Students are shown a line graph and asked to write the line equation.

The line is drawn in geogebra. m and b are randomised. 

The line equation is given as a fill-in-the-gaps, y = <gap>x + <gap>

Students are shown a graph of the value of a machine over time. The line equation is randomised.

They are asked to evaluate value at a given time, and the time at which a given value is reached. They are asked when the machine has no value, and the range of times over which the model is valid. They are also asked to explain the physical meaning of the gradient.

Students are given the equations of two lines in the form y=mx+b and asked if they are parallel.

The line equations are randomised.

The answer is yes or no. There is a 1 in 6 chance of the lines being parallel.

Students are given a parabola equation and 4 points. They need to determine which point lies on the parabola.

Students are given an exponential equation and asked to identify the y-intercept from a list of choices.

The constants in the exponential equation have been randomised.

Students are shown an exponential graph and asked to identify the equation from a selection of 4.

Students are shown an exponential graph and asked to identify its equation from 4 choices.

The graph is randomised.

Students are given a hyperbolic graph and asked to select the correct equation from 4 choices.

Student is shown a graph with a parabola and asked to identify the correct equation. Multiple choice question.

Students are shown a parabola and asked to identify its graph from a selection of choices.

Students are shown a hyperbola and asked to identify its equation from 4 choices.

Students are given 4 parabola equations and their respective graphs and asked to match them.

Students are given equations for a line, a parabola, a hyperbola and an exponential, and their respective graphs and are asked to match them.

Students are given 4 equations for hyperbolas and 4 graphs and asked to match them.

Students are shown a hyperbola and asked to identify it as such.

Students are given the equation of a hyperbola and asked to identify the hyperbolic graph out of a set of 4 graphs.

The student is shown an exponential graph and asked to evaluate the function at some given value.

They are also asked whether or not the model is valid for all real inputs, but they only give a yes/no response. The reasoning is explained in the advice but is not required from students.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Students are shown an exponential curve and asked to identify it as either linear, parabolic, hyperbolic or exponential.

Students are shown an exponential function formula and asked to identify the correct graph, given an exponential, a hyperbola, a parabola and a line.

Students are shown an exponential graph and asked to choose the correct formula for the graph.

Shows an exponential graph displaying the value of an investment under compound interest. Students have to identify the type of graph and answer 3 questions about the value of the investment from the graph.

Data from a compound interest are shown in a table. Students are asked to compute the value of an investment, and to identify the type of graph.

Students are given a formula for compound interest and asked to evaluate it for given initial investment values.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

Filling in the table of powers of ten.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

A question to practise the following skills in the context of Earth Sciences:

• using a data set to deduce a linear relationship
• using the graph to make predictions