GCSE Maths
Geometry
revision.
Pythagoras, trigonometry, circle theorems and the diagrams that earn method marks when they are labelled first.
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Students type: three figure bearings GCSE
Open guide Revision guideTransformationsStudents type: GCSE transformations translation vector
Open guide Revision guideSurface areaStudents type: surface area of cylinder GCSE
Open guide Revision guideVolume of 3D shapesStudents type: volume of cylinder GCSE
Open guide Revision guideArea of 2D shapesStudents type: area of compound shapes GCSE
Open guide Revision guideGeometric constructionsStudents type: geometric constructions GCSE
Open guide Revision guidePlans and elevationsStudents type: plans and elevations GCSE
Open guide Revision guideLociStudents type: loci GCSE maths
Open guide Revision guideArc length and sector areaStudents type: arc length sector area GCSE
Open guide Revision guideCongruence and similarityStudents type: congruence and similarity GCSE
Open guide Revision guideCircle theorems: writing reasonsStudents type: circle theorems reasons GCSE
Open guide Revision guideVectorsStudents type: GCSE vectors column vectors
Open guideTrigonometry
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.
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).
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.
Geometric constructions
GCSE Maths constructions: perpendicular bisector, angle bisector, perpendicular from a point, 60° angles, and loci with compasses and ruler only.
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.
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.
Surface area
GCSE Maths surface area: cuboids, cylinders (2πr² + 2πrh), spheres (4πr²), and nets where they help you see every face before adding areas.
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).
Bearings
GCSE Maths bearings: three-figure bearings measured clockwise from North, back bearings, scale drawings, and angle rules with parallel lines and triangles.
Keep going
More GCSE Maths
in the same style.
GCSE Maths revision that treats method as the mark scheme: reverse percentages, compound interest, quadratic formula, completing the square, SOHCAHTOA, sine and cosine rules, vectors, tree diagrams and histograms, with working shown line by line.
All Maths revision