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.

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.

Some questions which use JSXGraph to create interactive graphics.

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.

No description given

No description given

No description given

No description given

No description given

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

No description given

No description given

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. 

Draw Shear and Bending Moment Diagrams for a simply supported beam with triangular loading

 Students must derive the shear and bending moment functions for beam loaded with a parabolic distributed load described with a loading function.  Diagrams are given, but the students must derive the equations by integration.

Draw Shear and Bending Moment Diagrams for a simply supported or overhanging beam loaded with one or two concentrated forces.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

The full list of questions to choose from to build a bespoke Skills Audit for Maths and Stats