Pearson Edexcel GCSE (9-1) Mathematics study guide
Structure and calculation Study Guide
Review study guide for Structure and calculation in Edexcel Mathematics.
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Structure and calculation
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Positive powers and roots
A positive integer power means multiplying a number by itself a whole-number amount of times: for example, 4^3 = 4 × 4 × 4 = 64. Roots reverse powers: √64 = 8 because 8^2 = 64, while ∛125 = 5 because 5^3 = 125. Higher roots work in the same
A positive integer power means multiplying a number by itself a whole-number amount of times: for example, 4^3 = 4 × 4 × 4 = 64. Roots reverse powers: √64 = 8 because 8^2 = 64, while ∛125 = 5 because 5^3 = 125. Higher roots work in the same way, so the fourth root of 81 is 3 because 3^4 = 81. Recognising common powers helps you calculate efficiently and check answers.
Primes, factors and multiples
A prime number has exactly two positive factors: 1 and itself. A factor divides a number exactly, while a multiple is obtained by multiplying a number by an integer. Prime factorisation writes a number as a product of primes, using index no
A prime number has exactly two positive factors: 1 and itself. A factor divides a number exactly, while a multiple is obtained by multiplying a number by an integer. Prime factorisation writes a number as a product of primes, using index notation where useful, such as 360 = 2^3 × 3^2 × 5. The uniqueness of factorisation means that every integer greater than 1 has one prime factorisation, apart from the order of its factors. The HCF uses the common prime factors with the smaller powers, while the LCM uses every prime factor needed with the larger powers.
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