Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
31–40 of 41 · Easy
Question 31
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 32
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 33
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 34
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 35
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).
Question 36
5 marks · Easy
Answer and see the solution →A sector of a circle has a radius of 5 cm and angle 72°. A water tank is connected to a pipe with outflow rate modelled by a reciprocal graph.
(a)[2 marks]Calculate the length of the arc of the sector. Give your answer correct to 2 decimal places.
(b)[2 marks]The volume of water in the tank at time t hours after midnight is given by the equation \[ v = \frac{600}{t} \] where v is in litres and t ≥ 1. Using t = 5, find the volume v of water left in the tank at 5 a.m.
(c)[1 mark]Explain one feature of the graph of (such as its intercept or asymptote).
Question 37
5 marks · Easy
Answer and see the solution →A solid plastic cone has height 10 cm and base radius 4 cm. The equation y = x^3 – 2x^2 models the height (in cm) y above a point, for various x values along its base.
(a)[1 mark]Write the algebraic form of the equation for the graph y = x^3 – 2x^2. What type of function is this?
(b)[2 marks]Calculate the volume of the cone. Give your answer correct to 2 decimal places. (Use π = 3.14)
(c)[1 mark]For x = 2, find the value of y using the equation y = x^3 – 2x^2.
(d)[1 mark]Find the surface area of the curved part of the cone correct to 2 decimal places.
Question 38
5 marks · Easy
Answer and see the solution →Two solids, A and B, are similar cones. The radius of cone A is cm and the radius of cone B is cm.
The equation of a reciprocal function is given by , where .
(a)[2 marks]Explain how you would use the scale factor between cones A and B to find the ratio of their volumes.
(b)[1 mark]Find the ratio of the volume of cone B to the volume of cone A.
(c)[1 mark]The height of cone B (in cm) is substituted into the reciprocal function above. If the height of cone B is 15 cm, calculate the value of .
(d)[1 mark]Explain what happens to the value of as (the height of cone B) increases. Give a reason using the equation.
Question 39
5 marks · Easy
Answer and see the solution →The function models the height (in metres) of a walkway at position metres, for .
(a)[2 marks]Using the graph of , state the values of for which the walkway is below ground level (i.e. where ).
(b)[3 marks]Solve the inequality . Write your answer as a set of values of .
Question 40
5 marks · Easy
Answer and see the solution →A rectangular field is 20 metres longer than it is wide. The area of the field is 1200 m².
(a)[3 marks]Let the width of the field be metres. Form a quadratic equation in \( x \ ) for the area of the field and solve it to find the width and length of the field.
(b)[2 marks]The width you obtained in part (a) is used as the input in the function . Work out the value of , giving your answer to 2 decimal places.