Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
1–10 of 21 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A school is holding a sports day with relay races. There are 198 boys and 135 girls. Each relay team must have the same number of boys and the same number of girls, and no students can be left out.
Find the greatest number of teams that can be formed and state how many boys and how many girls would be in each team.
Question 2
5 marks · Hard
Answer and see the solution →Let N = 2940.
(a)[2 marks]Express 2940 as a product of its prime factors in index form.
(b)[2 marks]Given that M = 2940 × 42, write M as a product of its prime factors in index form.
(c)[1 mark]Hence or otherwise, find the highest common factor (HCF) of 2940 and 42.
Question 3
4 marks · Hard
Answer and see the solution →Three bells ring together at 09:00. The first bell rings every 36 minutes, the second every 54 minutes, and the third every 81 minutes.
What is the next time all three bells will ring together? Show your working clearly.
(a)[3 marks]Find the lowest common multiple (LCM) of 36, 54, and 81.
(b)[1 mark]State the next time (in hours and minutes) after 09:00 that all three bells will ring together.
Question 4
4 marks · Hard
Answer and see the solution →A number n is such that it has exactly 4 positive factors, and n is less than 100.
List all possible values of n and explain your reasoning.
(a)[2 marks]List all the numbers less than 100 with exactly 4 positive factors.
(b)[2 marks]Explain how you determined these numbers.
Question 5
4 marks · Hard
Answer and see the solution →A rectangular flower bed has a width that is 5 m less than its length. The area is 84 m².
Let the length of the bed be m. Form a quadratic equation for and solve it to find the dimensions of the flower bed.
Question 6
3 marks · Hard
Answer and see the solution →Write down an algebraic identity involving squares that is always true for any value of , and show why it is always true by expanding or simplifying it.
Question 7
4 marks · Hard
Answer and see the solution →Solve the following system of simultaneous equations using algebraic methods (substitution or elimination):
Question 8
4 marks · Hard
Answer and see the solution →Below is an extract from a distance–time graph that describes part of Rob's run:
Distance–time graph for Rob's run (part) Describe what Rob does between each of these time intervals: (a) 0–6 min, (b) 13–18 min, (c) 18–25 min, and (d) 25–30 min.
(a)[1 mark]0–6 min:
(b)[1 mark]13–18 min:
(c)[1 mark]18–25 min:
(d)[1 mark]25–30 min:
Question 9
4 marks · Hard
Answer and see the solution →Olivia walks from her home to the post office and back. Her journey is shown on this distance–time graph.
Olivia's walk (distance–time graph) a) Work out Olivia's speed on her journey from home to the post office.
b) Explain why Olivia takes more time to return home compared to her outward journey.
(a)[2 marks]Outward journey speed:
(b)[2 marks]Reason for increased return time:
Question 10
4 marks · Hard
Answer and see the solution →A distance–time graph for two people, Amira and Ben, is shown below. Both walk from the same starting point to the same destination.
Amira and Ben's walk (distance–time) a) Compare the journey times for Amira and Ben to reach the destination.
b) Find the time interval during which Ben is stationary and work out how far he is from the start during this time.
c) Calculate the speed (in km/h) for Amira over her whole journey.
(a)[1 mark]Time taken for Amira (min):
Time taken for Ben (min):
(b)[1 mark]Ben stationary from minute ___ to ___. Distance from start (km):
(c)[2 marks]Speed of Amira (km/h):