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2.4 Formulae

GCSE Maths Foundation · Edexcel · Chapter 2: Expressions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: word formulae, writing formulae from contexts, and using formulae including the volume of a cylinder. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Use formulae written in words
  • Write a formula using letters from a description
  • Substitute values into formulae, including area formulae
  • Use the formula V = πr²h for the volume of a cylinder

Key words

  • Formula: A rule that shows how one quantity is found from others, e.g. A = lw. The plural is formulae.
  • Subject: The letter on its own on one side. In A = lw, A is the subject.
  • Variable: A letter in a formula that can take different values.
  • Capacity: How much a container holds. 1 cm³ = 1 ml and 1000 cm³ = 1 litre.

Word formulae

A word formula tells you how to work something out in everyday words.

Worked example: pay

Pay = hourly rate × hours worked. Lena earns £11.40 an hour and works 8 hours. How much is she paid?
Pay = 11.40 × 8 = £91.20

Answer: £91.20

Worked example: working backwards

Using the same formula, Omar is paid £68.40 at £11.40 an hour. How many hours did he work?
Hours = pay ÷ rate = 68.40 ÷ 11.40 = 6

Answer: 6 hours

Writing formulae

Choose a letter for each quantity. Write the subject, then =, then the rule. A fixed charge is added once; a charge “per” item is multiplied by the number of items.

Worked example: tickets

Concert tickets cost £9 each plus a £3 booking fee per order. Write a formula for the total cost £T of n tickets.
n tickets cost 9n, then add 3 once.

Answer: T = 9n + 3

Worked example: taxi

A taxi charges £2.50 plus £1.60 per mile. Write a formula for the cost C pounds for m miles, then find the cost of 5 miles.
C = 2.5 + 1.6m. C = 2.5 + 1.6 × 5 = 2.5 + 8 = 10.5

Answer: C = 2.5 + 1.6m; £10.50

Units: Check that units match. If one price is in pence and another in pounds, change them to the same unit first.

Using area formulae

  • Rectangle; Formula Area A = lw, perimeter P = 2l + 2w
  • Triangle; Formula A = ½bh
  • Square; Formula A = s², P = 4s

Worked example: triangle

Use A = ½bh with b = 9 and h = 6.
A = ½ × 9 × 6 = ½ × 54 = 27

Answer: 27 cm²

Volume of a cylinder

A cylinder has the same circle all the way up. Its volume is the area of the circle times the height.

Formula: V = πr²h, where r is the radius and h is the height. Square the radius first, then multiply by π and by h.

Worked example: a can (calculator)

V = π × 4² × 11 = π × 16 × 11 = 176π
= 552.92… cm³ = 552.9 cm³ (1 d.p.)
The can holds about 553 ml.

Answer: 552.9 cm³

Common mistakes

  • Multiplying the fixed charge by the number of items: £9 per ticket plus £3 per order is 9n + 3, not 3n + 9 or 12n.
  • Using the slanted side of a triangle instead of the height measured at right angles to the base.
  • Working out (π × 4)² instead of π × 4². Only the radius is squared.
  • Using the diameter instead of the radius in V = πr²h. Halve the diameter first.

Revision questions

Try these, then check your answers below each one.

Question 1. Use the word formula: pay = hours worked × hourly rate. Mia works 7 hours at £10.80 per hour. How much is she paid, in £?

Answer: 75.6

Working: 7 × 10.80 = £75.60.

Question 2. Stamps cost 85p each and an envelope costs 40p. Which formula gives the total cost C, in pence, of one envelope and n stamps? (Choose from: C = 85n + 40, C = 40n + 85, C = 125n, C = 85 + 40n.)

Answer: C = 85n + 40

Working: n stamps cost 85n pence. Add 40p for the envelope: C = 85n + 40.

Question 3. Use A = 1/2bh to find the area of a triangle with base b = 12 cm and height h = 7 cm.

Answer: 42 cm²

Working: 1/2 × 12 × 7 = 42 cm².

Related lessons

Continue in the full course

This lesson is section 2.4 (EGCMF0204) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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