Maths Library

Substitution into Formulae: Year 8 maths

This topic covers substituting numerical values into algebraic expressions and formulae. Students practise applying order of operations (BIDMAS) to evaluate expressions with positive and negative numbers.

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What this covers

Substitution into Formulae is taught in Year 8 (age 13 to 14) as a main teaching focus. It sits in the Algebra strand.

Worked example

Find the value of 3a^2 - 2b when a = 4 and b = -5

  1. Calculate a^2: 4^2 = 16
  2. Multiply by 3: 3 x 16 = 48
  3. Calculate -2b: -2 x (-5) = +10
  4. Combine: 48 + 10 = 58

Answer: 58

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Single-variable linear expressions with positive integers, e.g. 3x + 2 with x = 4
  2. Two-variable linear expressions with positive integers, e.g. 2a + 5b
  3. Expressions containing negative substitution values, e.g. 4 - 3x with x = -2
  4. Expressions with powers and roots, e.g. 2x^2 - 3 with x = 3 or x = -3
  5. Complex formulae with fractions and brackets, or evaluating kinematic equations

Common mistakes

  • Squaring 3x by squaring 3 as well when written as 3x^2
  • Squaring a negative without brackets yielding a negative, e.g. (-3)^2 evaluated as -9

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M8A03 Solve two-step linear equations and check solutions through substitution.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Substitution into Formulae

Year 8 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Work out 5x2 − 7 when x = −1.
[3]
2.
Work out 9x2 − 3 when x = −1.
[3]
3.
Work out 2x2 − 1 when x = −1.
[3]
4.
Work out 4x2 − 6 when x = −1.
[3]
5.
Work out 5x2 − 1 when x = −5.
[3]
6.
Work out 7x2 − 8 when x = −2.
[3]

Answer key

  1. −2x2 = 1; 5 × 1 − 7 = -2
  2. 6x2 = 1; 9 × 1 − 3 = 6
  3. 1x2 = 1; 2 × 1 − 1 = 1
  4. −2x2 = 1; 4 × 1 − 6 = -2
  5. 124x2 = 25; 5 × 25 − 1 = 124
  6. 20x2 = 4; 7 × 4 − 8 = 20