TopMyGrade

GCSE/Mathematics/Edexcel

A2Substitute numerical values into formulae and expressions

Notes

Substitution

Substituting values into a formula is one of the most reliable mark-earners on Edexcel. Always:

  1. Write out the formula first (M1 mark for stating the correct formula).
  2. Replace each variable with its value in brackets.
  3. Apply BIDMAS carefully.
  4. Give your final answer in the units stated.

Worked exampleWorked example — speed

Formula: speed = distance ÷ time. distance = 240 km, time = 3 hours. speed = 240 ÷ 3 = 80 km/h.

Worked exampleWorked example — area of a trapezium

Formula: A = ½(a + b)h. a = 5 cm, b = 9 cm, h = 4 cm. A = ½ × (5 + 9) × 4 = ½ × 14 × 4 = 28 cm².

Substitution with negatives — danger zone

Always bracket negative substitutions. Formula: y = x² − 3x. At x = −2: y = (−2)² − 3(−2) = 4 + 6 = 10.

A common Edexcel error: writing −2² (which equals −4) instead of (−2)² (which equals 4). The brackets matter.

Substitution with fractions and decimals

Formula: A = πr². At r = 0.5: A = π × (0.5)² = π × 0.25 ≈ 0.785 m². At r = 1/3: A = π × (1/3)² = π/9.

Substitution into formulae from other subjects

Edexcel uses physics formulae (F = ma, P = IV) and statistics formulae (mean = Σfx/Σf) as substitution opportunities. Always state the formula even if it is given.

"Show that" questions (Higher)

Edexcel "show that" questions require all working. Substitute, simplify step by step, and reach the stated result. Skipping a step loses C1.

Example: Show that when x = 2 and y = −3, the value of 2x² + 3xy + y² is 8 − 18 + 9 = −1. Working: 2(2)² + 3(2)(−3) + (−3)² = 2(4) + 3(−6) + 9 = 8 − 18 + 9 = −1 ✓.

Common mistakes

  1. Misplaced negatives as above.
  2. Order of operations ignored: 3 + 2 × 5 = 13 (not 25).
  3. Powers and roots evaluated wrongly: 5² = 25, not 10.
  4. Units missing or incorrect in the final answer.

AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 16 marks

    Substitute into a linear and quadratic expression

    Edexcel Paper 1F (non-calculator)

    (a) Find the value of 5x − 3 when x = 4. (1 mark)
    (b) Find the value of x² + 2x when x = −5. (3 marks)
    (c) Find the value of 3a − 2b when a = 6 and b = −4. (2 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  2. Question 25 marks

    Substitute into the area formula of a trapezium

    Edexcel Paper 2F (calculator)

    The formula for the area of a trapezium is A = ½(a + b)h.

    (a) Find A when a = 7 cm, b = 11 cm, h = 5 cm. (2 marks)
    (b) Find A when a = 6.5 m, b = 9.3 m, h = 4 m. State units. (3 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  3. Question 33 marks

    Show that — substitution and simplification

    Edexcel Paper 1H — Higher

    Show that the expression 2x² − 3xy + 4y² evaluates to 39 when x = 3 and y = −2. (3 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Flashcards

A2 — Substitute numerical values into formulae and expressions

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves topic A2

7 cards · spaced repetition (SM-2)