Math

Addition and subtraction

Inverse operations.

Multiplication and division

Inverse operations.

Expand brackets

Multiply the term outside by every term inside: $a(b+c)=ab+ac$.

Collect like terms

Combine terms with the same variables and powers: $2a+3a=5a$.

Substitution

Replace letters with their given values.

Check an equation solution

Substitute your answer into the original equation.

Square root

The number that multiplies by itself to give the original number.

Diameter formula

$$d=2r$$

Radius formula

$$r=\frac{d}{2}$$

Circumference using diameter

$$C=\pi d$$

Circumference using radius

$$C=2\pi r$$

Area of a circle

$$A=\pi r^2$$

Area of a semicircle

$$A=\frac{1}{2}\pi r^2$$

Area of a quarter circle

$$A=\frac{1}{4}\pi r^2$$

Area of a sector

$$A=\frac{\theta}{360}\times\pi r^2$$

Arc length

$$L=\frac{\theta}{360}\times2\pi r$$

Area of a rectangle

$$A=l\times w$$

Area of a parallelogram

$$A=b\times h$$

Area of a triangle

$$A=\frac{1}{2}\times b\times h$$

Area of a trapezium

$$A=\frac{1}{2}(a+b)\times h$$

Area of a square

$$A=s^2$$

Radius symbol

$$r$$

Diameter symbol

$$d$$

Circumference symbol

$$C$$

Area symbol

$$A$$

Sector angle symbol

$$\theta$$

Centre of a circle

The middle point of the circle.

Radius

A line from the centre to the circumference.

Diameter

A line across the circle through the centre; twice the radius.

Circumference

The distance all the way around a circle.

Chord

A line segment joining two points on a circle.

Arc

A part of the circumference.

Sector

The region between two radii and the arc between them.

Segment

The region between a chord and its arc.

Tangent

A straight line that touches a circle at exactly one point.

Point of tangency

The point where a tangent touches a circle.

Secant

A straight line that intersects a circle at two points.

Semicircle

Half a circle, formed by a diameter.

Quadrant

One quarter of a circle; $90^\circ$ of $360^\circ$.

Perimeter of a semicircle

$$\pi r+2r$$

Perimeter of a quarter circle

$$\frac{\pi r}{2}+2r$$

Composite shape

A shape made from two or more simpler shapes, or one with a section removed.

Area of joined shapes

Find each area and add them together.

Area with a cut-out

Find the total area, then subtract the missing section.

Shaded area

Find the whole area, then subtract or add the relevant sections.

Perimeter of a composite shape

Add the lengths of the outside edges only.

Missing side length

Use the total length minus the known lengths.

Curved perimeter

Add the straight edges and the relevant arc lengths.

Area units

Square units, such as $\text{cm}^2$ or $\text{m}^2$.

Perimeter units

Normal length units, such as cm or m.

Point

An exact position, labelled with a capital letter.

Line

Extends infinitely in both directions.

Line segment

A part of a line with two endpoints.

Ray

Has one endpoint and extends infinitely in one direction.

Angle

Formed by two rays that share an endpoint.

Vertex

The point where the arms of an angle meet.

Parallel lines

Lines in the same plane that never meet.

Perpendicular lines

Lines that intersect at $90^\circ$.

Transversal

A line that crosses two or more other lines.

Bisect

Divide something into two equal parts.

Midpoint

The point halfway along a line segment.

Diagonal

A line segment joining non-adjacent vertices of a polygon.

Polygon

A closed 2D shape made from straight sides.

Adjacent angles

Angles sharing a vertex and a common arm.

Angle notation

In $\angle ABC$, B is the vertex.

Acute angle

An angle less than $90^\circ$.

Right angle

An angle exactly equal to $90^\circ$.

Obtuse angle

An angle greater than $90^\circ$ but less than $180^\circ$.

Straight angle

An angle exactly equal to $180^\circ$.

Reflex angle

An angle greater than $180^\circ$ but less than $360^\circ$.

Full turn

$360^\circ$.

Zero angle

$0^\circ$.

Angles on a straight line

Add up to $180^\circ$.

Angles around a point

Add up to $360^\circ$.

Vertically opposite angles

Angles opposite each other when two lines cross; they are equal.

Complementary angles

Two angles that add up to $90^\circ$.

Supplementary angles

Two angles that add up to $180^\circ$.

Triangle angle sum

The interior angles add up to $180^\circ$.

Quadrilateral angle sum

The interior angles add up to $360^\circ$.

Exterior angle of a triangle

Equals the sum of the two opposite interior angles.

Corresponding angles

On parallel lines, corresponding angles in an F shape are equal.

Alternate angles

On parallel lines, alternate angles in a Z shape are equal.

Co-interior angles

On parallel lines, co-interior angles in a C shape add up to $180^\circ$.

Equilateral triangle

Three equal sides and three equal angles of $60^\circ$.

Isosceles triangle

Two equal sides and two equal base angles.

Scalene triangle

A triangle with no equal sides.

Right-angled triangle

A triangle with one $90^\circ$ angle.

Parallelogram

Opposite sides are parallel and equal; opposite angles are equal.

Rectangle

Four right angles; opposite sides equal; diagonals equal.

Rhombus

Four equal sides; opposite angles equal; diagonals are perpendicular.

Trapezium

A quadrilateral with one pair of opposite sides parallel.

Kite

Two pairs of equal adjacent sides; diagonals are perpendicular.

Square

Four equal sides and four right angles.

Parallelogram diagonals

Diagonals bisect each other.

Rectangle diagonals

Diagonals are equal and bisect each other.

Rhombus diagonals

Diagonals are perpendicular and bisect each other.

Square diagonals

Diagonals are equal, perpendicular and bisect each other.

Kite diagonals

Diagonals are perpendicular; one diagonal bisects the other.