,4 @@ It also demonstrates how to create sample Parsons problems. In particular, how - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_infinite_primes.xml b/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_infinite_primes.xml index c6d81d08e67..dccd28a14f9 100755 --- a/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_infinite_primes.xml +++ b/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_infinite_primes.xml @@ -1,6 +1,5 @@ - W6 Q6 PC (Infinitely many primes) @@ -14,7 +13,7 @@ 1.Suppose there are only finitely many primes, label them \(p_1 = 2 < p_2 = 3 < \cdots < p_n\). 2.Let \(N = p_1p_2\cdots p_n +1\). 3.Then \(N\) is an integer greater than each of \(p_1, \dots, p_n\), thus \(N\) cannot be prime. -4.Thus we can write \(N\) as a product of primes. /* say \(N = q_1q_2 \cdots q_m\) where \(q_1, \dots, q_m\) are prime. */ +4.Thus we can write \(N\) as a product of primes. 5.Hence there is some prime \(p\) which divides \(N\). 6.\(p\) can not be any of the \(p_1, \dots p_n\) otherwise \(p\) would divide the difference \(N - p_1 p_2 \cdots p_n = \) [[validation:ans0]] [[input:ans0]] which cannot happen.[[feedback:prt0]] 7.Thus \(p\) must be a new prime and our initial list \(p_1,p_2,\dots, p_n\) is not an exhaustive list of the primes. @@ -42,9 +41,9 @@ The aim of the proof is to show a contradiction to line 1, which is accomplished 1 0.1 0 - + - 2021120900 + 2024111900 - + - + - + 1 0 @@ -83,7 +82,7 @@ ta3:matrix([1,7]);]]> cos-1 lang [ - + ans0 algebraic @@ -91,16 +90,16 @@ ta3:matrix([1,7]);]]> 5 1 5 - + 0 - - + + 1 0 0 1 3 - + ans1 @@ -109,16 +108,16 @@ ta3:matrix([1,7]);]]> 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans2 @@ -127,16 +126,16 @@ ta3:matrix([1,7]);]]> 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans3 @@ -145,16 +144,16 @@ ta3:matrix([1,7]);]]> 3 1 0 - + 0 - - + + 1 0 0 1 2 - + ans4 @@ -163,16 +162,16 @@ ta3:matrix([1,7]);]]> 50 1 0 - + 0 - - + + 1 0 0 1 1 - + ansp @@ -181,16 +180,16 @@ ta3:matrix([1,7]);]]> 15 1 0 - + 0 - - + + 1 0 0 0 0 - + prt0 @@ -198,31 +197,31 @@ ta3:matrix([1,7]);]]> 1 1 - + 0 - + AlgEquiv ans0 ta0 - + 1 = - 1.0000000 - + 1 + -1 prt0-1-T - + = - 0.0000000 - + 0 + -1 prt0-1-F - + @@ -232,31 +231,31 @@ ta3:matrix([1,7]);]]> 1 1 - + 0 - + AlgEquiv ans1 ta1 - + 0 = - 1.0000000 - + 1 + -1 prt1-1-T - + = - 0.0000000 - + 0 + -1 prt1-1-F - + @@ -266,31 +265,31 @@ ta3:matrix([1,7]);]]> 1 1 - + 0 - + AlgEquiv ans2 ta2 - + 0 = - 1.0000000 - + 1 + -1 prt2-1-T - + = - 0.0000000 - + 0 + -1 prt2-1-F - + @@ -304,27 +303,27 @@ ta3:matrix([1,7]);]]> 0 - + Sets sa setify(args(ta3)) - + 0 = - 1.0000000 - + 1 + -1 prt3-1-T - + = - 0.0000000 - + 0 + -1 prt3-1-F - + @@ -334,37 +333,37 @@ ta3:matrix([1,7]);]]> 1 1 - + 0 - + AlgEquiv ansp taa - + 1 = - 1.0000000 - + 1 + -1 prtp-1-T - + = - 0.0000000 - + 0 + -1 prtp-1-F - + 1 - + ans0 ta0 @@ -383,7 +382,7 @@ ta3:matrix([1,7]);]]> ans4 - + ansp @@ -422,7 +421,7 @@ ta3:matrix([1,7]);]]> 2 - + ans0 ta0-1 @@ -441,7 +440,7 @@ ta3:matrix([1,7]);]]> ans4 - + ansp @@ -480,7 +479,7 @@ ta3:matrix([1,7]);]]> 3 - + ans0 ta0 @@ -499,7 +498,7 @@ ta3:matrix([1,7]);]]> ans4 - + ansp @@ -537,5 +536,4 @@ ta3:matrix([1,7]);]]> - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_roots_unity.xml b/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_roots_unity.xml index 59766eb276e..3d2e718ef19 100755 --- a/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_roots_unity.xml +++ b/samplequestions/stacklibrary/Topics/Proof/Proof_comprehension_roots_unity.xml @@ -1,6 +1,5 @@ - W5 Q9 PC (Roots of unity) @@ -62,7 +61,7 @@ Steps 1. to 5. show the forwards direction and steps 6. to 8. show the backwards 1 0.1 0 - + 2020020300 @@ -79,13 +78,13 @@ tal4: [[A, false, "A. The proof is a proof by contradiction."], [B, false, "B. T ta4:mcq_correct(tal4);]]> - + - + - + 1 0 @@ -107,7 +106,7 @@ ta4:mcq_correct(tal4);]]> cos-1 lang [ - + ans1 algebraic @@ -115,16 +114,16 @@ ta4:mcq_correct(tal4);]]> 15 1 0 - + 0 - - + + 1 0 0 1 1 - + ans2 @@ -133,16 +132,16 @@ ta4:mcq_correct(tal4);]]> 5 1 0 - + 0 - - + + 1 0 0 1 1 - + ans3 @@ -151,16 +150,16 @@ ta4:mcq_correct(tal4);]]> 15 1 0 - + 0 - - + + 1 0 0 1 1 - + ans4 @@ -169,16 +168,16 @@ ta4:mcq_correct(tal4);]]> 15 1 0 - + 0 - - + + 1 0 0 1 1 - + prt1 @@ -186,31 +185,31 @@ ta4:mcq_correct(tal4);]]> 1 1 - + 0 - + AlgEquiv ans1 ta1 - + 0 = 1.0000000 - + -1 prt1-1-T - + = 0.0000000 - + -1 prt1-1-F - + @@ -220,31 +219,31 @@ ta4:mcq_correct(tal4);]]> 1 1 - + 0 - + AlgEquiv ans2 ta2 - + 0 = 1.0000000 - + -1 prt2-1-T - + = 0.0000000 - + -1 prt2-1-F - + @@ -254,31 +253,31 @@ ta4:mcq_correct(tal4);]]> 1 1 - + 0 - + AlgEquiv ans3 ta3 - + 0 = 1.0000000 - + -1 prt3-1-T - + = 0.0000000 - + -1 prt3-1-F - + @@ -288,37 +287,37 @@ ta4:mcq_correct(tal4);]]> 1 1 - + 0 - + AlgEquiv ans4 ta4 - + 0 = 1.0000000 - + -1 prt4-1-T - + = 0.0000000 - + -1 prt4-1-F - + 1 - + ans1 ta1 @@ -362,7 +361,7 @@ ta4:mcq_correct(tal4);]]> 2 - + ans1 r^n*e^(n*i*theta) @@ -405,5 +404,4 @@ ta4:mcq_correct(tal4);]]> - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Proof/Proof_gaps_induction_series.xml b/samplequestions/stacklibrary/Topics/Proof/Proof_gaps_induction_series.xml index e4871737a8c..627db29c4e3 100755 --- a/samplequestions/stacklibrary/Topics/Proof/Proof_gaps_induction_series.xml +++ b/samplequestions/stacklibrary/Topics/Proof/Proof_gaps_induction_series.xml @@ -1,6 +1,5 @@ - Q02 Q8 Proof by induction (general) sum (2k-1)^3 = n^2(2n^2-1) @@ -63,7 +62,7 @@ At this point the goal is to algebraically manipulate your expression so that yo 5 0.1 0 - + 2023010400 @@ -85,13 +84,13 @@ ta4:[[A, false, "(algebraic simplification)"], [B, true, "(by the induction hypo ta5:rh1;]]> - + {@pn@} - + 0 0 @@ -113,7 +112,7 @@ ta5:rh1;]]> cos-1 lang [ - + ans1 numerical @@ -121,16 +120,16 @@ ta5:rh1;]]> 5 1 0 - + 0 - - + + 1 0 0 1 3 - + ans2 @@ -139,16 +138,16 @@ ta5:rh1;]]> 5 1 0 - + 0 - - + + 1 0 0 1 3 - + ans3 @@ -159,14 +158,14 @@ ta5:rh1;]]> 4 sum(?,k,1,n)+? 0 - - + + 1 0 0 1 3 - + ans4 @@ -175,16 +174,16 @@ ta5:rh1;]]> 15 1 0 - + 0 - - + + 1 0 0 0 0 - + ans5 @@ -193,16 +192,16 @@ ta5:rh1;]]> 15 1 4 - + 0 - - + + 1 0 0 1 3 - + prtbase @@ -210,44 +209,44 @@ ta5:rh1;]]> 1 2 - + 0 - + EqualComAss ans1 ta1 - + 1 = 0.5 - + 2 prtbase-1-T - + = 0 - + 1 prtbase-1-F - + 1 - + AlgEquiv ans1 ta1 - + 1 + 0 - + 2 prtbase-2-T @@ -255,49 +254,49 @@ ta5:rh1;]]> - 0 - + 2 prtbase-2-F - + 2 - + EqualComAss ans2 ta2 - + 1 + 0.5 - + -1 prtbase-3-T - + - 0 - + 3 prtbase-3-F - + 3 - + AlgEquiv ans2 ta2 - + 1 + 0 - + -1 prtbase-4-T @@ -305,11 +304,11 @@ ta5:rh1;]]> - 0 - + -1 prtbase-4-F - + @@ -319,28 +318,27 @@ ta5:rh1;]]> 0 2 - A3:if atom(ans3) then {} else setify(args(ans3)); - + A3:if atom(ans3) then {} else setify(args(ans3)); 0 - + AlgEquiv elementp('sum(ak,k,1,n),A3) true - + 1 = 0.5 - + 1 prtind-1-T - + = 0 - + 1 prtind-1-F @@ -349,40 +347,40 @@ ta5:rh1;]]> 1 - + EqualComAss ans3 ta3 - + 1 = 1 - + -1 prtind-2-T - + - 0 - + 2 prtind-2-F - + 2 - + AlgEquiv ans3 ta3 - + 0 = 1 - + -1 prtind-3-T @@ -390,11 +388,11 @@ ta5:rh1;]]> - 0 - + -1 prtind-3-F - + @@ -404,27 +402,27 @@ ta5:rh1;]]> 0 2 - + 0 - + AlgEquiv ans5 ta5 - + 0 = 1 - + -1 prtind2-1-T - + = 0 - + -1 prtind2-1-F @@ -438,37 +436,37 @@ ta5:rh1;]]> 1 3 - + 0 - + AlgEquiv ans4 B - + 0 = 1 - + -1 prtindjustify-1-T - + = 0 - + -1 prtindjustify-1-F - + 1 - + ans1 ta1 @@ -518,5 +516,4 @@ ta5:rh1;]]> Incorrect answer. - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Topics_units_basic.xml b/samplequestions/stacklibrary/Topics/Topics_units_basic.xml index 51a2eaa031c..ac59c3892af 100644 --- a/samplequestions/stacklibrary/Topics/Topics_units_basic.xml +++ b/samplequestions/stacklibrary/Topics/Topics_units_basic.xml @@ -1,57 +1,55 @@ - Scientific units template - You run {@d@} in {@t@}. What is your average speed?

    -

    [[input:ans1]] [[validation:ans1]]

    + You run {@d@} in {@t@}. What is your average speed?

    +

    [[input:ans1]] [[validation:ans1]]

    Please give your answer to \(4\) significant figures.

    ]]>         - + 1 0.1 0 - + 2024092500 - + [[feedback:prt1]] - + - 1 @@ -74,7 +72,7 @@ Note some of the feedback in the question tests.]]> cos-1 lang [ - + ans1 units @@ -82,10 +80,10 @@ Note some of the feedback in the question tests.]]> 15 1 0 - + 0 - - + + 0 0 0 @@ -99,7 +97,7 @@ Note some of the feedback in the question tests.]]> 1 1 - + 0 @@ -111,19 +109,19 @@ Note some of the feedback in the question tests.]]> 0 = 1 - + -1 prt1-1-T - + = 0 - + -1 prt1-1-F - + @@ -150,8 +148,8 @@ Note some of the feedback in the question tests.]]> prt1 - - + + NULL @@ -164,14 +162,14 @@ Note some of the feedback in the question tests.]]> prt1 - - + + NULL 4 - + ans1 ta2 @@ -184,5 +182,4 @@ Note some of the feedback in the question tests.]]>     - -     \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/Vector-Calculus.xml b/samplequestions/stacklibrary/Topics/Vector-Calculus.xml index ad5639964e7..044eb8f56ff 100644 --- a/samplequestions/stacklibrary/Topics/Vector-Calculus.xml +++ b/samplequestions/stacklibrary/Topics/Vector-Calculus.xml @@ -1,6 +1,5 @@ - Vector Calculus @@ -39,7 +38,7 @@ f & g & h 1 0.1 0 - + 2024092500 @@ -66,7 +65,7 @@ ta3: curl(f,vars); ta4: EMPTYANSWER;]]> - + \[ \mathbf{F}(x,y,z) = {@f@}\] \[ \mathbf{\nabla} \cdot \mathbf{F} = {@ta2@}\] \[ \mathbf{\nabla} \times \mathbf{F} ={@ta3@}\] @@ -94,7 +93,7 @@ ta4: EMPTYANSWER;]]> cos-1 lang [ - + ans1 matrix @@ -102,10 +101,10 @@ ta4: EMPTYANSWER;]]> 15 1 0 - + 0 - - + + 1 0 0 @@ -120,10 +119,10 @@ ta4: EMPTYANSWER;]]> 15 1 0 - + 0 - - + + 1 0 0 @@ -138,10 +137,10 @@ ta4: EMPTYANSWER;]]> 15 1 0 - + 0 - - + + 1 0 0 @@ -156,10 +155,10 @@ ta4: EMPTYANSWER;]]> 15 1 0 - + 0 - - + + 1 0 0 @@ -173,19 +172,19 @@ ta4: EMPTYANSWER;]]> 1 1 - + 0 - + AlgEquiv ans2 ta2 - + 0 = 1 - + 1 prt1-1-T @@ -193,11 +192,11 @@ ta4: EMPTYANSWER;]]> = 0 - + 1 prt1-1-F - + @@ -206,19 +205,19 @@ ta4: EMPTYANSWER;]]> AlgEquiv ans1 matrix([null],[null],[null]) - + 1 + 0 - + -1 prt1-2-T - + = 0 - + -1 prt1-2-F @@ -232,19 +231,19 @@ ta4: EMPTYANSWER;]]> 1 1 - + 0 - + AlgEquiv ans3 ta3 - + 0 = 1 - + 1 prt2-1-T @@ -252,32 +251,32 @@ ta4: EMPTYANSWER;]]> = 0 - + 1 prt2-1-F - + 1 - + AlgEquiv ans4 EMPTYANSWER - + 1 + 0 - + -1 prt2-2-T - + = 0 - + -1 prt2-2-F @@ -318,15 +317,14 @@ ta4: EMPTYANSWER;]]> prt1 1.0000000 0.0000000 - prt1-1-T + prt1-2-T prt2 1.0000000 0.0000000 - prt2-1-T + prt2-2-T - - \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/equivalence_reasoning_example.xml b/samplequestions/stacklibrary/Topics/equivalence_reasoning_example.xml index dc913d7d37a..523e3357545 100644 --- a/samplequestions/stacklibrary/Topics/equivalence_reasoning_example.xml +++ b/samplequestions/stacklibrary/Topics/equivalence_reasoning_example.xml @@ -1,6 +1,5 @@ - stack_equiv_find_step(ex, ex1) example @@ -10,12 +9,12 @@

    [[input:ans1]] [[validation:ans1]]

    ]]> - + 1 0.1 0 - + 2018120500 @@ -25,9 +24,12 @@ [[feedback:prt1]] - + {@ta@} + + + 0 0 1 @@ -41,12 +43,14 @@ Incorrect answer.]]> . + *10 cross 1 i cos-1 + lang [ - + ans1 equiv @@ -56,64 +60,67 @@ 0 firstline 0 - - + + 1 0 0 1 2 - + prt1 1.0000000 0 + 1 w1:stack_equiv_find_step(lg(5^2,5), ans1) 0 + EquivFirst ans1 ta - + 0 = 0.5000000 - + 1 prt1-1-T - + = 0.0000000 - + -1 prt1-1-F - + 1 + EqualComAss last(ans1) last(ta) - + 0 + 0.5000000 - + 2 prt1-2-T - + - 0.0000000 - + -1 prt1-2-F @@ -122,14 +129,15 @@ 2 + AlgEquiv emptyp(w1) true - + 0 + 0.0000000 - + -1 prt1-3-T @@ -137,16 +145,17 @@ - 0.0000000 - + -1 prt1-3-F - + 1 + ans1 ta @@ -160,6 +169,7 @@ 2 + ans1 [lg(25,5),stackeq(lg(5^2,5)),stackeq(2*lg(5,5)),stackeq(2*1)] @@ -173,6 +183,7 @@ 3 + ans1 [lg(25,5),stackeq(2)] @@ -185,5 +196,4 @@     - -     \ No newline at end of file + diff --git a/samplequestions/stacklibrary/Topics/plot-Discrete_mathematics_graph_theory-1.xml b/samplequestions/stacklibrary/Topics/plot-Discrete_mathematics_graph_theory-1.xml index a345e374f54..43a283b7e70 100644 --- a/samplequestions/stacklibrary/Topics/plot-Discrete_mathematics_graph_theory-1.xml +++ b/samplequestions/stacklibrary/Topics/plot-Discrete_mathematics_graph_theory-1.xml @@ -1,6 +1,5 @@ - @@ -11,12 +10,12 @@

    [[input:ans1]] [[validation:ans1]]

    ]]> - + 1 0.1 0 - + 2024092500 @@ -40,7 +39,7 @@ ta1b: C5 [[feedback:prt1]]     - + This is a graph theory which illustrates maxima's plot function. This is the question outlined in the `discrete maths and graph theory` page of mathematical topics in the documentation. This can be found on your server at `[YOUR SERVER ADDRESS]/question/type/stack/doc/doc.php/Topics/Discrete_mathematics.md`. More info about `plot()` can be found at `[YOUR SERVER ADDRESS]/question/type/stack/doc/doc.php//Plots/Plots/`, but note that maxima plot function is not actively updated, in favour of JSX graphs support. @@ -65,7 +64,7 @@ ta1b: C5 cos-1 lang [ - + ans1 algebraic @@ -73,16 +72,16 @@ ta1b: C5 15 1 0 - + 0 - - + + 1 0 0 1 1 - + prt1 @@ -90,56 +89,56 @@ ta1b: C5 1 1 - + 0 - + AlgEquiv ans1 ta1 - + 0 = 1 - + -1 prt1-1-T - + = 0 - + 1 prt1-1-F - + 1 - + AlgEquiv ans1 ta1b - + 0 + 1 - + -1 prt1-2-T - + - 0 - + -1 prt1-2-F - + @@ -159,7 +158,7 @@ ta1b: C5 2 - + ans1 C5 @@ -173,7 +172,7 @@ ta1b: C5 3 - + ans1 C_6 @@ -186,5 +185,4 @@ ta1b: C5 - - \ No newline at end of file +