Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
31–40 of 47 · Normal
Question 31
3 marks · Normal
Answer and see the solution →In a solid with a rectangular base 7 cm × 10 cm, a point P is vertically above the centre of the base at a height of 12 cm. Explain how you would use trigonometry to find the angle between the edge from P to a base corner and the base plane.
Question 32
4 marks · Normal
Answer and see the solution →The diagram shows a rectangular box (cuboid) with length 7 cm, width 5 cm and height 12 cm.
Diagram of cuboid ABCDEFGH Calculate the length of the diagonal from point A to point G (opposite corners of the box). Give your answer correct to 3 significant figures.
Question 33
2 marks · Normal
Answer and see the solution →A grouped frequency table shows the lengths of sticks (in cm), grouped as follows:
Length (cm) Frequency 10 < l \leq 15 5 15 < l \leq 20 8 20 < l \leq 25 7 What does the area of each bar in a histogram drawn for this data represent?
Question 34
3 marks · Normal
Answer and see the solution →The table shows the time (in minutes) spent online by a group of students one evening.
Time (minutes) Frequency 0 < t \leq 10 4 10 < t \leq 20 16 20 < t \leq 40 20 The first bar on the corresponding histogram has a width of 10 units and a height of 0.4. Work out the frequency density for each group and use them to find the height of the second bar.
Question 35
4 marks · Normal
Answer and see the solution →The grouped frequency table shows the masses of parcels delivered in one day.
(a)[2 marks]Complete the following table by calculating the class width and the frequency density for each group.
Mass (kg) Frequency Class width Frequency density 0 < m \leq 2 10 2 < m \leq 5 24 5 < m \leq 9 16 (b)[2 marks]Use your table to draw a histogram for this data. Label your axes clearly.
Question 36
2 marks · Normal
Answer and see the solution →Two histograms represent the marks for two different exams, Exam X and Exam Y. The modal class of Exam X is 30–40 marks, while the modal class of Exam Y is 50–60 marks.
Which exam did more students score higher marks in, and how can you tell from the histograms?
Question 37
3 marks · Normal
Answer and see the solution →A grouped frequency table shows the heights (in cm) of a sample of plants:
Height (cm) Frequency 0 < h \leq 10 4 10 < h \leq 20 10 20 < h \leq 40 12 Work out the frequency density for each group.
Question 38
3 marks · Normal
Answer and see the solution →A histogram shows the times taken by 60 runners to complete a race. The modal class interval is 40–50 minutes.
Explain, using evidence from the histogram, how you can estimate the number of runners who finished in less than 40 minutes.
Question 39
3 marks · Normal
Answer and see the solution →The histograms below each show the distribution of the finishing times (in minutes) for two groups, Group P and Group Q, in a 10 km race. Both groups contain exactly 60 runners. Both axes are labelled the same and the scales match.
Histogram distributions for Group P and Group Q Table: Histogram class data for Group P and Group Q Time (min) Frequency density (P) Frequency density (Q) 30 < t ≤ 40 1.8 0.7 40 < t ≤ 50 1.2 2.0 50 < t ≤ 60 0.7 1.3 60 < t ≤ 70 0.3 0.4 (a)[1 mark]Which group had a greater proportion of fast runners? Give a reason for your answer.
(b)[2 marks]Which group had finishing times more spread out? Explain why using the histogram.
Question 40
4 marks · Normal
Answer and see the solution →The histogram below shows the time taken, in minutes, for a group of students to complete a test.
Histogram for test completion times The class widths for all intervals are equal except for the last bar, which covers a wider interval.
(a)[1 mark]Use the histogram to write down the class width for the interval 50 < t ≤ 60.
(b)[1 mark]Work out the frequency (number of students) for the interval 40 < t ≤ 50.
(c)[2 marks]Write down the total number of students in the group.