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Complete revision guide covering all 9 topics in Geometry & Trigonometry for the Edexcel IGCSE Mathematics (9-1) specification. From angle rules to circle theorems — free worked examples, exam tips, and practice resources.
Geometry & Trigonometry is the fourth of six topic areas in IGCSE Edexcel Mathematics, worth 18-24% of the total exam mark. It covers angle rules and reasoning, polygon properties, 2D and 3D mensuration, similarity and congruence, Pythagoras' theorem, basic and advanced trigonometry (sine rule, cosine rule), 3D geometry, and circle theorems. This is the most visual topic area and rewards students who can identify the correct triangle or shape within a complex diagram.
Source: Edexcel IGCSE Mathematics (9-1) Specification 4MA1
Geometry builds in layers: angle rules feed into polygon problems, mensuration formulae feed into 3D calculations, and Pythagoras feeds into every trigonometry topic. Start with the foundations (angles, polygons, 2D mensuration) and work upwards. Always draw and label diagrams — most geometry marks are lost to missing labels, not wrong methods. Use our free worksheets for targeted practice and keep the formula sheet open as a quick reference.
Each guide below covers the key concepts, worked examples from Grade 5 through Grade 9, common exam mistakes, and targeted revision tips. Click any topic to access the full study guide.
Apply angle rules at parallel lines (alternate, corresponding, co-interior). Use angle reasoning to construct geometric proofs with clear justifications.
Study GuideCalculate interior and exterior angles of regular and irregular polygons. Find the number of sides from angle information. Tessellation and angle sums.
Study GuideFind circumference, area of circles, arc length, sector area, and segment area. Apply compound shape strategies to complex 2D problems.
Study GuideCalculate volume and surface area of prisms, cylinders, pyramids, cones, spheres, and composite solids. Convert between units of volume and capacity.
Study GuideProve triangles similar or congruent. Apply linear, area, and volume scale factors. Solve problems involving similar shapes and geometric proof.
Study GuideApply Pythagoras theorem to find missing sides. Use SOH CAH TOA to find sides and angles in right-angled triangles. Exact trigonometric values.
Study GuideApply the sine rule and cosine rule to non-right-angled triangles. Calculate area using ½absinC. Solve ambiguous case problems.
Study GuideIdentify right-angled triangles within 3D shapes. Apply Pythagoras and trigonometry to find lengths, angles, and diagonals in cuboids, pyramids, and prisms.
Study GuideApply all circle theorems including angle at centre, angles in semicircle, cyclic quadrilateral, tangent-radius, and alternate segment theorem. Construct geometric proofs.
Study GuideGeometry questions appear on both Paper 1 (non-calculator) and Paper 2 (calculator). On Paper 1, expect angle reasoning, polygon angle calculations, basic Pythagoras, and exact trigonometric values. On Paper 2, expect mensuration problems requiring formulae, advanced trigonometry with sine and cosine rules, 3D problems, and circle theorem proofs. The final questions on each paper frequently combine geometry with algebra — for example, setting up an equation from a circle theorem or using trigonometry within a coordinate geometry context.
Pythagoras & Trigonometry
8-12 marks, foundation skill
Mensuration (2D & 3D)
8-10 marks, formula application
Circle Theorems (H)
4-8 marks, proof questions
Angles & Polygons
4-6 marks, reasoning chains
Similarity & Congruence (H)
4-6 marks, scale factor problems
Advanced Trig & 3D (H)
4-8 marks, later questions
Not giving reasons with angle calculations
IGCSE mark schemes require geometric reasons (e.g. "alternate angles are equal", "angles in a triangle sum to 180°"). The numerical answer alone does not earn full marks.
Using the wrong trigonometric ratio
Label the sides as opposite, adjacent, and hypotenuse relative to the angle you are working with. Then select the correct ratio from SOH CAH TOA.
Forgetting to use the correct scale factor for area and volume
Linear scale factor k gives area scale factor k² and volume scale factor k³. Many students apply the linear factor to all three — this is the most common similarity error.
Rounding too early in multi-step calculations
Keep intermediate answers to at least 4 significant figures or use the ANS button on your calculator. Round only at the final step to 3 significant figures (or as instructed).
Drawing diagrams too small or without labels
Large, clearly labelled diagrams help you identify the correct triangles and theorems. Always mark right angles, equal lengths, and parallel lines.
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Last updated: March 2026
Common questions about this IGCSE Maths topic area.
Our specialist IGCSE maths tutors build confident geometry and trigonometry skills from angle rules through to circle theorem proofs. In-home sessions across Dubai.