Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Apply and combine logarithm laws in a given equation to find the value of $x$.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Rolling a pair of dice. Find probability that at least one die shows a given number.

Update: you can now use the conditional visibility button to do this more easily - see the documentation.

If the statement or advice for your question differs greatly depending on a random variable (for instance, if you're picking from a selection of scenarios), you only want to show content for the relevant scenario.

This question shows one way of doing that.

Template question. Seven statements given and student should determine if they are true or false.  It is possible that 1,2,3,4,5 or 6 out of the 7 statements will be true and these are all equally likely.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Compute the standard error of a sample mean, given the sample size and standard deviation.

Using differentiation to find the tangent and normal to a line at a given point

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Calculate the annual interest rate for a savings account where A, P and n are given.

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