EDEXCEL GCSE MATHS · HIGHER
Exam Practice: More Similarity
More similarity · Similarity and congruence · Lesson 4 of 5 · 18 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 WORK OUT (3 marks)
In triangle ABC, DE is parallel to BC. AD = 4 cm, DB = 2 cm and DE = 5 cm. Work out the length of BC.
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(Total for Question 1 = 3 marks)
Question 2 WORK OUT (3 marks)
Two similar rectangles have lengths of 12 cm and 18 cm. The area of the smaller rectangle is 40 cm². Work out the area of the larger rectangle.
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(Total for Question 2 = 3 marks)
Question 3 WORK OUT (3 marks)
Two similar triangles have areas of 12 cm² and 27 cm². Work out the ratio of the lengths of their corresponding sides. Give your answer in the form 1 : n or in its simplest form.
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(Total for Question 3 = 3 marks)
Question 4 WORK OUT (3 marks)
Two similar shapes have corresponding lengths in the ratio 3 : 5. The area of the smaller shape is 36 cm². Work out the area of the larger shape.
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(Total for Question 4 = 3 marks)
Question 5 WORK OUT (3 marks)
A 1.5 m post casts a shadow 2 m long at the same time as a tree casts a shadow 12 m long. Work out the height of the tree.
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(Total for Question 5 = 3 marks)
Question 6 EXPLAIN (3 marks)
Explain why triangle ADE is similar to triangle ABC when DE is parallel to BC.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 18 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
Triangles ADE and ABC are similar. AB = 6, so the scale factor is 6/4 = 1.5. BC = 5 × 1.5 = 7.5 cm.
• Similar triangles ADE and ABC M1
• Scale factor 6/4 M1
• 7.5 A1
Question 2 (3 marks)
The length scale factor is 18/12 = 1.5, so the area scale factor is 1.5² = 2.25. The area is 40 × 2.25 = 90 cm².
• Length scale factor 1.5 M1
• 1.5² = 2.25 M1
• 90 A1
Question 3 (3 marks)
The area ratio is 12 : 27 = 4 : 9. The length ratio is √4 : √9 = 2 : 3.
• 4 : 9 M1
• Square roots M1
• 2 : 3 A1
Question 4 (3 marks)
The area ratio is 3² : 5² = 9 : 25. The area is 36 × 25/9 = 100 cm².
• 9 : 25 M1
• 36 × 25/9 M1
• 100 A1
Question 5 (3 marks)
The triangles are similar. The scale factor is 12 ÷ 2 = 6. The tree is 1.5 × 6 = 9 m tall.
• Scale factor 6 M1
• 1.5 × 6 M1
• 9 A1
Question 6 (3 marks)
Angle ADE = angle ABC and angle AED = angle ACB (corresponding angles on parallel lines). Angle A is common. All three angles are equal, so the triangles are similar.
• Corresponding angles on parallel lines M1
• Angle A common M1
• All angles equal, so similar C1