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

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

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

Given a graph, the student is asked to determine the quadratic function.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$.

Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

Integration by susbtitution, no hint given

Two players collide. Given the masses, final speeds and impulse imparted on each, find their initial speeds.

Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.

(Added to calculator test.)

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

Given an oracle function that will output its value given an input, and an interval within which a root exists, find the root to a given precision.

Makes use of a Geogebra applet.

Given the derivatives of a cubic function at a point, find the value of the function at another point.

Given the derivatives of a cubic function at a point, find the value of the function at another point.

Given the ratio of ingredients and the total amount of ingredients work out how much of one of the ingredients is needed.

Find angle and side in a right angled triangle.

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A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

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.

Added to calculator test.

Added advice on using decimals.

Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.

Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.

(Used in Non-Calculator test.)

Given the selling price of an item both as a cash amount and as a percentage of the cost of production, find the cost of production and the profit.

Based on question 1 from section 3 of the Maths-Aid workbook on numerical reasoning.

Added to Calculator test.

Given an annual salary, tax allowance, tax rate and pension deduction, work out a person's take-home pay per month.

Used in Calculator Test.

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

Implicit differentiation.

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

Find the magnitude of the momentum of some objects, given mass and speed. Apply the formula $\rho = mv$.

Students are given a graph of a cubic, and are asked to find the equation for it.

Students are given a graph of a cubic, and are asked to find the equation for it.

Given the derivatives of a cubic function at a point, find the value of the function at another point.

Reading information from the equation of the line. Graph shown

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