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

Inputting ratios of algebraic expressions.

Expressions of the form (ax+b)(cx+d) are to be multiplied out and simplified.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Examples of the following custom part types: Yes/no, List of numbers, Give a numerical input for an expression, Number entry modulo.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Simplify logarithmic expressions using rules on logarithms.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

More work on differentiation with fractional coefficients.

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})$.

A basic introduction to differentiation

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

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

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

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 $\neg q \to \neg p$.

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 $\neg q \to \neg p$.

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 $\neg q \to \neg p$.

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 $\neg q \to \neg p$.

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 $\neg q \to \neg p$.

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

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

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

Multiplication and addition of complex numbers. Four parts.

Factorising algebraic expressions

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Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

One question on determining whether statements are propositions.

Four questions on find truth tables for various logical expressions.