Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Two double integrals with numerical limits

Double integrals (2) with numerical limits

Dealing with functions in Numbas.

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

Solve a Differential equation with an irreducible quadratic factor 

Provided with information on a sample (>30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Warning: may take up to 60 seconds to load question!

Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is a simple question to ensure they understand the index can change without affecting the sum.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Some practice collecting like terms of algebraic expressions, with detailed advice.

Adapted from 'Collecting like terms' by Ben Brawn.