GCSE Year 2 Scheme of Work - Higher

Parallel Line Angle Properties

Alternate angles are equal; corresponding angles are equal; allied (co-interior) angles sum to $180^\circ$.

Interior Angle Sum of a Polygon

The sum of interior angles in an $n$-sided polygon is given by $(n - 2) \times 180^\circ$.

Pythagoras' Theorem

In a right-angled triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

Primary Trigonometric Ratios

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, and $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$.

The Sine Rule

$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$

The Cosine Rule for Sides

$a^2 = b^2 + c^2 - 2bc \cos(A)$

Angle at Centre Theorem

The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.

Alternate Segment Theorem

The angle between a tangent and a chord equals the angle subtended by the chord in the alternate segment.

Compound Measures Formulas

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$, $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$, and $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$.

Magnitude of a Vector

For a vector $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$, the magnitude is $\|\mathbf{v}\| = \sqrt{x^2 + y^2}$.

Sector Formulas

$\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r$ and $\text{Sector Area} = \frac{\theta}{360^\circ} \times \pi r^2$.

Sphere Volume and Surface Area

$\text{Volume} = \frac{4}{3}\pi r^3$ and $\text{Surface Area} = 4\pi r^2$.

Parallel Line Angle Properties

Alternate angles are equal; corresponding angles are equal; allied (co-interior) angles sum to $180^\circ$.

Interior Angle Sum of a Polygon

The sum of interior angles in an $n$-sided polygon is given by $(n - 2) \times 180^\circ$.

Pythagoras' Theorem

In a right-angled triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

Primary Trigonometric Ratios

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, and $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$.

The Sine Rule

$$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$

The Cosine Rule for Sides

$$a^2 = b^2 + c^2 - 2bc \cos(A)$$

Angle at Centre Theorem

The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.

Alternate Segment Theorem

The angle between a tangent and a chord equals the angle subtended by the chord in the alternate segment.

Compound Measures Formulas

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$, $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$, and $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$.

Magnitude of a Vector

For a vector $\mathbf{v} = \begin{pmatrix} x \ y \end{pmatrix}$, the magnitude is $|\mathbf{v}| = \sqrt{x^2 + y^2}$.

Sector Formulas

$\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r$ and $\text{Sector Area} = \frac{\theta}{360^\circ} \times \pi r^2$.

Sphere Volume and Surface Area

$\text{Volume} = \frac{4}{3}\pi r^3$ and $\text{Surface Area} = 4\pi r^2$.