GCSE Mathematics · Edexcel 1MA1 · Topic N.1

Structure and calculation

Key points

Order of operations (BIDMAS): brackets, indices, division/multiplication, addition/subtraction.
Prime factor decomposition: write a number as a product of primes, e.g. $60 = 2^2 \times 3 \times 5$ . Use it to find the HCF (shared primes, lowest powers) and LCM (all primes, highest powers).
Index laws: $a^m \times a^n = a^{m+n}$ , $a^m \div a^n = a^{m-n}$ , $(a^m)^n = a^{mn}$ , $a^{-n} = \frac{1}{a^n}$ , $a^{\frac{1}{n}} = \sqrt[n]{a}$ , $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$ .
Standard form: $A \times 10^n$ where $1 \le A < 10$ ; multiply by multiplying the numbers and adding the powers.
Surds (higher): $\sqrt{ab} = \sqrt{a}\sqrt{b}$ ; rationalise denominators, e.g. $\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ .
Product rule for counting: if there are $m$ ways to do one thing and $n$ ways to do another, there are $m \times n$ ways to do both.

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Structure and calculation is the toolkit every other topic leans on: ordering numbers, negatives, primes and factors, powers and roots, standard form and, at Higher tier, surds. Paper 1 has no calculator, so these methods must be quick and…

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