Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
11–20 of 21 · Hard
Question 11
4 marks · Hard
Answer and see the solution →A ladder leans against a vertical wall and reaches a point 7.2 m above the ground. The foot of the ladder is 2.7 m from the base of the wall.
Calculate the angle, to the nearest degree, that the ladder makes with the ground.
(a)[4 marks]Find the angle described and show your full working.
(b)[0 marks](c)[0 marks]Question 12
5 marks · Hard
Answer and see the solution →(a)[4 marks]The diagram below shows triangle PQR. PQ = 9.0 cm, PR = 6.2 cm and angle QPR = 48°.
Triangle PQR with PQ = 9.0 cm, PR = 6.2 cm, angle QPR = 48°. Calculate the length QR, giving your answer correct to 3 significant figures.
(b)[1 mark]Write down which side in triangle PQR is the hypotenuse relative to angle QPR.
Question 13
3 marks · Hard
Answer and see the solution →A helicopter hovers above a straight road. From a point 120 m along the road from the point directly below the helicopter, the angle of elevation to the helicopter is 28°.
Calculate the height of the helicopter above the ground. Give your answer to the nearest metre.
Question 14
4 marks · Hard
Answer and see the solution →Explain, using step-by-step reasoning and a diagram, how you would use Pythagoras’ Theorem to check whether a triangle with sides 10 cm, 16 cm, and 18 cm is a right-angled triangle.
Question 15
5 marks · Hard
Answer and see the solution →The frequency table shows the lengths, in cm, of a sample of 40 pencils measured in a classroom.
Lengths of pencils Length (L, cm) Frequency 10 ≤ L < 12 5 12 ≤ L < 14 12 14 ≤ L < 16 17 16 ≤ L ≤ 18 6 (a)[3 marks]Estimate the mean length of the pencils. Give your answer to 2 decimal places.
(b)[1 mark]State the modal class.
(c)[1 mark]Find the class interval that contains the median length.
Question 16
5 marks · Hard
Answer and see the solution →The table shows the results of a survey into how long 60 customers spent in a shop.
Customer times in a shop Time (t, min) Frequency (f) 0 ≤ t < 10 9 10 ≤ t < 20 14 20 ≤ t < 30 22 30 ≤ t < 40 11 40 ≤ t ≤ 50 4 (a)[3 marks]Estimate the percentage of customers who spent at least 20 minutes in the shop.
(b)[1 mark]Find the modal class of the time spent.
(c)[1 mark]Calculate an estimate for the mean time spent in the shop. Give your answer to 2 decimal places.
Question 17
5 marks · Hard
Answer and see the solution →In a board game, two fair eight-sided dice are thrown, one after the other. Each die is numbered from 1 to 8.
(a)[2 marks]List all the possible outcomes if the order is important for the combination (show your working).
(b)[1 mark]What is the probability that both dice show the same number?
(c)[2 marks]Calculate the probability that the sum of the two dice is 10.
Question 18
5 marks · Hard
Answer and see the solution →A bag contains 4 white balls and 5 black balls. Two balls are drawn one after another without replacement.
(a)[2 marks]Draw a tree diagram to show all the possible outcomes of selecting each ball in order of being drawn (white/black).
(b)[2 marks]Calculate the probability that both balls are the same colour.
(c)[1 mark]What is the probability that at least one white ball is drawn?
Question 19
7 marks · Hard
Answer and see the solution →A factory buys two lengths of cable of 168 m and 252 m. They are to be cut into equal-length pieces with no cable left over.
(a)[2 marks]Express 168 and 252 as products of their prime factors.
(b)[2 marks]Find the greatest possible length of each piece.
(c)[3 marks]The total number of pieces obtained from both cables is used to buy identical boxes. Each box costs £x, and the total cost is £30 more than the value of x squared. Write down an equation in x, and solve it.
Question 20
6 marks · Hard
Answer and see the solution →Freya measured the heights, in cm, of 60 sunflowers in her garden. The results are grouped in the table below:
Sunflower heights Height (cm) Frequency 60 ≤ h < 80 8 80 ≤ h < 100 15 100 ≤ h < 120 22 120 ≤ h < 140 12 140 ≤ h < 160 3 (a)[3 marks]Estimate the mean height of the sunflowers.
(b)[1 mark]State the group that contains the median height.
(c)[2 marks]The group with the highest frequency is selected for a science project. The average speed at which these sunflowers grew from 0 cm to the lower bound of the group is 2 cm per day. Calculate how many days it took for them to reach the lower bound height.