Sheet № 194 · Foundation + Higher · AQA · Edexcel · OCR
Substitution into Expressions –
Substitution into expressions is a core algebra skill that appears on almost every GCSE Maths paper. You replace letters with given numbers, then use BIDMAS to evaluate the result accurately.
§Key definitions
Question:
Find the value of 3x + 2y when x = 4 and y = -1.
Answer:
S = 245.0 (1 d.p.)
Q1 (Foundation):
Find the value of 5a - 2b when a = 3 and b = 4.
Q2 (Foundation):
Find the value of x² + 3x when x = -2.
Q3 (Higher):
Given that p = 4, q = -3 and r = 0.5, find the value of pq² - 2r.
§Formulas to memorise
Replace every occurrence of the variable with the given value, using brackets around negative numbers
Follow BIDMAS order when evaluating: Brackets → Indices → Division/Multiplication → Addition/Subtraction
Worked example
Find the value of 3x + 2y when x = 4 and y = -1.
Working:
⚠ Common mistakes
- ✗Confusing -x² and (-x)². If x = 3, then -x² = -(3²) = -9, but (-x)² = (-3)² = 9. Always check where the negative sign sits.
- ✗Ignoring BIDMAS after substitution. Students sometimes evaluate left to right instead of respecting the order of operations, especially with mixed addition and multiplication.
- ✗Forgetting that 2x means 2 × x. When x = 5, the expression 2x = 10, not 25. The multiplication sign is implied.
✦ Exam tips
- →Write out every substitution step — do not try to do it in your head for multi-term expressions.
- →Use brackets around negative numbers every time to avoid sign slips.
- →If the question says "give your answer to" a certain accuracy, you must round at the end, not during the calculation.