Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
21–30 of 39 · Easy
Question 21
1 mark · Easy
Answer and check →In a cuboid, the length is 3 cm, the width is 4 cm, and the height is 5 cm. Work out the length of the space diagonal (the longest line from one corner to the opposite corner) to 1 decimal place.
Question 22
2 marks · Easy
Answer and see the solution →In a square-based pyramid, each base edge is 6 cm and the vertex is 8 cm vertically above the centre of the base. Calculate, to 3 significant figures, the length of the slope from a corner of the base to the vertex.
Question 23
2 marks · Easy
Answer and see the solution →Explain how to use Pythagoras’ theorem to calculate the direct distance from one corner of a cuboid to the opposite corner (the space diagonal).
Question 24
3 marks · Easy
Answer and see the solution →A triangular prism has a right-angled triangle as its cross-section with side lengths 5 cm, 12 cm and 13 cm. The prism is 8 cm long.
(a)[2 marks]Calculate the length of the diagonal joining one vertex at the base to the opposite vertex at the top, across the full length of the prism.
(b)[1 mark]Find, to 1 decimal place, the angle that this diagonal makes with the base of the prism.
Question 25
3 marks · Easy
Answer and see the solution →The table below shows the lengths (in cm) of the edges of three different cuboids.
Edge lengths of cuboids (in cm) Cuboid Length Width Height A 4 3 9 B 6 5 2 C 8 7 3 Work out the length of the longest space diagonal for each cuboid, giving your answers to 1 decimal place.
Question 26
2 marks · Easy
Answer and see the solution →The grouped frequency table below shows the masses of apples in a box.
Mass (g) Frequency 60 < m ≤ 80 6 80 < m ≤ 100 18 100 < m ≤ 120 12 Calculate the frequency density for the 80 < m ≤ 100 class.
Question 27
2 marks · Easy
Answer and see the solution →A histogram displays the time (in minutes) customers spend in a shop. The bar for 0–10 minutes has a frequency density of 3, and the bar for 10–30 minutes has a frequency density of 2.
Which interval contains more customers? Explain your answer.
Question 28
3 marks · Easy
Answer and see the solution →The frequency table below shows the time (in minutes) spent by people waiting at a station.
Waiting time (min) Frequency 0 < t ≤ 2 5 2 < t ≤ 5 15 5 < t ≤ 10 20 Complete the table below to include the class widths and frequency densities for each group.
Complete the missing values. Waiting time (min) Frequency Class width Frequency density 0 < t ≤ 2 5 2 < t ≤ 5 15 5 < t ≤ 10 20 Question 29
1 mark · Easy
Answer and see the solution →A histogram shows a bar for 20 < x ≤ 40 with frequency density 2 and class width 20. What is the frequency for this bar?
Question 30
1 mark · Easy
Answer and see the solution →Here are two histograms showing the heights of plants in two different greenhouses, A and B.
Histogram for Greenhouse A Histogram for Greenhouse B Which greenhouse has more plants with heights between 40 cm and 60 cm? Write your answer: Greenhouse A or Greenhouse B.