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

Two part question, student has to rearrange the parallel resistors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the parallel inductors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the heat flow formula (stated in the question) to make T_1 or T_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Exercises for HELM Book 2.5.3.

Find the gradient and y-axis intercept of a line through 2 points. The line is not vertical.

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.

Find the gradient of a line through 2 given points. Part of HELM Book 2.5.2.

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

Exercises for HELM Book 2.5.1

Identify the gradient and y-axis intercept of a random non-vertical line.

Given one of ax+b, a/x, x^(1/a), a, is it a straight line.  a is a randomised integer.

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

Compare the gradients of 3 lines and choose the steepest. Part of HELM Book 2.5.1.

Find the gradients of 3 lines. Part of HELM Book 2.5.1.

Find the vertical intercept of 4 lines. Part of HELM book 2.5.1

Describe the effect of changing the value of a constant term in a linear function. Part of HELM Book 2.5.1.

Exercises for HELM Book 2.4.3

Identify whether a function is odd, even or neither from its graph. Part of HELM Book 2.4.3.

Given the period of a repeating function, determine the number of repeats in a given amount of time. Part of HELM Book 2.4.

Exercises for HELM Book 2.4.1

Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.

This question gives a text encrypted with an affine cipher and asks students to decrypt it.

This question asks students to decrypt a message using a simple Caesar cipher, without giving them the key.

Compute the inverse of a linear or hyperbolic function. Part of HELM book 2.3.

Find the inverse of a linear function. Part of HELM book 2.3.

Determine whether three graphs are functions or not. Part of HELM Book 2.3.

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.