Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 4
104 practice questions
Topics covered
Practice questions
11–19 of 19 · Hard
Question 11
4 marks · Hard
Answer and see the solution →Consider the straight line with equation .
(a)[1 mark]For what value of does this line pass through the point (2, 7)?
(b)[1 mark]Find the gradient and explain its meaning in the context of any straight line graph.
(c)[1 mark]Calculate the x-coordinate where the line crosses the x-axis.
(d)[1 mark]Given a second line with equation , what value of would make the two lines parallel and intersect at y = 10?
Question 12
4 marks · Hard
Answer and see the solution →A ship is sailing directly towards a lighthouse. From one point at sea, the angle of elevation from the ship to the top of the lighthouse is 14°. After the ship sails 200 metres closer to the lighthouse in a straight line, the angle of elevation increases to 22°. The height of the lighthouse is h metres.
Calculate the height h of the lighthouse.
Give your answer correct to 3 significant figures.
Question 13
3 marks · Hard
Answer and see the solution →Explain, with reference to the properties of parallelograms and right triangles, how you can use Pythagoras’ theorem to prove that the diagonals of a rhombus are perpendicular.
Write your answer in full sentences.
Question 14
5 marks · Hard
Answer and see the solution →The diagram below shows quadrilateral ABCD with AB = AD = 10 cm, BC = CD = 7 cm, and angle BAD = 120°.
Calculate:
(a)[3 marks]The length of diagonal BD.
(b)[2 marks]The area of quadrilateral ABCD.
Question 15
4 marks · Hard
Answer and see the solution →The number of hours spent on homework by a group of nine students in a week are as follows:
Hours spent on homework Student A B C D E F G H I Hours 10 13 9 15 11 20 22 13 12 Calculate the median, lower quartile (Q1), upper quartile (Q3), and inter-quartile range (IQR) for these hours.
(a)[0 marks]Write the values in order before calculation.
(b)[1 mark]Find the median value.
(c)[1 mark]Find the lower quartile (Q1).
(d)[1 mark]Find the upper quartile (Q3).
(e)[1 mark]Calculate the inter-quartile range.
Question 16
4 marks · Hard
Answer and see the solution →The table gives the frequencies of heights (in cm) for a group of sunflowers.
Heights of sunflowers Height (cm) Frequency 40 < h ≤ 60 8 60 < h ≤ 80 17 80 < h ≤ 100 24 100 < h ≤ 120 11 a) Complete the cumulative frequency table. b) On graph paper, draw a cumulative frequency graph using your table (plot cumulative frequency against the upper boundary of each height interval, scale not required). c) Estimate the median and inter-quartile range for the heights of these sunflowers from your graph.
(a)[1 mark]Complete the cumulative frequency table with required totals.
(b)[1 mark]Draw the cumulative frequency graph. Label axes clearly. (You may sketch with reasonable accuracy if graph paper is not available.)
(c)[2 marks]Estimate the median and inter-quartile range from your graph (show clearly how these are found).
Question 17
4 marks · Hard
Answer and see the solution →Two classes record the number of pages read by each student in a week:
Pages read (per student) Class A (pages) 20 21 21 22 22 22 23 23 23 25 26 Pages read (per student) Class B (pages) 4 10 13 16 23 26 31 35 35 37 41 Both classes have the same mean number of pages read. Compare the distribution of the two classes, supporting your answer using appropriate statistical measures.
Question 18
7 marks · Hard
Answer and see the solution →A circle has equation . The point P(3, 4) lies on the circle.
(a)[4 marks]Find the equation of the tangent to the circle at point P in the form .
(b)[3 marks]If this tangent is written as , write down the value of m and interpret its meaning in the context of the circle.
Question 19
9 marks · Hard
Answer and see the solution →A data analyst investigates the scores of students in a mathematics test. He finds the following results:
Scores of 12 students Student Score A 43 B 47 C 55 D 58 E 62 F 64 G 65 H 67 I 73 J 78 K 81 L 82 (a)[3 marks]Calculate the interquartile range (IQR) of the scores.
(b)[4 marks]The analyst models the relationship between score, S, and student position, n (when students are ordered by their score from lowest to highest), with the equation where c is a constant. Using the data for students C and J, form two simultaneous equations to find the value of c.
(c)[2 marks]Suppose another student M joins, scoring 50, and is inserted in the correct position. Recalculate the median score for the new group.