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

Graph a linear or quadratic function and state its domain and range. Part of HELM Book 2.2.1.

Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value

Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)

Reading gradient and intercept from y=mx+c.

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.

Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.

Plot the Fourier series coefficients for a piece-wise linear function.  Write a Python script to reproduce the same figure.

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

Evaluate a linear function at 3 numerical inputs.

Evaluate a given, randomised, linear function at a given, randomised, value.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

evaluate the function y=ax+b for given values of a,b and x, each of which may be positive or negative.

Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

The statement contains two blank geogebra applets: one with the computer algebra view, which can be used as a calculator, and the other with algebra and geometry views.

There are custom functions which set the perspective of a geogebra applet and show the toolbar or algebra input line. These will probably be included in the geogebra extension eventually.

The statement contains two blank geogebra applets: one with the computer algebra view, which can be used as a calculator, and the other with algebra and geometry views.

There are custom functions which set the perspective of a geogebra applet and show the toolbar or algebra input line. These will probably be included in the geogebra extension eventually.

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

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In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Solving a pair of linear simultaneous equations with integer solutions.

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

Tests the ability to find the gradient and intercept of a straight line graph.

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.