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

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.

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

Simplifying an expression of the form $\frac{a^4b^3}{\sqrt{a^4b^2}}$ to $a^2b^2$, for integers $a$ and $b$.

Simplifying an expression of the form $a^3 \times (a^4)^{1/2}$ to $a^5$, where $a$ is an integer. 

Simplifying expressions from $\left(\frac{x^m}{x^n}\right)^p$ to $x^{(m-n)p}$.

Simplifying expressions from $(ax^n)^m$ to $a^mx^{mn}$, where $a$, $m$ and $n$ are positive integers.

Simplifying algebraic expressions

Simple exercise in collecting terms in different powers of \(x\)

Simple exercise in collecting terms in different powers of \(x\)

Simple exercise in collecting terms in different powers of \(x\)

Equivalent fractions, simplifying, adding, subtracting, multiplying and dividing fractions. Converting between mixed numbers and improper fractions.

Simple exercise in collecting terms in different powers of \(x\)

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Use a substitution to simplify an integral.

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Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression. The word problem is about the costs of sweets in a sweet shop. The quantity of each type of sweet is randomised.

This question was modified from a Newcastle University question.

No description given

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 fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

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.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

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