This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. SP = Statistics & Probability strand. Students read the annual hours worked from the chart and calculate the weekly hours given the number of weeks annual leave. There are 7 different versions of this question.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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Looking at gradients and values for x and y for straight-line graphs

Solving pair of simultaneous (linear) equations

Find a regression equation.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Add, subtract, multiply and divide algebraic fractions.

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

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

Factorising basic quadratics into linear expressions

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Add, subtract, multiply and divide algebraic fractions.

Factorising further basic quadratics into linear expressions

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Horizontal and vertical shifts and scales of a random cubic spline

The student is shown a diagram with a line between two points. They must make the line cross the axes at $x=1$ and $y=2$. They can drag the points around, or type a gradient in to move the points accordingly.

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.