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Student is asked whether a quadratic equation can be factorised. If they say "yes", they're asked to give the factorisation.

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Basic differentiation techniques, including evaluations, brackets/fractions, solving equation, and an application

To assess interpretation of a statistical software output and use corresponding equation to make prediction.

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Find a regression equation.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

Solve a system of linear equations using Gaussian elimination.

Shows how to define variables to stop degenerate examples.

Questions around quadratic equations over finite fields of the form $\mathbb F_p$, $p$ a prime number.

Straightforward solving linear equations question

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

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

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 negative gradient.

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An applied example of the use of two points on a graph to develop a straight line function, then use the t estimate and predict. MCQ's are also used to develop student understanding of the uses of gradient and intercepts as well as the limitations of prediction.

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.

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

Identifying y=mx+b given two points

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

rebelmaths

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.

Identifying y=mx+b given two points

Identifying y=mx+b given two points