GCSE Mathematics₈₃₀₀

1. Students are expected to know the following formulae included in the subject content; they will not be given in the exam. Refer to the Subject content section to determine the tier at which these formulae could be used.

The quadratic formula

The solutions of ${\mathit{a}\mathit{x}}^{\mathsf{2}}\mathsf{+}{\mathit{b}\mathit{x}}^{}\mathsf{+}{\mathit{c}}^{}\mathsf{=}\mathsf{0}$ , where $\mathit{a}\mathsf{\ne }\mathsf{0}$

$\mathit{x}\mathsf{=}\frac{\mathsf{-}\mathit{b}\mathsf{\pm }\sqrt{{\mathsf{(}\mathit{b}}^{\mathsf{2}}\mathsf{-}\mathsf{4}\mathit{a}\mathit{c}\mathsf{)}}}{\mathsf{2}\mathit{a}}$

Circumference and area of a circle

Where $\mathit{r}$ is the radius and $\mathit{d}$ is the diameter:

Circumference of a circle = $\mathsf{2}\mathit{\pi }\mathit{r}$ = $\mathit{\pi }\mathit{d}$

Area of a circle = $\mathit{\pi }{\mathit{r}}^{\mathsf{2}}$

Pythagoras’ theorem

In any right-angled triangle where $\mathit{a}$ , $\mathit{b}$ and $\mathit{c}$ are lengths of the sides and $\mathit{c}$ is the hypotenuse:

${\mathit{a}}^{\mathsf{2}}\mathsf{+}{\mathit{b}}^{\mathsf{2}}\mathsf{=}{\mathit{c}}^{\mathsf{2}}$

Trigonometry formulae

In any right-angled triangle $\mathit{A}\mathit{B}\mathit{C}$ where $\mathit{a}$ , $\mathit{b}$ and $\mathit{c}$ are lengths of the sides and $\mathit{c}$ is the hypotenuse:

$\mathsf{sin}\mathit{A}\mathsf{=}\frac{\mathit{a}}{\mathit{c}}$ , $\mathsf{cos}\mathit{A}\mathsf{=}\frac{\mathit{b}}{\mathit{c}}$ , $\mathsf{tan}\mathit{A}\mathsf{=}\frac{\mathit{a}}{\mathit{b}}$

In any triangle $\mathit{A}\mathit{B}\mathit{C}$ where $\mathit{a}$ , $\mathit{b}$ and $\mathit{c}$ are lengths of the sides:

sine rule: $\frac{\mathit{a}}{\mathsf{sin}\mathit{A}}\mathsf{=}\frac{\mathit{b}}{\mathsf{sin}\mathit{B}}\mathsf{=}\frac{\mathit{c}}{\mathsf{sin}\mathit{C}}$

cosine rule: ${\mathit{a}}^{\mathsf{2}}\mathsf{=}{\mathit{b}}^{\mathsf{2}}\mathsf{+}{\mathit{c}}^{\mathsf{2}}\mathsf{-}\mathsf{2}\mathit{b}\mathit{c}\mathit{ }\mathsf{cos}\mathit{A}$

Area = $\frac{\mathsf{1}}{\mathsf{2}}\mathit{a}\mathit{b}\mathit{ }\mathsf{sin}\mathit{C}$

2. Students are expected to know the following formulae or be able to derive them; they will not be given in the exam. Refer to the Subject content section to determine the tier at which these formulae could be used.

Perimeter, area, surface area and volume formulae

Where $\mathit{a}$ and $\mathit{b}$ are the lengths of the parallel sides and $\mathit{h}$ is their perpendicular separation:

Area of a trapezium = $\frac{\mathsf{1}}{\mathsf{2}}\left(\mathit{a}\mathsf{+}\mathit{b}\right)\mathit{h}$

Volume of a prism = area of cross section x length

Compound interest

Where $\mathit{P}$ is the principal amount, $\mathit{r}$ is the interest rate over a given period and $\mathit{n}$ is number of times that the interest is compounded:

Total accrued = $\mathit{P}{\mathsf{(}\mathsf{1}\mathsf{+}\frac{\mathit{r}}{\mathsf{100}}\mathsf{)}}^{\mathit{n}}$

Probability

Where $\mathit{P}\mathsf{\left(}\mathit{A}\mathsf{\right)}$ is the probability of outcome $\mathit{A}$ and $\mathit{P}\mathsf{\left(}\mathit{B}\mathsf{\right)}$ is the probability of outcome $\mathit{B}$ :

$\mathit{P}\left(\mathit{A}\mathit{ }\mathsf{or}\mathit{ }\mathit{B}\right)\mathsf{=}\mathit{P}\left(\mathit{A}\right)\mathsf{+}\mathit{P}\left(\mathit{B}\right)\mathsf{-}\mathit{P}\mathsf{\left(}\mathit{A}\mathit{ }\mathsf{and}\mathit{ }\mathit{B}\mathsf{\right)}$

$\mathit{P}\left(\mathit{A}\mathit{ }\mathsf{and}\mathit{ }\mathit{B}\right)\mathsf{=}\mathit{P}\left(\mathit{A}\mathit{ }\mathsf{given}\mathit{ }\mathit{B}\right)\mathit{P}\left(\mathit{B}\right)$

3. Students are not expected to memorise the following formulae; they will be given in the exam in the relevant question. Refer to the Subject content section to determine the tier at which these formulae could be used.

Perimeter, area, surface area and volume formulae

Where $\mathit{r}$ is the radius of the sphere or cone, $\mathit{l}$ is the slant height of a cone and $\mathit{h}$ is the perpendicular height of a cone:

Curved surface area of a cone = $\mathit{\pi }\mathit{r}\mathit{l}$

Surface area of a sphere = $\mathsf{4}\mathit{\pi }{\mathit{r}}^{\mathsf{2}}$

Volume of a sphere = $\frac{\mathsf{4}}{\mathsf{3}}\mathit{\pi }{\mathit{r}}^{\mathsf{3}}$

Volume of a cone = $\frac{\mathsf{1}}{\mathsf{3}}\mathit{\pi }{\mathit{r}}^{\mathsf{2}}\mathit{h}$

Kinematics formulae

Where $\mathit{a}$ is constant acceleration, $\mathit{u}$ is initial velocity, $\mathit{v}$ is final velocity, $\mathit{s}$ is displacement from the position when $\mathit{t}\mathsf{=}\mathsf{0}$ and $\mathit{t}$ is time taken:

$\mathit{v}\mathsf{=}\mathit{u}\mathsf{+}\mathit{a}\mathit{t}$

$\mathit{s}\mathsf{=}\mathit{u}\mathit{t}\mathsf{+}\frac{\mathsf{1}}{\mathsf{2}}\mathit{a}{\mathit{t}}^{\mathsf{2}}$

${\mathit{v}}^{\mathsf{2}}\mathsf{=}{\mathit{u}}^{\mathsf{2}}\mathsf{+}\mathsf{2}\mathit{a}\mathit{s}$