GCSE Mathematics · Edexcel 1MA1 · Topic A.1

Notation, vocabulary and manipulation

Key points

Simplify by collecting like terms: $3x + 2y - x = 2x + 2y$ .
Expand brackets: $3(x + 4) = 3x + 12$ ; double brackets: $(x + 2)(x - 5) = x^2 - 3x - 10$ .
Factorise by taking out common factors, e.g. $6x^2 + 9x = 3x(2x + 3)$ ; quadratics, e.g. $x^2 + 7x + 12 = (x + 3)(x + 4)$ ; difference of two squares $a^2 - b^2 = (a + b)(a - b)$ .
Rearrange formulae by doing the same to both sides, e.g. make $r$ the subject of $A = \pi r^2$ : $r = \sqrt{\frac{A}{\pi}}$ .
Substitute values carefully, using brackets for negative numbers.
An identity ( $\equiv$ ) is true for all values. Algebraic proof (higher): use $2n$ for even and $2n + 1$ for odd numbers.
Functions (higher): composite $fg(x)$ means do $g$ first; inverse $f^{-1}(x)$ undoes $f$ .

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This sub-topic is the grammar of algebra: writing expressions correctly, expanding, factorising, substituting and rearranging. At Higher tier it extends to algebraic fractions, proof and functions, and nearly every other algebra question…

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