Year 11 similarity and congruence test to download as PDF

This Year 11 similarity and congruence test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 15-16, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Similar shapes
Two rectangles are similar. The first is 6 cm by 8 cm. The second has length 15 cm on the side corresponding to 6 cm.
1. Find the scale factor. (1 mark)
2. Find the other side of the second rectangle. (1 mark)
3. Find the ratio of the areas. (2 marks)
Question 2 – Parallel line in a triangle
In triangle \(ABC\), \(DE\) is parallel to \(BC\). \(AD=3\) cm, \(DB=5\) cm and \(DE=4.5\) cm.
1. Explain why \(ADE\) and \(ABC\) are similar. (1 mark)
2. Find \(BC\). (3 marks)
Question 3 – Area and volume (Higher)
Two similar shapes have lengths in the ratio \(3:5\).
1. The area of the smaller is 90 cm². Find the area of the larger. (2 marks)
2. The volume of the smaller solid is 108 cm³. Find the volume of the larger. (2 marks)
Question 4 – Congruence proof
\(ABCD\) is a rectangle and \(M\) is the midpoint of \(AB\). Prove that \(MC=MD\).
Question 5 – Problem: a model lorry (Higher)
A model lorry is built to a scale of \(1:12\). The model is 30 cm long and holds 2 litres.
1. Find the length of the real lorry in metres. (1 mark)
2. Find the capacity of the real lorry in litres. (3 marks)

How to use this Year 11 similarity and congruence test

First, revise with the similarity and congruence lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the similarity and congruence test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 11 similarity and congruence test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.