Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\cos(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\cos(\theta)-B\sin(\theta)$ to $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\sin(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Simplifying the trigonometric expression $\frac{\sin^2(x)}{1\pm \cos(x)}$ using the trigonometric identity $\sin^2(x)+\cos^2(x)=1$.

Rewriting expressions of the form $n \log(a)\pm m \log(b) \pm p \log(c)$ as a single logarithm.

Rewriting expressions of the form $\log(a)\pm \log(b)$ as a single logarithm.

Rewriting $\log_{10}\left(\frac{\sqrt{x}}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Rewriting $\log_{10}(\sqrt{x})$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Rewriting $\log_{10}\left(\frac{x}{y}\right)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$, $x$ and $y$ are given.

Create a truth table with 3 logic variables to see if two logic expressions are equivalent.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Part (a): Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, give an expression for the function $f(x)$, where $f(x)=g(x)-2h(x)$. 

Part (b): Solve $f(x)=0$.

Given a cubic expression and a linear factor, calculate the remaining quadratic factor.

Calculating two unknown coefficients of a cubic expression when given two of the expression's linear factors.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

This question shows how to use the JSXGraph extension to show the student a plot of a function that they enter.

In the first part, the student enters an expression for $f(x)$. Once they've done that, they can reveal a plot of the function.

No description given

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Dividing Cubic expressions to find the quotient

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

What is the value of the expression given a choice of n?

Dealing with expressions in online tests and in Matlab.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.