EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Pythagoras' Theorem 2
Pythagoras' theorem 2 · Angles and trigonometry · Lesson 5 of 7 · 15 marks · 25 minutes
Name Date
Answer all questions. Show your working. The calculator is allowed where the question says so.
Question 1 NON-CALCULATOR [3 marks]
Point A has coordinates (−2, 3) and point B has coordinates (4, 11). Work out the length of AB.
Question 2 NON-CALCULATOR [4 marks]
An isosceles triangle has sides of 13 cm, 13 cm and 10 cm. Work out the area of the triangle.
Question 3 NON-CALCULATOR [4 marks]
The diagram shows two right-angled triangles, ABC and ACD. AB = 5 cm, BC = 12 cm and CD = 5 cm. Work out the length of AD.
Question 4 CALCULATOR [4 marks]
An isosceles trapezium has parallel sides of 10 cm and 16 cm. Its perpendicular height is 8 cm. Work out the perimeter of the trapezium. Give your answer to 1 decimal place.
Answers
Check your answer only once you have written one.
Question 1 [3 marks]
Horizontal 4 − (−2) = 6, vertical 11 − 3 = 8. AB = √(6² + 8²) = √100 = 10
▸ 6 and 8 M1
▸ 6² + 8² M1
▸ 10 A1
Question 2 [4 marks]
Half the base is 5 cm. Height = √(13² − 5²) = √(169 − 25) = √144 = 12 cm. Area = ½ × 10 × 12 = 60 cm².
▸ Half base 5 used in a right-angled triangle with hypotenuse 13 P1
▸ 13² − 5² P1
▸ Height 12 P1
▸ 60 cm² A1
Question 3 [4 marks]
Triangle ABC: AC = √(5² + 12²) = √169 = 13 cm. Triangle ACD: AD = √(13² − 5²) = √144 = 12 cm.
▸ 5² + 12² P1
▸ AC = 13 P1
▸ 13² − 5² P1
▸ AD = 12 cm A1
Question 4 [4 marks]
Each end overhangs (16 − 10) ÷ 2 = 3 cm. Slant side = √(3² + 8²) = √73 = 8.544… cm. Perimeter = 10 + 16 + 2 × 8.544…= 43.1 cm.
▸ 3 found P1
▸ 3² + 8² P1
▸ 10 + 16 + 2√73 P1
▸ 43.1 cm A1