IGCSE Maths Specification

Edexcel A 4MA1

Section 1.4: Powers and roots

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#1.4A

identify square numbers and cube numbers

#1.4B

calculate squares, square roots, cubes and cube roots

#1.4C

use index notation and index laws for multiplication and division of positive and negative integer powers including zero

#1.4D

express integers as a product of powers of prime factors

\(720 = 2^4 × 3^2 × 5\)

#1.4E

find highest common factors (HCF) and lowest common multiples (LCM)

#1.4F

understand the meaning of surds

Simplify: \(\sqrt{8} + 3\sqrt{32}\)

#1.4G

manipulate surds, including rationalising a denominator

Express in the form \(a + b\sqrt{2}\): \((3 + 5\sqrt{2})^2\)

Rationalise: \(\dfrac{2}{\sqrt{8}}; \quad \dfrac{1}{2-\sqrt{3}}\)

#1.4H

use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

Evaluate: \(\sqrt[3]{8^2}, \quad 625^{-\frac{1}{2}}, \quad \Big(\dfrac{1}{25}\Big)^{\frac{3}{2}}\)