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Formulae and changing the subject
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Formulae are used everywhere in science and everyday life. Rearranging them lets you find whichever quantity you need.
Substituting into formulae
Replace each letter with its value and follow the order of operations.
v = u + at with u = 5, a = 2, t = 6: v = 5 + 2 × 6 = 17.
F = ma: force = mass × acceleration.
v = u + at with u = 5, a = 2, t = 6: v = 5 + 2 × 6 = 17.
F = ma: force = mass × acceleration.
Changing the subject
The subject is the letter on its own. To change it, undo operations in reverse order, doing the same to both sides.
y = 4x + 3 → y − 3 = 4x → x = (y − 3)4
C = 2πr → r = C2π
y = 4x + 3 → y − 3 = 4x → x = (y − 3)4
C = 2πr → r = C2π
Rearrange, then substitute
A = 12bh. Find h when A = 24 and b = 8.
Rearrange: h = 2Ab = 488 = 6.
Or substitute first and solve the equation: 24 = 4h, so h = 6.
Rearrange: h = 2Ab = 488 = 6.
Or substitute first and solve the equation: 24 = 4h, so h = 6.
Use C = 5(F − 32)9 to change 68 °F into °C.
- F − 32 = 36
- 5 × 36 = 180
- 180 ÷ 9 = 20
Answer: 20 °C
Substitute carefully using the order of operations. To change the subject, undo the operations around the letter in reverse order, doing the same to both sides.
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