GCSE · Formulae & rearranging

Substituting into formulaeExam-style questions

Why substitution is "replace the letter, keep the structure", why negatives must go in with brackets, and why the order of operations still rules once the numbers are in.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$v^2 = u^2 + 2as$

(a) Work out the value of $v$ when $u = 3$ , $a = 4$ and $s = 5$ , given that $v > 0$ . (2 marks)

(b) Make $s$ the subject of the formula. (2 marks)
Level 3 · 4 marksTry it
2
This formula gives an estimate of the braking distance, $d$ metres, of a car travelling at $v$ km/h on a dry road.

$d = \frac{v^2}{160}$

Car $A$ is travelling at $40$ km/h when its driver brakes.

Car $B$ is travelling at $80$ km/h when its driver brakes.

How much longer is the braking distance of car $B$ than the braking distance of car $A$ ?

(2 marks)
Level 3 · 2 marksTry it
3
$v = u + at$

(a) Work out the value of $v$ when $u = -6$ , $a = 3$ and $t = 4$

(b) $P = 3q^2$

Work out the value of $P$ when $q = -5$
Level 3 · 3 marksTry it
4
$s = ut + \dfrac{1}{2}at^2$

Work out the value of $s$ when $u = 5$ , $a = -2$ and $t = 6$
Level 3 · 2 marksTry it
5
$E = \dfrac{1}{2}mv^2$

Work out the value of $E$ when $m = 8$ and $v = 5$ .
Level 3 · 2 marksTry it