GCSE Maths · Substitution and Formulae · Higher · Summary

GCSE Maths Substitution and Formulae (Higher): summary and key words

Part of the GCSE Maths substitution and formulae chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page

Chapter summary

Skill	Method
Vocabulary	Expression: no =. Equation: true for some values. Formula: a rule linking quantities. Identity (≡): true for all values. A term is one part of an expression.
Writing algebra from words	Choose a letter; “more than” is +, “less than” is − (start from the quantity), “times” is ×, “shared between” is ÷. Test with a number.
Substituting	Replace each letter with its number (put the × sign back, brackets round negatives), then use BIDMAS.
Negative numbers	Subtracting a negative = adding. Same signs multiply to give a positive. (−3)² = 9 but −3² = −9.
Using a formula	Write the formula, substitute, work out, write the answer with units. Keep units consistent. Round only at the end.
Writing a formula	Say what each letter stands for. Typical shape: total = fixed part + rate × amount. Test with a simple number.
Change the subject: one or two steps	Undo the operations in reverse order using inverse operations, doing the same to both sides each time.
Brackets, fractions, powers, roots	Divide to undo a bracket multiplier; multiply to undo a division; take the square root of the whole side to undo a square; square to undo a root.
Higher: subject appears twice	Clear fractions, expand brackets, collect subject terms on one side, factorise the subject out, divide by the bracket.
Checking	Test the formula or the rearranged formula with simple numbers. A rearrangement should take you back to where you started.

I can say whether something is an expression, an equation, a formula or an identity.
I can write an expression or a formula from words and from a diagram.
I can substitute positive and negative numbers into an expression, using BIDMAS.
I can use formulae from science and geometry and give answers with units.
I can write a formula for a real situation and test it.
I can change the subject of a formula in one or two steps.
I can change the subject when the formula has brackets, fractions, powers or roots.
Higher: I can change the subject when the subject appears twice, by factorising.
I can check a rearranged formula by substituting numbers.

Variable: A letter that stands for a number that can change.
Expression: Numbers and letters combined with operations, with no equals sign, such as 3n + 5.
Equation: Two expressions joined by an equals sign, true only for some values of the letter.
Formula: A rule, written with letters and an equals sign, that links quantities, such as A = lw.
Identity: An equation that is true for every value of the letters, written with ≡.
Term: One part of an expression, separated from the others by + or − signs.
Substitute: Replace a letter with its number value.
Subject: The letter on its own on one side of a formula.
Change the subject: Rearrange a formula so that a different letter is on its own.
Inverse operation: An operation that undoes another: adding and subtracting, multiplying and dividing, squaring and square rooting.
BIDMAS: The order of operations: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
Factorise: Write an expression as a product, for example xy − x = x(y − 1).