EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Pythagoras' Theorem 1
Pythagoras' theorem 1 · Angles and trigonometry · Lesson 4 of 7 · 10 marks · 20 minutes
Name Date
Answer all questions. Show your working. The calculator is allowed where the question says so.
Question 1 NON-CALCULATOR [2 marks]
A right-angled triangle has shorter sides of 7 cm and 24 cm. Work out the length of the hypotenuse.
Question 2 CALCULATOR [3 marks]
A ladder 5 m long leans against a vertical wall. The foot of the ladder is on horizontal ground, 1.8 m from the wall. How far up the wall does the ladder reach? Give your answer to 2 decimal places.
Question 3 NON-CALCULATOR [2 marks]
A triangle has sides of 9 cm, 12 cm and 16 cm. Is it a right-angled triangle? Show how you decide.
Question 4 NON-CALCULATOR [3 marks]
A rectangular field is 20 m long and 15 m wide. Jo walks diagonally across it, from one corner to the opposite corner. Tom walks along two sides. How much further does Tom walk than Jo?
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
7² + 24² = 49 + 576 = 625, √625 = 25 cm
▸ 7² + 24² M1
▸ 25 cm A1
Question 2 [3 marks]
h² = 5² − 1.8² = 25 − 3.24 = 21.76, so h = √21.76 = 4.6647…= 4.66 m
▸ 5² − 1.8² M1
▸ √21.76 M1
▸ 4.66 A1
Question 3 [2 marks]
9² + 12² = 81 + 144 = 225. 16² = 256. 225 ≠ 256, so it is not right-angled.
▸ 9² + 12² = 225 and 16² = 256 M1
▸ Not right-angled, with the comparison C1
Question 4 [3 marks]
Jo: √(20² + 15²) = √(400 + 225) = √625 = 25 m. Tom: 20 + 15 = 35 m. Tom walks 35 − 25 = 10 m further.
▸ 20² + 15² P1
▸ 25 m P1
▸ 10 m A1