Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
81–90 of 104
Question 81
2 marks · Normal
Answer and see the solution →A spinner is spun twice. The outcomes for each spin are shown below:
First and Second Spin Outcomes First spin Second spin A A A B B A B B List all the possible outcomes of the two spins.
Question 82
2 marks · Normal
Answer and see the solution →In a class, the numbers of pets owned by each of 12 students are found:
0, 1, 0, 2, 3, 2, 1, 2, 2, 1, 3, 2
Write down the mode of the data.
Question 83
3 marks · Normal
Answer and see the solution →The table shows the time, t (minutes), several students spent revising for a test.
Revision Times Time (t, min) Frequency 0 ≤ t < 10 2 10 ≤ t < 20 5 20 ≤ t < 30 8 30 ≤ t < 40 3 Draw a frequency polygon using this data. Plot the mid-points of each group on the horizontal axis and frequency on the vertical axis.
Question 84
2 marks · Normal
Answer and see the solution →A bag contains 2 red balls and 3 blue balls. One ball is chosen at random, replaced, and another is chosen.
What is the probability that both balls are red?
Question 85
3 marks · Normal
Answer and see the solution →A bag contains 2 yellow counters and 3 green counters. One counter is taken at random, not replaced, and then a second counter is taken at random. The counters are identical except for colour.
(a)[1 mark]List all the possible ordered pairs of counters that could be taken from the bag.
(b)[2 marks]What is the probability that both counters taken are green?
Question 86
3 marks · Normal
Answer and see the solution →The grouped frequency table below shows the weights of apples, in grams, in a crate.
Weights of Apples in a Crate Weight (w, g) Frequency 60 \leq w < 80 7 80 \leq w < 100 13 100 \leq w < 120 18 120 \leq w < 140 12 (a)[1 mark]Write down the modal class of apple weights from the table.
(b)[1 mark]State the class interval that contains the median weight.
(c)[1 mark]Estimate the mean weight of the apples. Give your answer to 1 decimal place.
Question 87
5 marks · Hard
Answer and see the solution →The frequency table shows the lengths, in cm, of a sample of 40 pencils measured in a classroom.
Lengths of pencils Length (L, cm) Frequency 10 ≤ L < 12 5 12 ≤ L < 14 12 14 ≤ L < 16 17 16 ≤ L ≤ 18 6 (a)[3 marks]Estimate the mean length of the pencils. Give your answer to 2 decimal places.
(b)[1 mark]State the modal class.
(c)[1 mark]Find the class interval that contains the median length.
Question 88
5 marks · Hard
Answer and see the solution →The table shows the results of a survey into how long 60 customers spent in a shop.
Customer times in a shop Time (t, min) Frequency (f) 0 ≤ t < 10 9 10 ≤ t < 20 14 20 ≤ t < 30 22 30 ≤ t < 40 11 40 ≤ t ≤ 50 4 (a)[3 marks]Estimate the percentage of customers who spent at least 20 minutes in the shop.
(b)[1 mark]Find the modal class of the time spent.
(c)[1 mark]Calculate an estimate for the mean time spent in the shop. Give your answer to 2 decimal places.
Question 89
5 marks · Hard
Answer and see the solution →In a board game, two fair eight-sided dice are thrown, one after the other. Each die is numbered from 1 to 8.
(a)[2 marks]List all the possible outcomes if the order is important for the combination (show your working).
(b)[1 mark]What is the probability that both dice show the same number?
(c)[2 marks]Calculate the probability that the sum of the two dice is 10.
Question 90
5 marks · Hard
Answer and see the solution →A bag contains 4 white balls and 5 black balls. Two balls are drawn one after another without replacement.
(a)[2 marks]Draw a tree diagram to show all the possible outcomes of selecting each ball in order of being drawn (white/black).
(b)[2 marks]Calculate the probability that both balls are the same colour.
(c)[1 mark]What is the probability that at least one white ball is drawn?