Year 9 similarity and enlargement test to download as PDF

This Year 9 similarity and enlargement test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 13-14, and the full answers are on a separate page.

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

Mark/20

Question 1 – Scale factors
Rectangle \(P\) is 6 cm by 4 cm. Rectangle \(Q\) is an enlargement of \(P\).
1. \(Q\) is made with scale factor 2.5. Find the sides of \(Q\). (2 marks)
2. Another rectangle \(R\) has a long side of 4.5 cm. Find the scale factor from \(P\) to \(R\). (1 mark)
3. Find the short side of \(R\). (1 mark)
Question 2 – Similar triangles
Triangle \(ABC\) has \(AB=6\) cm, \(BC=8\) cm and \(AC=7\) cm. Triangle \(DEF\) is similar to \(ABC\) with \(DE=9\) cm, \(D\) matching \(A\) and \(E\) matching \(B\).
1. Find the scale factor. (1 mark)
2. Find \(EF\) and \(DF\). (2 marks)
3. A triangle has sides 12 cm, 16 cm and 14 cm. Is it similar to \(ABC\)? Explain. (1 mark)
Question 3 – Enlargement on a grid
Triangle \(T\) has vertices \((1,1)\), \((3,1)\) and \((1,2)\).
1. Enlarge \(T\) with scale factor 3 and centre \((0,0)\). Write down the coordinates of the new vertices. (2 marks)
2. Describe fully the transformation that maps the new triangle back onto \(T\). (2 marks)
Question 4 – Problem: the tree
A 1.2 m stick casts a shadow 1.8 m long. At the same time a tree casts a shadow of 13.5 m.
1. Find the height of the tree. (2 marks)
2. Later the stick's shadow is 3 m long. Find the length of the tree's shadow at that time. (2 marks)
Question 5 – Problem: the model building
A model of a building is made to scale 1 : 50.
1. The real building is 30 m tall. Find the height of the model in centimetres. (1 mark)
2. The model is 14 cm wide. Find the width of the real building in metres. (1 mark)
3. The floor area of the model is 120 cm\(^2\). Find the real floor area in square metres. (2 marks)

How to use this Year 9 similarity and enlargement test

First, revise with the similarity and enlargement 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 enlargement test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 9 similarity and enlargement 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.