Mathematics

Ordering and inequalities

Place value and decimals

Four operations

Written methods

Negative number calculations

Inverse operations

BIDMAS and brackets

Factors and multiples

Prime numbers

Prime factorisation

HCF and LCM

Squares, cubes, roots

Index laws

Fractional indices

Surds and simplification

Rationalising surds

Standard form

Fraction–decimal conversion

Recurring decimals to fractions

Fraction calculations

Fractions in context

Percentages as operators

Percentage change

Reverse percentages

Simple interest

Standard units

Compound units

Time and money calculations

Rounding and significant figures

Estimation and checks

Error intervals

Upper and lower bounds

Algebra notation

Substitution

Expressions and terms

Collecting like terms

Expanding brackets

Factorising expressions

Quadratic factorising

Difference of two squares

Algebraic fractions

Simplifying algebraic fractions

Rearranging formulae

Identities and proof

Linear equations

Quadratic equations

Completing the square

Quadratic formula

Simultaneous equations

Linear inequalities

Quadratic inequalities

Coordinates and plotting

Straight line graphs

Gradient and intercept

Parallel and perpendicular lines

Graphs of quadratic functions

Graphs of cubic functions

Reciprocal graphs

Exponential graphs

Trig function graphs

Transformations of graphs

Iteration methods

Sequences from rules

Arithmetic sequences

Quadratic sequences

Fibonacci-type sequences

Functions and notation

Equation of a circle

Tangents to circles

Rates from graphs

Areas under graphs

Ratio notation

Simplifying ratios

Sharing in a ratio

Ratio and fractions

Ratio and algebra

Best buys and unit pricing

Direct proportion

Inverse proportion

Proportion graphs

Proportion equations

Percentage as “per hundred”

Percentage comparisons

Percentage increase/decrease

Percentage multipliers

Growth and decay

Compound interest

Repeated percentage change

Speed calculations

Density calculations

Pressure calculations

Rates of pay

Scale factors

Scale drawings and maps

Similarity in shapes

Similarity in area/volume

Gradient as rate of change

Average and instantaneous rate

Geometric language and notation

Angle facts

Angles on lines

Angles in triangles

Angles in polygons

Parallel line angles

Bearings

Constructions

Loci

Perimeter and area

Area of triangles

Area of trapezia

Circles: circumference

Circles: area

Arc length

Sector area

Surface area

Volume of prisms

Volume of cylinders

Volume of pyramids and cones

Spheres: volume and surface area

Congruence criteria

Similarity and enlargement

Transformations

Reflections and rotations

Translations and vectors

Combined transformations

Pythagoras’ theorem

Trigonometry in right triangles

Sine, cosine, tangent ratios

Exact trig values

Sine rule

Cosine rule

Area of triangle (½ab sin C)

Circle theorems

Tangents and radii

Vectors in geometry

Vector proofs

Randomness and fairness

Probability scale (0 to 1)

Relative frequency

Theoretical probability

Sample spaces

Listing outcomes systematically

Frequency tables and trees

Mutually exclusive events

Complementary events

Tree diagrams

Independent events

Dependent events

Conditional probability

Two-way tables

Venn diagrams

Expected outcomes

Sampling and bias

Data types

Frequency tables

Bar charts

Pie charts

Pictograms

Line graphs and time series

Frequency polygons

Histograms (equal classes)

Histograms (unequal classes)

Cumulative frequency graphs

Box plots

Mean, median, mode

Modal class

Range and outliers

Quartiles and IQR

Comparing distributions

Scatter graphs

Correlation and causation

Line of best fit

Interpolation and extrapolation