Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised and can be positive or negative numbers.

Part of HELM Book 1.2

Simplify n1.v^k1.(n2.v^k2), where n1, n2 are positive integers, v is a random letter variable, and k1 and k2 are nonzero integers.

The answer should be expressed as n.v^k

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

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.

No description given

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 $q$.

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).

No description given