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2.7 Using Expressions and Formulae

GCSE Maths Foundation · Edexcel · Chapter 2: Expressions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: expressions, equations, formulae and identities, substituting into harder 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

  • Tell the difference between an expression, an equation, a formula and an identity
  • Substitute positive, negative and decimal values into formulae such as s = ut + ½at²
  • Rearrange a simple formula to change its subject
  • Form a formula from a context and use it to solve a problem

Key words

  • Identity: True for every value of the letters. The sign ≡ means “is identical to”.
  • Subject: The single letter on its own on one side of a formula.
  • Rearrange: Change a formula so that a different letter is the subject.
  • Inverse operation: The operation that undoes another: + and −, × and ÷, squaring and square rooting.

Expressions, equations, formulae and identities

  • Expression; Example 5x − 2; How to spot it no equals sign
  • Equation; Example 5x − 2 = 13; How to spot it true for one value only (x = 3)
  • Formula; Example A = lw; How to spot it links different quantities
  • Identity; Example 5(x − 2) ≡ 5x − 10; How to spot it true for every value of x

Worked example: identity or equation?

Is 2(x + 3) = 2x + 6 an identity?
Expand the left-hand side: 2x + 6. Both sides are the same for every x.

Answer: yes, 2(x + 3) ≡ 2x + 6

Substituting into harder formulae

These formulae for motion are given in the exam. Substitute carefully, use brackets for negatives and follow BIDMAS.

Formulae: v = u + at s = ut + ½at² v² = u² + 2as u = start speed, v = final speed, a = acceleration, t = time, s = distance

Worked example: distance

Find s when u = 3, a = 4 and t = 5.
s = 3 × 5 + ½ × 4 × 5² = 15 + ½ × 4 × 25 = 15 + 50 = 65

Answer: s = 65

Worked example: with a square root (calculator)

Find v when u = 4, a = 3 and s = 10, using v² = u² + 2as.
v² = 16 + 2 × 3 × 10 = 16 + 60 = 76
v = √76 = 8.717… = 8.72 (2 d.p.)

Answer: 8.72

Changing the subject

Think of the formula as a function machine. To make a different letter the subject, undo the steps in reverse order, doing the same thing to both sides.

Worked example: perimeter formula

Make l the subject of P = 2l + 2w, then find l when P = 30 and w = 6.
Subtract 2w: P − 2w = 2l. Divide by 2: l = (P − 2w)/2
l = (30 − 12)/2 = 18/2 = 9

Answer: l = (P − 2w)/2; l = 9

Forming and using formulae

Worked example: fencing a field

A field is w m wide and 3w m long. Write a formula for its perimeter P. A farmer has 200 m of fencing to go all the way round. How wide is the field?
P = 3w + w + 3w + w = 8w
8w = 200, so w = 200 ÷ 8 = 25

Answer: P = 8w; 25 m wide

Common mistakes

  • Squaring the whole term: in ½at² only t is squared. With a = 4, t = 5: ½ × 4 × 25 = 50, not ½ × (4 × 5)².
  • Undoing steps in the wrong order. For y = 4x − 7, add 7 first, then divide by 4.
  • Doing an inverse operation to only part of one side: from P = 2l + 2w, l is not P/2 − 2w.
  • Forgetting the square root at the end when the formula gives v².

Revision questions

Try these, then check your answers below each one.

Question 1. Use v = u + at to find v when u = 20, a = -4 and t = 3.

Answer: 8

Working: v = 20 + (-4)(3) = 20 - 12 = 8.

Question 2. Use s = ut + 1/2at² to find s when u = 0, a = 10 and t = 3.

Answer: 45

Working: s = 0 + 1/2 × 10 × 9 = 45.

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

Answer: x = (y - 5)/(3)

Working: y - 5 = 3x, so x = (y - 5)/(3).

Related lessons

Continue in the full course

This lesson is section 2.7 (EGCMF0207) 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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