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.