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Expressions and formulae

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Expressions and formulae

The big idea: A formula is a rule linking quantities. You can use it forwards (substitute), write it from a description (derive), or turn it round so a different letter is on its own (change the subject). Rearranging is solving an equation, done with letters.

Summary — What This Chapter Covers

A letter may stand for an unknown number or for a variable that changes.
Write algebra in the conventional way: 3x not x3, ab not a × b, x/2 for x ÷ 2.
Substitute integers, negatives, decimals and fractions, using brackets for negatives.
Turn words or diagrams into a formula, and derive formulae of your own.
Change the subject when it appears once; Higher: when it appears twice or as a power.

1. Letters and Conventions

Foundation & Higher

Writing algebra correctly

In x + 5 = 9, x is an unknown: it has one value. In P = 4s, P and s are variables: they change together. Standard conventions:

Write	Meaning	Not
3x	3 × x	x3
ab	a × b	a × b or ba (alphabetical is preferred)
x²	x × x	2x (that is x + x)
x/4	x ÷ 4	—
3(x + 1)	3 lots of (x + 1)	3x + 1

Practice Question 1

Write in conventional form: (a) y × 7 × x (b) a × a × 5 (c) (m + 2) ÷ 3

2. Substitution

Foundation & Higher

Negatives, decimals and fractions

Replace each letter by its value inside brackets, then follow the order of operations (powers before multiplication, multiplication before addition). Brackets stop sign errors: −5 squared is (−5)² = 25.

Worked Example

Evaluate 2x − 3y when x = 4 and y = −5.

Worked Example

Use s = ut + ½at² to find s when u = 12, t = 3 and a = −4.

Practice Question 2

v² = u² + 2as. Find v when u = 3.5, a = −9.8 and s = 0.5, given v > 0. Give your answer correct to 3 significant figures.

3. Writing and Deriving Formulae

Foundation & Higher

From words or a diagram to symbols

Pick a letter for each quantity, state what it means and its units, then translate the rule word by word. When deriving a formula from a diagram, write each length in terms of the letters given, then combine.

Worked Example

To cook a chicken, allow 40 minutes per kilogram plus an extra 20 minutes. Write a formula for the cooking time T minutes for a chicken of mass w kg, and find T for a 2.5 kg chicken.

Practice Question 3

A rectangle has length (2x + 3) cm and width x cm. Derive a formula for its perimeter P cm, in its simplest form.

Practice Question 4

A taxi charges a fixed $3 plus $1.50 per kilometre. Write a formula for the cost C dollars of a journey of d km, and find the cost of a 12 km journey.

4. Changing the Subject

Foundation & Higher

When the subject appears once

Treat the formula as an equation and undo the operations on the new subject in reverse order, doing the same to both sides. A square is undone by a square root; a root by squaring.

Worked Example

Make t the subject of v = u + at.

Worked Example

Make r the subject of A = πr². Hence find r when A = 50, correct to 3 significant figures.

Practice Question 5

Memorise

Can You…?

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Subject twice, or raised to a power

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Expressions and formulae

Expressions and formulae

Writing algebra correctly

Negatives, decimals and fractions

From words or a diagram to symbols

When the subject appears once

Past papers that test Expressions and formulae

More Mathematics A topics