Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
91–100 of 104
Question 91
4 marks · Easy
Answer and see the solution →Express 60 as a product of its prime factors. Then solve the equation 2x + 35 = 125.
(a)[2 marks]Express 60 as a product of its prime factors in index form.
(b)[2 marks]Solve the equation 2x + 35 = 125.
Question 92
4 marks · Easy
Answer and see the solution →2. A cyclist travels for 20 minutes at a speed of 12 km/h and then for 40 minutes at a speed of 18 km/h.
(a)[1 mark]Write the time taken for each part of the journey in hours.
(b)[2 marks]Calculate the total distance travelled.
(c)[1 mark]What is the cyclist's average speed for the whole journey?
Question 93
4 marks · Easy
Answer and see the solution →3. A triangle has sides of lengths 6 cm, 8 cm and 10 cm.
(a)[2 marks]Is this a right triangle? Explain your answer using Pythagoras' Theorem.
(b)[2 marks]Write all the factors of 10.
Question 94
4 marks · Easy
Answer and see the solution →A triangle has sides of lengths 9 cm, 12 cm and 15 cm.
(a)[2 marks]State whether this triangle is a right triangle. Show your reasoning using Pythagoras’ Theorem.
(b)[2 marks]List all the multiples of 9 up to 36.
Question 95
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 96
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 97
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 98
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 99
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 100
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.