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.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

rebelmaths

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

The student will be given 2 integers between -9 and +9 to add together.

Choosing whether given random variables are qualitative or quantitative.

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

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

Graphs are given and students are required to match them with their equation.

Three graphs are given with areas underneath them shaded. Student is asked to determine the minimum and maximum $x$-values of the regions. This will involve solving a linear equation and two trigonmetric equations.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

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

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

Several quadratics are given and students are asked to factorise them.

Given a table of data, complete a frequency distribution table and use it to calculate the mean, mode, median and range.

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

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.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determining the equation of the line.

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

Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

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

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

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.

35 simple subtraction questions are given with a 2 minute time limit.

Implicit differentiation.

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

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

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