Two triangles are similar. The smaller triangle has a side of length 4 cm; the corresponding side of the larger triangle is 12 cm. What is the linear scale factor from the smaller triangle to the larger triangle?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Similarity Topical Past Papers.
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These Similarity Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Geometry (E4.4) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Use the properties of similar shapes (equal corresponding angles, sides in the same ratio). At Extended, use ratios of areas (k²) and volumes (k³) for similar figures.
Two triangles are similar. The smaller triangle has a side of length 4 cm; the corresponding side of the larger triangle is 12 cm. What is the linear scale factor from the smaller triangle to the larger triangle?
Two similar rectangles have widths in the ratio 2 : 5. State the ratio of their lengths.
[1 mark]Triangle ABC is similar to triangle DEF. AB = 6 cm and BC = 9 cm. DE (corresponding to AB) is 10 cm. Find the length of EF.
[2 marks]Two similar triangles have linear scale factor 2. The smaller triangle has area 9 cm². Find the area of the larger triangle.
[2 marks]Two similar shapes have sides in the ratio 3 : 5. What is the ratio of their areas?
Two similar containers are filled with sand. The smaller container has height 12 cm and holds 600 grams of sand. The larger container has height 18 cm.
Find the linear scale factor from the smaller to the larger container.
[1 mark]Assuming the sand has uniform density, find the mass of sand in the larger container, in grams.
[2 marks]Two similar cones have surface areas in the ratio 16 : 25. Find the ratio of their volumes.
[2 marks]Two similar bottles have capacities of 250 ml and 2 000 ml. The smaller bottle has a label of area 30 cm². Find the area of the corresponding label on the larger bottle.
[2 marks]