Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
71–80 of 107
Question 71
4 marks · Hard
Answer and see the solution →A closed cone has a base radius of 6 cm and a perpendicular height of 8 cm.
(a)[1 mark]Calculate the slant height of the cone. Give your answer to 3 significant figures.
(b)[3 marks]Calculate the total surface area of the cone. Give your answer to 3 significant figures.
Question 72
4 marks · Hard
Answer and see the solution →Two solid spheres are similar. The surface area of the smaller sphere is 48 cm² and the surface area of the larger sphere is 192 cm².
(a)[2 marks]Explain how you would find the ratio of the radii of the two spheres.
(b)[2 marks]Using your answer to (a), work out the ratio of the volumes of the smaller sphere to the larger sphere.
Question 73
2 marks · Hard
Answer and see the solution →Find the length of the arc of a circle with radius 12 cm and angle 40° at the centre. Give your answer to 2 decimal places.
Question 74
1 mark · Easy
Answer and check →A group of 40 students is surveyed. 18 students play tennis (set T), and 6 students play both tennis (T) and basketball (B). What is the number of students who play both tennis and basketball, n(T ∩ B)?
Question 75
2 marks · Easy
Answer and see the solution →In a club of 50 members, 32 members play chess (set C), 19 members play cards (set D), and 7 members play both chess and cards. Use set notation to calculate the number of members who play only chess.
Question 76
2 marks · Easy
Answer and see the solution →Set A = {students who play guitar}, Set B = {students who play piano}, in a class of 28 students. Explain using set notation how you would find the number of students who play either guitar or piano, but not both.
Question 77
3 marks · Easy
Answer and see the solution →In a survey of 60 people:
• 36 people like apples (A),
• 24 people like bananas (B),
• 12 people like both apples and bananas.
A person is chosen at random from the survey.
(a)[1 mark]Work out the probability that the person likes both apples and bananas.
(b)[2 marks]Work out the probability that the person likes bananas given that they like apples.
Question 78
3 marks · Easy
Answer and see the solution →The Venn diagram below shows information about a class of 50 students and whether they have a pet cat (C) or a pet dog (D).
Venn diagram for pets (a)[1 mark]How many students have only a pet cat?
(b)[1 mark]What is the probability that a student chosen at random has both a pet cat and a pet dog?
(c)[1 mark]How many students do not have a pet cat or a pet dog?
Question 79
1 mark · Easy
Answer and see the solution →Let S = {students who play a musical instrument}, U = {all students in class}. Write, in set notation, the set of students who do not play a musical instrument.
Question 80
2 marks · Easy
Answer and see the solution →In a class, n(A) = 18, n(B) = 12, and n(A ∩ B) = 5. Find n(A ∪ B).