Solve linear equations with one unknown. Including brackets and fractions.

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Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

A demonstration of embedding various kinds of media in a question.

Rounding integers and decimals to a specific number of sig figs.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Solving inequalities that involve a quadratic and where the right-hand side is 0.

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Solving inequalities that involve a quadratic and where the right-hand side is not 0. 

Randomly chooses one of the following

a) Divide numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Divide a negative whole number by a fraction. Simplifying is discussed in the advice but not required to get full marks.

Randomly chooses one of the following

a) Multiply numerical fractions. Simplifying is discussed in the advice but not required to get full marks.

b) Multiply a negative fraction by a whole number. Simplifying is discussed in the advice but not required to get full marks.

Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

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Find the remainder when dividing two polynomials, by algebraic long division.

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Manipulation of algebraic fractions

(a) Equation given, and five coordinates. Student should select those coordinates which lie on the line. (b) Gradient and a point on line is given. Student is to calculate coordinates of other points on the line.

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.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

The table uses the spreadsheet extension.

Draw shear and bending moment diagram for  beam with a uniformly distributed load and a concentrated force

Use this as a template to create Shear and Bending Moment diagram problems.   Supports concentrated forces and moments, uniformly distributed loads, and uniformly varying loads.

Draw shear and bending moment diagram for a symmetrically loaded beam resting on the ground.

Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction.