Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Match the relevant graph (sin, cos, tan) with its equation. 

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Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

You can enter an equation in 2 or more variables and rearrange it in the following steps. Numbas checks that the lines of working are all equivalent to the original equation. 

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

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Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Recognising the equation of a semi-circle centred at the origin. Top, bottom, left and right.

Recognising the equation of a circle.

Identifying y=mx+b given two points

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

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Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a right hyperbola except this time the equation will be written like y=(ax+b)/(cx+d)