Substitution
Substituting values into a formula is one of the most reliable mark-earners on Edexcel. Always:
- Write out the formula first (M1 mark for stating the correct formula).
- Replace each variable with its value in brackets.
- Apply BIDMAS carefully.
- Give your final answer in the units stated.
✦Worked example— Worked example — speed
Formula: speed = distance ÷ time. distance = 240 km, time = 3 hours. speed = 240 ÷ 3 = 80 km/h.
✦Worked example— Worked 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
- Misplaced negatives as above.
- Order of operations ignored: 3 + 2 × 5 = 13 (not 25).
- Powers and roots evaluated wrongly: 5² = 25, not 10.
- Units missing or incorrect in the final answer.
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