Introduces students to the floor and ceiling functions

This question summarizes the definitions of surjective and injective, and applies them to prove the existance of an inverse.

Students are given a line equation in the form y=mx+b and asked to graph it.

m and b are randomised.

The question is not auto-marked, students need to "reveal answers" to see a sample graph that they can compare to their own.

Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.

The line parameters and the given point are randomised.

Students are shown a graph and, in the context of a word problem, are asked to find the gradient and the y-intercept, to read points from the graph, and to identify the correct equation for the graph.

Students are given a line equation (where the coefficient of y is 1) and asked to rearrange it into gradient-intercept form.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.

Students need to substitute a value into an equation and solve it. The equation constant (gravity) and the value (time) are both randomised.

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Studnents are asked to write down equations for cost and income for a business.

They are then asked to graph the two lines.

Nursing question. Calculate drip rate in drops per minute if there are 20 drops per minute. Time given in minutes.

Nursing question. Calculate drip rate in drops per minute if there are 20 drops per minute. Time given in minutes.

Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.

They are asked to give the x- and y- coordinate values.

The graph is randomised, but it is set up so that the point of intersection lies on gridlines.

Sketch a function graph by using fist and second derivatives.

Slightly harder introductory exercises about the power set.

Converting between metres (m) and centimetres (cm). 

Round random numbers to the closest whole number, 1 to 3 decimals places. Also rounding that could show common misunderstandings.

Students are asked to draw a hyperbola from an equation by drawing a table of graphs and plotting them.

Students are asked to draw an exponential from an equation by drawing a table of graphs and plotting them.

Students are asked to draw a parabola from an equation by drawing a table of graphs and plotting them.

This is a very simple question with no randomisation.

Students are asked to identify an inverse relationship equation.

Students are given a formula and asked to evaluate it for a given input value, which is randomised.

Can you identify a parabola? Students are shown a parabola and asked to identify it as such.

Students are given the equation of a parabola and asked to identify its graph. They are given the parabolic curve, an exponential, a hyperbola and a line to choose from.

Given a parcel's width, height and length, calculate its volume and surface area. Additionally, classify its size based on a formula inspired by a real delivery company (as mad as it sounds!).

The student must give units with each measurement.

Substitute values into formulae for the area or volume of various geometric objects.