Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
11–18 of 18 · Hard
Question 11
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 12
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 13
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 14
2 marks · Hard
Answer and see the solution →Out of 80 participants in a charity run, 48 ran the full course, 35 took part in the half course, and 18 ran both the full and half course.
What is the probability that a randomly selected participant ran at least one of the two courses?
Question 15
4 marks · Hard
Answer and see the solution →In a group of 50 students:
(a)[2 marks]36 study Mathematics (set M), 31 study Biology (set B), and 20 study both subjects. Draw a Venn diagram to represent this information, labelling the numbers in each region.
(b)Calculate the probability that a randomly chosen student studies:
(i)[1 mark]both Mathematics and Biology
(ii)[1 mark]Mathematics but not Biology
Question 16
4 marks · Hard
Answer and see the solution →In a club, every member either plays table tennis (T), badminton (B), or both. There are 60 members in total. 42 members play table tennis, 28 play badminton, and members play both.
Given that a member is chosen at random and is known to play table tennis, the probability that they also play badminton is .
(a)[2 marks]Express the number of members who play both sports in terms of the information above.
(b)[2 marks]Find the value of .
Question 17
11 marks · Hard
Answer and see the solution →A circular garden has a radius of metres. A path of uniform width metres is built all around the edge of the garden, forming a larger circle.
The combined area of the garden and the path is . The area of just the garden is .
(a)[4 marks]Write down an expression for the area of the ring-shaped path in terms of and , and hence form a quadratic equation in .
(b)[2 marks]Find the value of , giving your answer to 3 significant figures.
(c)[3 marks]Using your value for , solve the quadratic equation you formed in part (a) to find the width of the path. Give your answer to 2 decimal places.
(d)[2 marks]Calculate the perimeter of the outer edge of the path. Give your answer to 1 decimal place and state the unit.
Question 18
11 marks · Hard
Answer and see the solution →Two rectangles, A and B, are similar. The length of rectangle A is cm and its width is cm. The length of rectangle B is 12 cm and its width is 8 cm.
(a)[3 marks]Show that the ratio of lengths to widths for both rectangles is equal. Write a quadratic equation for .
(b)[3 marks]Solve the quadratic equation you have formed in part (a). Give both solutions for .
(c)[2 marks]Explain which value of is valid for the dimensions of rectangle A, and justify your answer.
(d)[3 marks]One side of a third rectangle C is cm, and this rectangle is similar to rectangles A and B. Find the width of rectangle C.