Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 2
105 practice questions
Topics covered
Practice questions
11–19 of 19 · Hard
Question 11
4 marks · Hard
Answer and see the solution →The diagram below shows a circle with centre O. The point M is the midpoint of chord AB. AB = 14 cm and OM = 6 cm.
Circle with OM perpendicular to chord AB. Work out the radius of the circle.
Question 12
5 marks · Hard
Answer and see the solution →The diagram below shows a tangent to the circle with centre O. P is the point of contact, and the radius OP is 8 cm. The tangent TP meets a straight line passing through the centre O at point T, such that angle OTP = 35°.
Circle with tangent, radius, and angle marked. (a)[1 mark]State the relationship between the tangent and the radius at point P.
(b)[4 marks]Calculate the length TP. Give your answer to 3 significant figures.
Question 13
3 marks · Hard
Answer and see the solution →A pie chart is used to show the distribution of favourite types of movies chosen by 60 students at a school. The angles for three out of four sections are given below:
Pie Chart Angles for Movie Types Genre Angle Action 120° Comedy 90° Animation 60° Drama ? Work out the number of students who selected 'Drama' as their favourite genre and explain clearly how you found your answer.
Question 14
5 marks · Hard
Answer and see the solution →A group of 25 students were each asked how many books they had read in the last month. Their responses are summarised below:
(a)[2 marks]Construct a tally chart for the following data about the number of books read:
- Student 1–5
- 0, 2, 1, 2, 3
- Student 6–10
- 4, 2, 1, 0, 2
- Student 11–15
- 3, 2, 2, 5, 1
- Student 16–20
- 2, 3, 3, 2, 4
- Student 21–25
- 1, 2, 0, 3, 2
Books read by each student
(b)[2 marks]State both the mode and the median number of books read.
(c)[1 mark]Based on your tally chart, comment briefly on the reading habits of this group.
Question 15
4 marks · Hard
Answer and see the solution →The table shows the number of drinks of each type sold at a café in one day.
Drink Number sold Tea 28 Coffee 42 Hot chocolate 14 Smoothie 16 (a)[1 mark]Calculate the percentage of total drinks sold that were coffee.
(b)[2 marks]Draw an accurate bar chart to display this information. Clearly label your axes.
(c)[1 mark]Suggest a suitable average to summarise the number of each drink sold, giving a reason based on the data.
Question 16
5 marks · Hard
Answer and see the solution →A television station surveyed 120 viewers about their favourite type of programme: Sports, News, Drama, or Comedy. Their results are summarised as follows:
Programme type Frequency Sports 37 News 19 Drama 46 Comedy 18 (a)[1 mark]Calculate the mean number of viewers per programme type.
(b)[2 marks]The head of the station claims the survey shows most viewers like Drama. Is this justified? Support your answer with calculations.
(c)[2 marks]If the station wants to advertise to the largest possible audience, which average should they use and why?
Question 17
6 marks · Hard
Answer and see the solution →A scientist records the diameters of two distinct circular cells, Cell A and Cell B. The diameter of Cell A is 0.0036 mm and the diameter of Cell B is 2.8 × 10^{-2} mm.
(a)[2 marks]Express the diameter of each cell in standard form.
(b)[4 marks]The scientist wants to find out how many times bigger the area of Cell B is compared to the area of Cell A. Use the formula for the area of a circle, , and give your answer in standard form to 2 significant figures.
Question 18
5 marks · Hard
Answer and see the solution →The temperature of a chemical experiment is monitored every 2 minutes, giving the readings in °C: 20.7, 21.5, 21.9, 22.6, 23.1, 22.3. The experimenter models the temperature change with the linear equation T = a + bt, where t is the time in minutes.
(a)[2 marks]Calculate the mean and median temperature from the data.
(b)[2 marks]Given that at t = 0, T = 20.7, and at t = 10, T = 23.1, find the values of a and b.
(c)[1 mark]According to the model, what will the temperature be after 12 minutes? Give your answer to 1 decimal place.
Question 19
6 marks · Hard
Answer and see the solution →In the diagram below, points A and B lie on the circumference of the circle with centre O. The straight line AB is a chord, and OC is a radius perpendicular to AB, meeting AB at M. The length of OC is 7 cm and the distance from O to M is 4 cm.
Circle with centre O. AB is a chord. OC is a radius, perpendicular to AB, meeting AB at M. OC = 7 cm, OM = 4 cm. (a)[2 marks]Calculate the length MC.
(b)[3 marks]Find the length AB.
(c)[1 mark]Express your answer to part (b) in standard form.