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Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit

Unit 9

105 practice questions

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Practice questions

81–90 of 105

  1. Question 81

    2 marks · Normal

    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?

    Answer and see the solution →

  2. Question 82

    3 marks · Normal

    A grouped frequency table shows the heights (in cm) of a sample of plants:

    Height (cm)Frequency
    0 < h \leq 104
    10 < h \leq 2010
    20 < h \leq 4012

    Work out the frequency density for each group.

    Answer and see the solution →

  3. Question 83

    3 marks · Normal

    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.

    Answer and see the solution →

  4. Question 84

    3 marks · Normal

    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: 10 km Race Finishing Times00.511.52Group P: 30<t≤40Group Q: 30<t≤40Group P: 40<t≤50Group Q: 40<t≤50Group P: 50<t≤60Group Q: 50<t≤60Group P: 60<t≤70Group Q: 60<t≤70Finishing time (minutes)Frequency densityHistogram: 10 km Race Finishing Times
    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 ≤ 401.80.7
    40 < t ≤ 501.22.0
    50 < t ≤ 600.71.3
    60 < t ≤ 700.30.4
    (a)

    Which group had a greater proportion of fast runners? Give a reason for your answer.

    [1 mark]
    (b)

    Which group had finishing times more spread out? Explain why using the histogram.

    [2 marks]
    Answer and see the solution →

  5. Question 85

    4 marks · Normal

    The histogram below shows the time taken, in minutes, for a group of students to complete a test.

    Test Completion Times00.61.21.82.420 < t ≤ 3030 < t ≤ 4040 < t ≤ 5050 < t ≤ 60Time taken (minutes)Frequency densityTest Completion Times
    Histogram for test completion times

    The class widths for all intervals are equal except for the last bar, which covers a wider interval.

    (a)

    Use the histogram to write down the class width for the interval 50 < t ≤ 60.

    [1 mark]
    (b)

    Work out the frequency (number of students) for the interval 40 < t ≤ 50.

    [1 mark]
    (c)

    Write down the total number of students in the group.

    [2 marks]
    Answer and see the solution →

  6. Question 86

    2 marks · Hard

    The grouped frequency table below shows the ages of people attending a workshop.

    Age (years)Frequency
    10 < a \leq 208
    20 < a \leq 3016
    30 < a \leq 5012

    What is the frequency density for the group 20 < a \leq 30?

    Answer and see the solution →

  7. Question 87

    4 marks · Hard

    The histogram shows the times taken by 60 students to finish a computer game.

    Game Completion Times01230-1010-1515-2525-40Time (minutes)Frequency densityGame Completion Times

    Calculate the total number of students who finished the game in more than 10 minutes but no more than 25 minutes.

    Answer and see the solution →

  8. Question 88

    4 marks · Hard

    The histograms below show the distribution of journey times (in minutes) to school for two local schools, Alpha and Beta. Both schools had the same total number of students surveyed.

    bar graph of Frequency density against Journey time (minutes)00.511.522.50–10 (A)10–20 (A)20–40 (A)0–15 (B)15–35 (B)35–60 (B)Journey time (minutes)Frequency density
    Journey Times to School

    Compare the two distributions. Give two differences and what they show about the journey times for Alpha and Beta.

    Answer and see the solution →

  9. Question 89

    8 marks · Easy

    A function is defined by the curve . The diagram below shows part of this curve.

    (a)
    Geometry diagram with points O, A, BOABOAB
    The curve \( y = x^2 \) and two highlighted points.

    Find the gradient of the curve at the point A.

    (i)

    Draw a tangent at point A and estimate its gradient. Show your working.

    [3 marks]
    (b)

    A cuboid has an edge OA of 6 cm and OB of 8 cm. OC is perpendicular to both OA and OB and has a length of 5 cm. O, A, B, and C are adjacent vertices joining at one corner.

    Use Pythagoras’ theorem in 3D to find the length of the diagonal OC.

    (i)

    Calculate the length OC, giving your answer correct to one decimal place.

    [2 marks]
    (c)

    Explain how the ideas of gradient (from part a) and using Pythagoras’ theorem in three dimensions (from part b) are similar when working with curves and 3D shapes.

    [3 marks]
    Answer and see the solution →

  10. Question 90

    8 marks · Easy

    The graph of for is sketched below.

    (a)
    Geometry diagram with points A, B, C
    Graph sketch of \( y = f(x) \)

    Write down the equation of the graph reflected in the x-axis.

    [2 marks]
    (b)

    A right-angled triangle has sides AB = 4 cm, BC = 3 cm and the right angle is at B. The triangle is a face on a cuboid.

    Calculate the length AC.

    [2 marks]
    (c)

    The cuboid from part b has a height BD = 8 cm, perpendicular to triangle ABC. Find the length from A to D.

    [2 marks]
    (d)

    Describe how the transformation in part a and the 3D length calculation in part c both involve symmetry or distance.

    [2 marks]
    Answer and see the solution →