Given mass and volume of an object in SI units, calculate its density. The units are given at different orders of magnitude.

Given $m \in \mathbb{N}$, find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$.

There are at most two such solutions in this question.

This question involves matching images of graphings to descriptions of the relationships between variables.

Find the dot product and the angle between two vectors

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Calculating particular harmonic components of a Fourier series expansion.

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This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Drag a point into the specified quadrant. Uses jsxgraph

Couting application where repitition is allowed and order does not matter.

Applicaiton of the pigeonhole principle

Definition of the pigeonhole principle, and some examples

Simple counting exercise. Students are encouraged to look for the smart way of counting.

Intorduces strong induction and uses it to verify the solutions of a second order linear recurrence.

Intorduction to using the defnition to prove simple stamtements.

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aij  notation and definition of the order of a matrix.

Differentiation question with customised feedback to catch some common errors and corresponding partial marks.

malrules

Simple ratio question with custom marking and partial credit possible

The marking checks for some common errors and awards partial credit and appropriate feedback. The errors that give different levels of partial credit include: forgetting to add one to the denominator, forgetting to change to a percentage.

LSD and Tukey yardsticks on three treatments. Also one-way Anova test on same set of data.

Kruskal-Wallis test with ties.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

LSD and Tukey yardsticks on five treatments. Also two-way Anova test on same set of data.

Spearman rank correlation calculated. 8 paired observations.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Practical questions