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5.6 Using Formulae

GCSE Maths Foundation · Edexcel · Chapter 5: Equations, Inequalities and Sequences

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: substituting into word and algebraic formulae, writing formulae and changing the subject. 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

  • Substitute numbers, including negatives and decimals, into a formula
  • Write a formula from a description in words
  • Change the subject of a simple formula
  • Use a formula backwards to find an unknown value

Key words

  • Formula: A rule connecting two or more quantities, e.g. P = 2l + 2w. Plural: formulae.
  • Substitute: Replace the letters with numbers.
  • Subject: The letter on its own on one side of a formula. In v = u + at the subject is v.
  • Rearrange: Change the subject of a formula using inverse operations.
  • Variable: A letter that can take different values.

Word formulae

A word formula uses words instead of letters. Put in the numbers and follow the order of operations (BIDMAS).

Worked example: cooking time

Time in minutes = 40 × mass in kg + 20. Find the time to cook a 3.5 kg joint of meat.
Time = 40 × 3.5 + 20 = 140 + 20 = 160 minutes
160 minutes = 2 hours 40 minutes

Answer: 2 hours 40 minutes

Substituting into algebraic formulae

Remember the hidden operations: at means a × t, and 3x² means 3 × x². Put negative numbers in brackets.

  • v = u + at; Values u = 4, a = 3, t = 6; Working 4 + 3 × 6 = 4 + 18; Answer v = 22
  • P = 2l + 2w; Values l = 7.5, w = 4; Working 2 × 7.5 + 2 × 4 = 15 + 8; Answer P = 23
  • A = bh/2; Values b = 9, h = 5; Working 9 × 5 ÷ 2 = 45 ÷ 2; Answer A = 22.5
  • F = 1.8C + 32; Values C = −10; Working 1.8 × (−10) + 32 = −18 + 32; Answer F = 14
  • y = x² + 5; Values x = −3; Working (−3)² + 5 = 9 + 5; Answer y = 14

Key fact: (−3)² = (−3) × (−3) = +9. A negative number squared is always positive.

Writing a formula

Worked example: from words

Concert tickets cost £8 each and there is a £3 booking fee for the whole order. Write a formula for the total cost £C of n tickets.
Cost of tickets = 8 × n = 8n. Add the booking fee once.

Answer: C = 8n + 3

Changing the subject

To make a different letter the subject, use inverse operations, just like solving an equation. Undo the operations in reverse order.

Worked example: one step

Make s the subject of P = 4s.
Divide both sides by 4.

Answer: s = P/4

Worked example: two steps

Make x the subject of y = 3x + 7.
Subtract 7: y − 7 = 3x
Divide by 3: x = (y − 7)/3

Answer: x = (y − 7)/3

Worked example: a physics formula

Make t the subject of v = u + at. Then find t when v = 30, u = 6 and a = 4.
Subtract u: v − u = at. Divide by a: t = (v − u)/a
t = (30 − 6)/4 = 24/4 = 6

Answer: t = (v − u)/a, t = 6

Worked example: undo a division

Make k the subject of M = k/4 + 3.
Subtract 3: M − 3 = k/4. Multiply by 4: k = 4(M − 3)

Answer: k = 4(M − 3)

Common mistakes

  • Writing at as 36 when a = 3 and t = 6. The letters are multiplied: at = 3 × 6 = 18.
  • Working out −3² as −9. With x = −3, x² = (−3)² = 9.
  • Ignoring BIDMAS: in 4 + 3 × 6, multiply first.
  • When rearranging, dividing only one term: from y − 7 = 3x, x = (y − 7)/3, not y − 7/3.

Revision questions

Try these, then check your answers below each one.

Question 1. v = u + at. Work out v when u = 3, a = 9.8 and t = 2.

Answer: 22.6

Working: v = 3 + 9.8 × 2 = 3 + 19.6 = 22.6

Question 2. Cooking time in minutes = 40 × mass in kg + 20. How many minutes does a 2.5 kg chicken need?

Answer: 120 minutes

Working: 40 × 2.5 + 20 = 100 + 20 = 120 minutes.

Question 3. Make x the subject of y = 5x - 2. (Choose from: x = (y + 2)/(5), x = y/5 + 2, x = (y - 2)/(5), x = 5y + 2.)

Answer: x = (y + 2)/(5)

Working: y + 2 = 5x, so x = (y + 2)/(5).

Related lessons

Continue in the full course

This lesson is section 5.6 (EGCMF0506) 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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