Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
81–90 of 104
Question 81
3 marks · Normal
Answer and see the solution →Sunny records whether it rains on each of 12 days in July. Her results are:
Rain on 12 days in July Day 1 2 3 4 5 6 7 8 9 10 11 12 Rain? ✓ ✗ ✓ ✗ ✓ ✗ ✗ ✓ ✓ ✗ ✓ ✓ (a)[2 marks]Estimate the experimental probability that it rains on a randomly chosen day.
(b)[1 mark]Estimate how many days in a 30-day month you would expect to have rain.
Question 82
2 marks · Normal
Answer and see the solution →Write down all the possible outcomes when a coin is tossed and a 4-sided spinner (numbered 1, 2, 3, 4) is spun. How many possible outcomes are there in total?
Question 83
4 marks · Normal
Answer and see the solution →A regular 6-sided die is rolled. Find the probability that the number shown is:
(a)[2 marks](i) a prime number
(ii) a number greater than 3
(b)[2 marks]Work out the probability that the number is a prime number or greater than 3.
Question 84
2 marks · Normal
Answer and see the solution →A two-way table shows the numbers of Year 11 students who study French and Spanish.
Language study in Year 11 French No French Total Spanish 12 5 17 No Spanish 18 7 25 Total 30 12 42 A student from this group is chosen at random. Find:
(a)[1 mark]The probability that the student studies both French and Spanish.
(b)[1 mark]Given that a student studies French, what is the probability that they also study Spanish?
Question 85
4 marks · Normal
Answer and see the solution →A bag contains 5 red balls and 3 blue balls. Two balls are taken out one after the other, without replacement.
(a)[2 marks]Draw a tree diagram to represent all possible outcomes.
(b)[2 marks]Calculate the probability that both balls are the same colour.
Question 86
3 marks · Normal
Answer and see the solution →A coin is tossed 10 times. The results are as follows:
Coin toss results Toss number 1 2 3 4 5 6 7 8 9 10 Result H H T H T T H H T T a) Plot a relative frequency diagram for getting a head after each toss (on the vertical axis, plot the relative frequency of heads after each toss).
b) What value does the experimental probability appear to be approaching?
(a)[2 marks]Draw a relative frequency diagram (graph) for heads after each toss.
(b)[1 mark]What value does the probability appear to be approaching?
Question 87
5 marks · Hard
Answer and see the solution →A club has 80 members. The table summarizes the ages of its members:
Age (years) Number of members 10–19 23 20–34 18 35–49 25 50–64 9 65–80 5 The mid-interval values for the age groups are: 14.5, 27, 42, 57, and 72.5 respectively.
(a)[3 marks]Estimate the mean age of the members. Give your answer to 1 decimal place.
(b)[2 marks]A member is chosen at random. Estimate the probability that this member is younger than 35 years old.
Question 88
6 marks · Hard
Answer and see the solution →A six-sided die is rolled 48 times. The frequencies for each face are shown below:
Face 1 2 3 4 5 6 Frequency 10 9 12 6 7 4 (a) Calculate the experimental probability of rolling a 5.
(b) If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
(c) Based on the table, discuss whether the die is likely to be fair, giving a reason for your answer.
(a)[2 marks]Calculate the experimental probability of rolling a 5.
(b)[2 marks]If the die is fair, calculate the expected frequency of rolling a 5 in 48 throws.
(c)[2 marks]Based on the frequencies in the table, discuss whether the die is likely to be fair, giving a reason for your answer.
Question 89
7 marks · Hard
Answer and see the solution →The Venn diagram below shows the results of a survey of 100 students about whether they prefer football (F), hockey (H), or tennis (T).
Venn diagram of student sports preferences The numbers indicate how many students are in each region. The '?' represents the number of students who did not prefer any of these sports.
(a)[1 mark]Calculate the value of '?'.
(b)[2 marks]Find the probability that a randomly selected student preferred at least two of the sports.
(c)[2 marks]Given that a randomly selected student preferred hockey, find the probability that the student also preferred football.
(d)[2 marks]A student is chosen at random. What is the probability that this student preferred exactly one sport?
Question 90
3 marks · Easy
Answer and see the solution →The curve y = x^2 - 9 cuts the x-axis at two points.
(a)[2 marks]Solve the equation x^2 - 9 = 0 to find the x-coordinates where the curve cuts the x-axis.
(b)[1 mark]On the grid below, sketch the graph and indicate the points where it crosses the x-axis.