What this covers
Substitution into Formulae is taught in Year 7 (age 11 to 12, KS3) 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
- Calculate a^2: 4^2 = 16
- Multiply by 3: 3 x 16 = 48
- Calculate -2b: -2 x (-5) = +10
- Combine: 48 + 10 = 58
Answer: 58
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Single-variable linear expressions with positive integers, e.g. 3x + 2 with x = 4
- Two-variable linear expressions with positive integers, e.g. 2a + 5b
- Expressions containing negative substitution values, e.g. 4 - 3x with x = -2
- Expressions with powers and roots, e.g. 2x^2 - 3 with x = 3 or x = -3
- 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 National Curriculum for England. Check wording and codes against the official document.
- Substitute numerical values into formulae and expressions, including those with negative numbers.