Substitution into formulae

Substitution is one of the highest-yield, lowest-effort topics on OCR J560. Every paper has at least one substitution question, and the marks are essentially "do you understand BIDMAS and brackets".

The basic process

1. Replace each letter with the given value, using brackets around negatives and fractions.
2. Apply BIDMAS to evaluate.

Substituting into physics-style formulae

OCR maths questions often borrow from science contexts.

Example: kinetic energy E = ½mv². Find E when m = 0.5 kg and v = 4 m/s.

• E = ½ × 0.5 × 4² = 0.5 × 0.5 × 16 = 4 J.

Example: Pythagoras, c² = a² + b². Find c when a = 5, b = 12.

• c² = 25 + 144 = 169, so c = 13.

Formulae with brackets

Watch for compound expressions. Use brackets liberally when substituting.

Example: P = 2(l + w). Find P when l = 7.5, w = 3.

• P = 2 × (7.5 + 3) = 2 × 10.5 = 21.

If you write "2 × 7.5 + 3", BIDMAS gives 18 — wrong.

Negative number traps

• (−2)² = +4 (negative × negative).
• −2² = −4 (no brackets, so squaring binds tighter).
• (−2)³ = −8 (odd power keeps the sign).

Calculator skills

For Higher-tier formulas like the quadratic formula or trigonometry, use brackets carefully on the calculator:

• Type the whole numerator inside brackets.
• Type the whole denominator inside brackets.
• Use the calculator's fraction key when available.

OCR mark scheme conventions

• M1 for correct substitution (every value placed in correct slot).
• A1 cao for the final correct numerical answer.
• B1 sometimes for partial credit if BIDMAS error gives the wrong number but substitution is correct.