Year 9 Pythagoras' theorem test to download as PDF

This Year 9 Pythagoras' theorem 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 – Using the theorem
Find the lengths marked with a letter. Give answers to 1 decimal place if not exact.
1. A right-angled triangle has shorter sides 7 cm and 24 cm. Find the hypotenuse. (1 mark)
2. The shorter sides are 6 cm and 9 cm. Find the hypotenuse. (1 mark)
3. The hypotenuse is 15 cm and one side is 9 cm. Find the other side. (1 mark)
4. The hypotenuse is 8 cm and one side is 5 cm. Find the other side. (1 mark)
Question 2 – Right angle or not?
Decide whether each triangle is right-angled. Show your working.
1. Sides 8 cm, 15 cm, 17 cm. (2 marks)
2. Sides 5 cm, 6 cm, 8 cm. (2 marks)
Question 3 – Distance on a grid
Find the distance between each pair of points.
1. \(A(2,1)\) and \(B(8,9)\) (2 marks)
2. \(C(-3,4)\) and \(D(5,-2)\) (2 marks)
Question 4 – Problem: the ladder
A ladder 6.5 m long rests against a vertical wall. The ladder reaches 6 m up the wall.
1. How far is the foot of the ladder from the wall? (2 marks)
2. The foot is moved out to 3.9 m from the wall. How high up the wall does it now reach? (2 marks)
Question 5 – Problem: the field
A rectangular field is 60 m long and 80 m wide. Dan walks along two sides from one corner to the opposite corner. Eve walks straight across along the diagonal.
1. Find the length of the diagonal. (1 mark)
2. How much further does Dan walk? (1 mark)
3. Both walk at 1.5 m per second. Find how long each takes, to the nearest second. (2 marks)

How to use this Year 9 Pythagoras' theorem test

First, revise with the Pythagoras' theorem 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 Pythagoras' theorem test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 9 Pythagoras' theorem 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.