GCSE Maths OCR J560

Formulate simple formulae and expressions from real-world contexts.

e.g. Cost of car hire at £50 per day plus 10p per mile. The perimeter of a rectangle when the length is 2 cm more than the width.

See, for example, Direct proportion, 5.02a, Inverse proportion, 5.02b, Growth and decay, 5.03a

Substitute positive numbers into simple expressions and formulae to find the value of the subject.

e.g. Given that $v = u + at$, find $v$ when $t = 1$, $a = 2$ and $u = 7$

Subsitute positive or negative numbers into more complex formulae, including powers, roots and algebraic fractions.

e.g. $v = \sqrt{u^2 + 2as}$ with $u = 2.1$, $s = 0.18$, $a = -9.8$.

Rearrange formulae to change the subject, where the subject appears once only.

e.g. Make $d$ the subject of the formula $c = \pi d$.

Make $x$ the subject of the formula $y = 3x-2$.

Rearrange formulae to change the subject, including cases where the subject appears twice, or where a power or reciprocal of the subject appears.

e.g. Make $t$ the subject of the formulae

(i)$s = \dfrac{1}{2}at^2$

(ii) $v = \dfrac{x}{t}$

(iii) $2ty = t+1$

Examples may include manipulation of algebraic fractions, 6.01g

Recall and use:

Circumference of a circle $2 \pi r = \pi d$

Area of a circle $\pi r^2$

Recall and use:

Pythagoras’ theorem $a^2 + b^2 = c^2$

Trigonometry formulae $\sin{\theta} = \dfrac{o}{h}$, $\cos{\theta} = \dfrac{a}{h}$, $\tan{\theta} = \dfrac{o}{a}$

**Recall and use:

The quadratic formula $x = \dfrac{−b±\sqrt{b^2−4ac}}{2a}$

Sine rule $\dfrac{a}{\sin{A}} = \dfrac{b}{\sin{B}} = \dfrac{c}{\sin{C}}$

Cosine rule $a^2 = b^2 + c^2 - 2bc\cos{A}$

Area of a triangle $\dfrac{1}{2}ab\sin{C}$**

Use:

$v = u + at$

$s = ut + \frac{1}{2}at^2$

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

where $a$ is constant acceleration, $u$ is initial velocity, $v$ is final velocity, $s$ is displacement from position when $t = 0$ and $t$ is time taken.