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Similar shapes: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on G19 Similar shapes, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q13

    June 2025 · Paper 6

    3 marksG19 Similar shapes
    The whole paper ↗
    June 2025 Paper 6, question 13: The diagram shows two similar triangles, AEB and ADC. D Not to scale 17.5 cm E 5 cm C A B 8 cm AB = 8 cm, BE = 5 cm and CD = 17.5 cm Work out the length of BC.

  2. Q11

    November 2024 · Paper 4

    4 marksG19 Similar shapes
    The whole paper ↗
    November 2024 Paper 4, question 11: Triangles ABC and PQR are mathematically similar. Angle ACB = Angle PRQ. Angle ABC = Angle PQR. R Not to scale B 8 cm 45 cm C A 12 cm P Q The perimeter of trian

  3. Q19

    November 2024 · Paper 4

    6 marksG19 Similar shapes
    The whole paper ↗
    November 2024 Paper 4, question 19: Two ornaments, A and B, are mathematically similar. The table shows information about the two ornaments. Ornament A Ornament B Height (m) h 12 2 216 A Surface a

  4. Q16

    June 2024 · Paper 5

    3 marksG19 Similar shapes
    The whole paper ↗
    June 2024 Paper 5, question 16: Two prisms, A and B, are mathematically similar. The ratio of the volume of prism A to the volume of prism B is 8 : 27. The height of prism A is 6 cm. Work out

  5. Q15

    June 2023 · Paper 6

    4 marksG19 Similar shapesR12 Comparing lengths, areas and volumes
    The whole paper ↗
    June 2023 Paper 6, question 15: Two bottles are mathematically similar. The small bottle holds 0.5 litres and has a height of 35 cm. The large bottle holds 2 litres. Calculate the height of th

  6. Q12

    November 2022 · Paper 4

    6 marksG17 Circles, surface area and volumeG19 Similar shapes
    The whole paper ↗
    November 2022 Paper 4, question 12: The diagram shows a sphere and a cone. 15 cm Not to scale 4 cm 30 cm d cm The sphere has radius 4 cm. The cone has radius 15 cm and height 30 cm. The sphere is

  7. Q8

    November 2022 · Paper 6

    4 marksG19 Similar shapes
    The whole paper ↗
    November 2022 Paper 6, question 8: Triangles ABC and DEF are mathematically similar. Angle ABC = Angle DEF. 25 cm A C E Not to scale 7 cm 15 cm F D B 10 cm Calculate the perimeter of triangle ABC

  8. Q20

    June 2022 · Paper 6

    4 marksG19 Similar shapes
    The whole paper ↗
    June 2022 Paper 6, question 20: Two pyramids, A and B, are mathematically similar. Pyramid A has surface area 12 cm2 and volume 8 cm3. Pyramid B has surface area 75 cm2. Work out the volume of

  9. Q11

    November 2021 · Paper 4

    3 marksG19 Similar shapesG3 Angles and polygons
    The whole paper ↗
    November 2021 Paper 4, question 11: The diagram shows triangles ABC and ADE. A Not to scale C B E D B lies on AD and C lies on AE. BC is parallel to DE. Complete these statements to show that tria

  10. Q14

    November 2021 · Paper 5

    2 marksG19 Similar shapes
    The whole paper ↗
    November 2021 Paper 5, question 14: Two solid ornaments are mathematically similar. The larger ornament is twice as tall as the smaller ornament. The smaller ornament has a volume of 50 cm3. Work

  11. Q13

    November 2020 · Paper 6

    4 marksG19 Similar shapesR12 Comparing lengths, areas and volumes
    The whole paper ↗
    November 2020 Paper 6, question 13: In the diagram, AED and ABC are straight lines and BE is parallel to CD. D Not to scale E A B C The ratio of length AB to length BC is 2 : 3. 2. Triangle ABE ha

  12. Q13

    November 2019 · Paper 4

    6 marksG19 Similar shapesN5 Systematic listing and the product rule
    The whole paper ↗
    November 2019 Paper 4, question 13: (a) A transport lorry consists of a cab and a trailer. The trailer has a volume of 90 m3. Alfie makes a model of this lorry using a scale of 1 : 72. Work out th

  13. Q14

    June 2019 · Paper 5

    3 marksG19 Similar shapesG6 Geometric proof
    The whole paper ↗
    June 2019 Paper 5, question 14: In the diagram AB is parallel to CD. AED and BEC are straight lines. A B E Not to scale C D Prove that triangle ABE is similar to triangle CDE.

  14. Q21

    June 2019 · Paper 6

    4 marksG19 Similar shapes
    The whole paper ↗
    June 2019 Paper 6, question 21: Toy building bricks are available in two sizes, small and large. The small and large bricks are mathematically similar. 3and width 2.1 cm. A small brick has vol

  15. Q19

    November 2018 · Paper 4

    5 marksG19 Similar shapes
    The whole paper ↗
    November 2018 Paper 4, question 19: Two cylinders, A and B, are mathematically similar. Cylinder A has volume 2400 cm3 and height 12 cm. Cylinder B has volume 750 cm3. Find the height of cylinder

  16. Q17

    November 2018 · Paper 5

    4 marksG19 Similar shapes
    The whole paper ↗
    November 2018 Paper 5, question 17: The diagram consists of three mathematically similar shapes. The heights of the shapes are in the ratio 1 : 4 : 5. Not to scale Find the ratio total shaded area

  17. Q12

    June 2018 · Paper 6

    5 marksG6 Geometric proofG19 Similar shapes
    The whole paper ↗
    June 2018 Paper 6, question 12: The diagram below shows two right-angled triangles. R Not to scale 4 cm 8 cm Q S 10 cm P Prove that triangles PQS and QRS are similar.

  18. Q18

    June 2018 · Paper 6

    5 marksG19 Similar shapesR12 Comparing lengths, areas and volumes
    The whole paper ↗
    June 2018 Paper 6, question 18: Percy sells paint in standard tins and large tins. The standard tin covers 40 m2 and the large tin covers 60 m2. (a) Percy publishes this chart showing the area

  19. Q9

    June 2017 · Paper 6

    7 marksG7 TransformationsG19 Similar shapes
    The whole paper ↗
    June 2017 Paper 6, question 9: (a) Triangle A is drawn on the grid. y 9 8 7 A 6 5 4 3 2 1 x 0 -2 -1 1 2 3 4 5 6 7 8 9 -1 -2 1 and centre of enlargement (-1, 5). Enlarge triangle A with scale
All 19 questions on Similar shapes, as a list
  1. June 2025, Paper 6, Q13 (3 marks): The diagram shows two similar triangles, AEB and ADC. D Not to scale 17.5 cm E 5 cm C A B 8 cm AB = 8 cm, BE = 5 cm and CD = 17.5 cm Work out the length of BC.
  2. November 2024, Paper 4, Q11 (4 marks): Triangles ABC and PQR are mathematically similar. Angle ACB = Angle PRQ. Angle ABC = Angle PQR. R Not to scale B 8 cm 45 cm C A 12 cm P Q The perimeter of trian
  3. November 2024, Paper 4, Q19 (6 marks): Two ornaments, A and B, are mathematically similar. The table shows information about the two ornaments. Ornament A Ornament B Height (m) h 12 2 216 A Surface a
  4. June 2024, Paper 5, Q16 (3 marks): Two prisms, A and B, are mathematically similar. The ratio of the volume of prism A to the volume of prism B is 8 : 27. The height of prism A is 6 cm. Work out
  5. June 2023, Paper 6, Q15 (4 marks): Two bottles are mathematically similar. The small bottle holds 0.5 litres and has a height of 35 cm. The large bottle holds 2 litres. Calculate the height of th
  6. November 2022, Paper 4, Q12 (6 marks): The diagram shows a sphere and a cone. 15 cm Not to scale 4 cm 30 cm d cm The sphere has radius 4 cm. The cone has radius 15 cm and height 30 cm. The sphere is
  7. November 2022, Paper 6, Q8 (4 marks): Triangles ABC and DEF are mathematically similar. Angle ABC = Angle DEF. 25 cm A C E Not to scale 7 cm 15 cm F D B 10 cm Calculate the perimeter of triangle ABC
  8. June 2022, Paper 6, Q20 (4 marks): Two pyramids, A and B, are mathematically similar. Pyramid A has surface area 12 cm2 and volume 8 cm3. Pyramid B has surface area 75 cm2. Work out the volume of
  9. November 2021, Paper 4, Q11 (3 marks): The diagram shows triangles ABC and ADE. A Not to scale C B E D B lies on AD and C lies on AE. BC is parallel to DE. Complete these statements to show that tria
  10. November 2021, Paper 5, Q14 (2 marks): Two solid ornaments are mathematically similar. The larger ornament is twice as tall as the smaller ornament. The smaller ornament has a volume of 50 cm3. Work
  11. November 2020, Paper 6, Q13 (4 marks): In the diagram, AED and ABC are straight lines and BE is parallel to CD. D Not to scale E A B C The ratio of length AB to length BC is 2 : 3. 2. Triangle ABE ha
  12. November 2019, Paper 4, Q13 (6 marks): (a) A transport lorry consists of a cab and a trailer. The trailer has a volume of 90 m3. Alfie makes a model of this lorry using a scale of 1 : 72. Work out th
  13. June 2019, Paper 5, Q14 (3 marks): In the diagram AB is parallel to CD. AED and BEC are straight lines. A B E Not to scale C D Prove that triangle ABE is similar to triangle CDE.
  14. June 2019, Paper 6, Q21 (4 marks): Toy building bricks are available in two sizes, small and large. The small and large bricks are mathematically similar. 3and width 2.1 cm. A small brick has vol
  15. November 2018, Paper 4, Q19 (5 marks): Two cylinders, A and B, are mathematically similar. Cylinder A has volume 2400 cm3 and height 12 cm. Cylinder B has volume 750 cm3. Find the height of cylinder
  16. November 2018, Paper 5, Q17 (4 marks): The diagram consists of three mathematically similar shapes. The heights of the shapes are in the ratio 1 : 4 : 5. Not to scale Find the ratio total shaded area
  17. June 2018, Paper 6, Q12 (5 marks): The diagram below shows two right-angled triangles. R Not to scale 4 cm 8 cm Q S 10 cm P Prove that triangles PQS and QRS are similar.
  18. June 2018, Paper 6, Q18 (5 marks): Percy sells paint in standard tins and large tins. The standard tin covers 40 m2 and the large tin covers 60 m2. (a) Percy publishes this chart showing the area
  19. June 2017, Paper 6, Q9 (7 marks): (a) Triangle A is drawn on the grid. y 9 8 7 A 6 5 4 3 2 1 x 0 -2 -1 1 2 3 4 5 6 7 8 9 -1 -2 1 and centre of enlargement (-1, 5). Enlarge triangle A with scale

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