Add, subtract, multiply and divide algebraic fractions.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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.

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Using differentiation to find the tangent and normal to a line at a given point

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

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

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".

To understand matrix multiplication in terms of linear combinations of column vectors.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

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This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

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