Differentiate $ \sin(ax+b) e ^ {nx}$.

Using the chain rule within product rule problems

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More work on differentiation with trigonometric functions

More work on differentiation with trigonometric functions

Differentiation of trigonometric functions

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More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients

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Some basic tests of adding, scaling, and multiplying matrices.

Matrix by scalar and matrix by matrix multiplication exercises.

Matrix by scalar and matrix by matrix multiplication exercises.

Gentle intro to modular arithmetic through quotients and remainders

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Adding 2x2 matrices. Very simple question. Marks per correct entry.

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

This question tests a student's ability to add two fractions with the same denominator.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.

Marking algorithm that allows NA or any correct counterexample.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Matrix multiplication. Contains a function that will let you print the calculation steps of matrix multiplication, e.g. in the Advice.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Adding matrices of random size: two to four rows and two to four columns. Advice (i.e. solution) has conditional visibility to show only the correct size.

Adding vectors of random size. Advice (i.e. solution) has conditional visibility to show only the correct size.