Maths . Practice. Play. Progress.

All Number and ratio revision

Number and ratio

Number and ratio
made memorable.

Fractions, decimals, percentages, ratio, proportion, indices and standard form — the number skills every paper still tests.

Fractions, decimals and percentages

Convert fluently between fractions, decimals and percentages, then use multipliers for increase, decrease and reverse percentage.

Ratio and proportion

Share amounts in a ratio, scale recipes, and distinguish direct proportion from inverse proportion with a unitary method.

Indices and standard form

Use the index laws with confidence and write large or small numbers in standard form for science-style GCSE questions.

Reverse percentages

GCSE Maths reverse percentages: recover the original from a sale price or VAT-inclusive total by dividing by the multiplier, with the method written line by line.

Compound interest and depreciation

GCSE Maths compound interest: use multiplier to the power n, not simple interest, and apply the same method to depreciation, with a full line-by-line calculation.

Standard form calculations

GCSE Maths standard-form calculations: multiply and divide by combining a-values and powers of 10, then add or subtract by matching powers, rewriting into standard form.

Bounds and error intervals

GCSE Maths error intervals: write upper and lower bounds for rounded or truncated values, then find the maximum or minimum of a calculation from those bounds.

Recurring decimals to fractions

GCSE Maths recurring decimals to fractions: set x equal to the decimal, multiply to shift the repeating block, subtract, and simplify, including one-digit and two-digit repeats.

Direct proportion

GCSE Maths direct proportion: y = kx, graphs through the origin, and unitary method for recipes, maps and currency when quantities rise together.

Inverse proportion

GCSE Maths inverse proportion: y = k/x, product k = xy constant, and worker–days problems when one quantity rises as the other falls.

Algebra

Algebra
made memorable.

Linear equations, quadratics, simultaneous equations and graphs, built on the balance method rather than shortcuts.

All Algebra revision

Algebra

Collect like terms, expand and factorise, and solve linear equations with the balance method: whatever you do to one side, do to the other.

Quadratic equations

Solve ax² + bx + c = 0 by factorising, completing the square, or the quadratic formula, and know how many roots to expect.

Graphs

Plot and interpret y = mx + c, read gradient and intercept, and recognise linear, quadratic and other standard GCSE graphs.

Simultaneous equations

Solve two linear equations together by elimination or substitution, and read the solution as the intersection of two lines.

The quadratic formula

GCSE Maths quadratic formula: write a, b and c including signs, compute the discriminant, keep the ± until the last line, and round only when the question asks.

Completing the square

GCSE Maths completing the square: rewrite x² + bx + c as (x + p)² + q, read the turning point, and handle a ≠ 1 by factoring a out first.

Inequalities on a line

GCSE Maths inequalities: solve linear inequalities with the balance method, reverse the sign when multiplying or dividing by a negative, and show the answer on a number line.

Nth term of linear sequences

GCSE Maths linear sequences: find the common difference, write the nth term as an + b, and use it to generate terms or to decide whether a number is in the sequence.

Changing the subject of a formula

GCSE Maths changing the subject: use inverse operations in reverse order, including squares, fractions and brackets, and factorise when the new subject appears twice.

Factorising quadratics

GCSE Maths factorising quadratics: highest common factor first, then two brackets for x² + bx + c, and grouping when a ≠ 1 — expand every time as a check.

Open guide 11

Quadratic sequences

GCSE Maths quadratic sequences: constant second difference, nth term an² + bn + c — find a from half the second difference, then b and c from the first two terms.

Open guide 12

HCF and LCM

GCSE Maths HCF and LCM: prime factor trees, index form, the Venn method for two numbers, and HCF × LCM = product for a pair.

Open guide 13

Iteration and trial and improvement

GCSE Maths iteration: trial and improvement to find roots of equations, iterative formulas xₙ₊₁ = f(xₙ), and when a solution converges or diverges.

Open guide 14

Quadratic graphs

GCSE Maths quadratic graphs: parabola shape, roots, y-intercept, turning point from completing the square, and sketching y = ax² + bx + c.

Geometry

Geometry
made memorable.

Pythagoras, trigonometry, circle theorems and the diagrams that earn method marks when they are labelled first.

All Geometry revision

Trigonometry

Use SOHCAHTOA on right-angled triangles: label opposite, adjacent and hypotenuse from the angle, then choose sine, cosine or tangent.

Pythagoras

Use a² + b² = c² on right-angled triangles to find a missing side, including in 3D and in reverse to test for a right angle.

Circle theorems

Use the GCSE circle theorems with reasons: angle in a semicircle, centre and circumference, cyclic quadrilaterals, tangents and the alternate segment.

SOHCAHTOA

GCSE Maths SOHCAHTOA: label opposite, adjacent and hypotenuse from the angle, choose sine, cosine or tangent, and rearrange carefully when the unknown is on the denominator.

The sine rule

GCSE Maths sine rule: use a / sin A = b / sin B when you have a side and its opposite angle, including the ambiguous case on Higher if two triangles are possible.

The cosine rule

GCSE Maths cosine rule: use a² = b² + c² − 2bc cos A to find a side from two sides and the included angle, or rearrange for an angle when all three sides are known.

Vectors

GCSE Maths vectors: add column vectors, find a resultant or midpoint, and write a proof-style “show that” argument with directed segments such as AB = b − a.

Circle theorems: writing reasons

GCSE Maths circle-theorem reasons: write the official phrases on every line — angle in a semicircle, centre twice circumference, alternate segment, cyclic quadrilateral — as a drill beside the theorems hub.

Congruence and similarity

GCSE Maths congruence and similarity: congruent shapes are identical in size and shape; similar shapes have equal angles and sides in proportion — scale factor links matching lengths.

Arc length and sector area

GCSE Maths arc length and sector area: use θ/360 of the full circumference or circle area, with θ in degrees — or θ/2π and θ/2 for radian-ready Higher work.

Open guide 11

Loci

GCSE Maths loci: equidistant from a point (circle), equidistant from a line (parallel line), equidistant from two points (perpendicular bisector), and from two lines (angle bisector).

Open guide 12

Plans and elevations

GCSE Maths plans and elevations: draw front, side and plan views of 3D solids, read hidden detail as dashed lines, and match sketches to objects.

Open guide 13

Geometric constructions

GCSE Maths constructions: perpendicular bisector, angle bisector, perpendicular from a point, 60° angles, and loci with compasses and ruler only.

Open guide 14

Area of 2D shapes

GCSE Maths area: rectangles, triangles, parallelograms, trapeziums and circles (πr²), plus compound shapes split into parts, with units in cm² and m² and conversions between them.

Open guide 15

Volume of 3D shapes

GCSE Maths volume: prisms (cross-section × length), cuboids, cylinders, spheres (4/3πr³), units cm³ and m³, and the link to capacity in litres and millilitres.

Open guide 16

Surface area

GCSE Maths surface area: cuboids, cylinders (2πr² + 2πrh), spheres (4πr²), and nets where they help you see every face before adding areas.

Open guide 17

Transformations

GCSE Maths transformations: translation by vector, reflection in a mirror line, rotation (centre, angle, direction), and enlargement (centre, scale factor positive, negative or fractional).

Open guide 18

Bearings

GCSE Maths bearings: three-figure bearings measured clockwise from North, back bearings, scale drawings, and angle rules with parallel lines and triangles.

All Probability and statistics revision

Probability and statistics

Probability and statistics
made memorable.

Chance, tree diagrams, averages and grouped data, with the language of probability kept between 0 and 1.

Probability

Work with probabilities between 0 and 1, including tree diagrams, independent and dependent events, and the AND / OR rules.

Averages and data

Choose and calculate mean, median, mode and range, including from frequency tables, and estimate the mean of grouped data.

Product rule for counting

GCSE Maths product rule: multiply choices for independent stages — menus, outfits, PINs and multi-branch tree counts when order matters or not.

Frequency trees

GCSE Maths frequency trees: two-stage totals split on branches, missing values from row and column constraints, and link to two-way tables.

Stratified sampling

GCSE Maths stratified sampling: sample size proportional to each stratum, nᵢ = (Nᵢ/N) × n, and why subgroups are represented fairly.

Tree diagrams

GCSE Maths tree diagrams: multiply along a branch for AND, add complete pathways for OR, and change the second fraction without replacement, with full working shown.

Venn diagrams and probability

GCSE Maths Venn diagrams: use P(A ∪ B) = P(A) + P(B) − P(A ∩ B), fill the overlap first, and read “and”, “or” and “given that” from the regions.

Histograms

GCSE Maths histograms: frequency density equals frequency divided by class width, so unequal widths still have area equal to frequency, with a full reading and drawing method.

Cumulative frequency and box plots

GCSE Maths cumulative frequency and box plots: plot running totals at upper class boundaries, read the median and quartiles, then compare two distributions with IQR as well as average.

Scatter graphs and correlation

GCSE Maths scatter graphs: describe positive, negative or no correlation, draw a line of best fit by eye, and interpolate inside the data range rather than extrapolating beyond it.