Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
41–47 of 47 · Normal
Question 41
5 marks · Normal
Answer and see the solution →(a) Express 96 as a product of its prime factors in index form.
(b) The product of two numbers is 288. One of the numbers is 16. Using prime factors, find the other number.
(c) Factorise the expression completely.
(a)[2 marks]Express 96 as a product of its prime factors in index form.
(b)[1 mark]The product of two numbers is 288. One of the numbers is 16. Using prime factors, find the other number.
(c)[2 marks]Factorise the expression completely.
Question 42
4 marks · Normal
Answer and see the solution →(a) The heights (in metres) of hibiscus plants in a garden are grouped in the table below.
Heights of hibiscus plants. Height (m) Frequency 0.5 ≤ h < 1.0 4 1.0 ≤ h < 1.5 7 1.5 ≤ h < 2.0 11 2.0 ≤ h < 2.5 8 Estimate the mean height of the plants.
(b) Write down the modal class for this data.
(c) Expand and simplify .
(a)[2 marks]Estimate the mean height of the plants.
(b)[1 mark]Write down the modal class for this data.
(c)[1 mark]Expand and simplify .
Question 43
4 marks · Normal
Answer and see the solution →(a) A train travels 45 km at a constant speed in 40 minutes. Calculate its average speed in km/h.
(b) On the axes below, sketch a possible distance–time graph for this journey.
(c) Solve the equation \( 2x = 7 - x \ ).
(a)[2 marks]Calculate the average speed in km/h.
(b)[1 mark]On the axes below, sketch a possible distance–time graph for this journey.
(c)[1 mark]Solve \( 2x = 7 - x \ ) for x.
Question 44
4 marks · Normal
Answer and see the solution →(a) Anna shares £136 between herself and two friends in the ratio 4 : 3 : 1. Work out how much each person receives.
(b) The ratio of the lengths of two similar rectangles is 2 : 5. If the area of the smaller rectangle is 16 cm^2, find the area of the larger rectangle.
(a)[3 marks]Anna shares £136 between herself and two friends in the ratio 4 : 3 : 1. Work out how much each person receives.
(b)[1 mark]If the area of the smaller rectangle is 16 cm^2, what is the area of the larger?
Question 45
5 marks · Normal
Answer and see the solution →(a) Express 84 and 126 as products of their prime factors in index form.
(b) Find the HCF and LCM of 84 and 126.
(c) An event A and an event B are combined. Event A has 3 outcomes, event B has 4 outcomes. List the total number of possible combined outcomes.
(a)[2 marks]Express 84 and 126 as products of their prime factors in index form.
(b)[2 marks]Find the HCF and LCM of 84 and 126.
(c)[1 mark]List the total number of possible combined outcomes.
Question 46
4 marks · Normal
Answer and see the solution →(a) Solve for x:
(b) Write down the value of x if .
(c) The line y = 2x + 1 passes through the point (p, 11). Write down the value of p.
(a)[2 marks]Solve for x:
(b)[1 mark]What is x if ?
(c)[1 mark]The line y = 2x + 1 passes through the point (p, 11). Write down the value of p.
Question 47
4 marks · Normal
Answer and see the solution →(a) The probability of picking a red bead from bag A is 0.4. The probability of picking a red bead from bag B is 0.6. Each bag contains only red and blue beads. A bead is picked from each bag. What is the probability both beads are red?
(b) If the mean of four numbers is 12.5, what is their total?
(c) Write down all the factors of 30.
(a)[1 mark]Probability both beads are red.
(b)[1 mark]If the mean of four numbers is 12.5, what is their total?
(c)[2 marks]List all the factors of 30.