Year 8 Maths (Stage 4)

Operations with positive and negative integers (order of operations / BODMAS).

Decimal operations, rounding, and significant figures.

Terminating, recurring, and non-terminating decimals; converting between fractions and decimals.

Rational numbers and operations on rational numbers.

Operations with positive and negative fractions.

Percentage calculations, percentage of a quantity, and expressing one quantity as a percentage of another.

Percentage increase and decrease, and the unitary method with percentages.

Profit, loss, discount, and simple interest (I = Prt).

Reading a journey off a graph: rising, flat and falling sections, speed as gradient, drawing from a description, and average speed including stops.

Simplifying and equivalent ratios; dividing quantities in a given ratio.

Scale drawings, maps, and scale factor applications.

Rates and unit rates (e.g. speed = distance / time, cost per unit).

Time calculations, 12-hour/24-hour time, and time zones.

Index laws for numerical and algebraic bases (multiplication, division, power of a power, zero power).

Variables, terms, coefficients, and constant terms.

Adding and subtracting like terms.

Multiplying and dividing algebraic terms.

Expanding algebraic expressions using the distributive law: a(b + c).

Factorising algebraic expressions using the highest common factor (HCF).

Why squared equations have two answers, isolating x² before rooting, exact versus rounded answers, and rejecting the impossible one in real problems.

Solving one-step, two-step, and multi-step linear equations.

Solving equations containing grouping symbols (brackets).

Solving linear equations with fractions and variables on both sides.

Translating word problems into algebraic equations and solving.

Graphing inequalities on the number line and solving basic linear inequalities.

Prime versus composite, divisibility tests, factor trees, and using prime factorisation to find the HCF and LCM.

Positive integer powers, square roots, and cube roots.

Review and consolidation of index laws.

Scientific notation (standard form) for large and small numbers.

Rounding and significant figures in scientific notation.

Common differences, finding the rule dn + b from the position, jumping to any term, decreasing and non-arithmetic patterns, and matchstick patterns.

The Cartesian plane: reviewing quadrants and coordinates.

Generating tables of values from linear rules.

Graphing linear relationships by plotting coordinates.

Finding and interpreting the gradient (slope) of a line: m = rise / run.

The gradient-intercept form (y = mx + c) and horizontal/vertical lines (y = c, x = k).

Walking the boundary, deducing missing sides, semicircular edges, working backwards from a given perimeter, and getting the units right.

Where π comes from, choosing C = πd or 2πr, arc length as a fraction of the circumference, the perimeter of a sector, and exact answers.

Units of measurement and conversion of metric units.

Perimeter and area of basic and composite 2D shapes.

Why the formula halves, finding the perpendicular height in any triangle, working backwards from the area, and squared-unit conversion.

Where πr² comes from, halving the diameter first, sector area as a fraction, rings and holes, and working backwards.

Split or subtract, tracking missing lengths, mixing rectangles, triangles and circles, shaded regions, and a six-step method.

Special quadrilaterals: parallelograms, trapeziums, rhombuses, and kites.

V = cross-section × length for every prism, cuboids, triangular prisms and cylinders, cubic units and capacity, and composite solids.

Why area and volume conversions are squared and cubed, the metric ladders, the cm³/mL/L bridges, and filling rates.

Understanding right-angled triangles and the hypotenuse.

Stating and applying Pythagoras' theorem (c² = a² + b²).

Calculating the length of the hypotenuse: c = √(a² + b²).

Calculating the length of a shorter side: a = √(c² − b²).

Pythagorean triads and composite/practical 2D applications.

The ten reasons, working in steps, reading diagram markings, angles inside shapes, and setting out a full-mark solution.

Complementary, supplementary, vertically opposite angles, and angles around a point.

Alternate, corresponding, and co-interior angles.

Naming by sides and by angles, the 180° angle sum, the isosceles rule, exterior angles, and giving a reason for every step.

The 360° angle sum, the six special quadrilaterals and how they overlap, parallelogram angle rules, and what the diagonals prove.

Angle sums of triangles (interior and exterior angle theorem) and quadrilaterals.

Theoretical probability of simple events: P(E) = favourable outcomes / total outcomes.

Why probabilities sum to 1, and using the complement to solve problems faster.

Experimental probability and relative frequency.

Two-step chance experiments using sample space lists, tree diagrams, and tables.

Representing events using Venn diagrams and two-way tables.

Collecting and classifying data: categorical vs numerical; discrete vs continuous.

Frequency distribution tables, grouped data, and cumulative frequency.

Graphical representations: column graphs, histograms, dot plots, and stem-and-leaf plots.

Measures of central tendency: mean, median, and mode.

Measure of spread: range.

Analysing distributions (skewed vs symmetric data) and the effect of outliers.

Surface area of rectangular and triangular prisms.

Congruent figures and transformations: reflection, rotation, translation.

The four congruence tests for triangles: SSS, SAS, AAS, and RHS.

Formal geometric proofs using congruent triangles and quadrilateral properties.