Given a graph of a circle, write down its equation.

Find the equation of a line through 2 points. The line is not vertical.

Find the equation of a line passing through two points in the form y=mx+b. The question is set up so that m and b will be integers.

State the general form of the equation of a straight line explaining the role of each of the terms in your answer.

Given parametric equations, graph the function and obtain an explicit equation. Part of HELM Book 2.2.2.

Use parametric equations to find x for a given value of y. Part of HELM Book 2.2.2.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

Reading gradient and intercept from y=mx+c.

Solve linear equations with unknowns on one. Including brackets and fractions.

Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Simultaneous equation problem as circuit analysis to find unknown voltages. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

 Question asks student to find zeros of a quadratic equation. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem. 

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem. 

Finding the stationary points of a cubic equation and determining their nature.

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. 

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

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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.

Find the missing whole number power in an equation.