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.

Expanding two linear brackets multiplied together.

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.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

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

Given a point and a line, determine the distance between them.

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.

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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.

This exercise will help you rearrange a linear equation to find the value of a given variable

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.

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

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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.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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.