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

Straightforward solving linear equations question.

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

Finding the numerators & denominators of 4 equivalent fractions.

Some custom CSS restyles the matrix input so it looks like a fraction, with input boxes on top and bottom.

Ideally, there should be a fraction input part type, or an option for the number entry part to display a fraction input.

Selection of Quadratic Equations to Solve

Selection of Quadratic Equations to Solve

Solve $\displaystyle{ax ^ 2 + bx + c=0}$ by factorisation. 

This question provides practice at differentiating polynomials.

More work on differentiation with trigonometric functions

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Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question

A simultaneous equations question with integers only

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

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

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

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Using the chain rule within product rule problems.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

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

These 5 questions will introduce the student to the Numbas system-

1. Input 1          

2. Input 2

3. Input 3

4. Input 4     

5. Input 5                                           

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

SIngle long division

Finding surface area and volume; formulae not given.

Shows how to enter a logarithm to an arbitrary base, in a mathematical expression part.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

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Shows how to define variables to stop degenerate examples.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.