Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
31–39 of 39 · Easy
Question 31
3 marks · Easy
Answer and see the solution →The histograms show the test scores of two different classes in a maths test.
Histogram for Class X Histogram for Class Y (a)[1 mark]Which class had more students scoring between 40% and 70%?
(b)[1 mark]Which class has the largest number of students with low scores (0–40%)?
(c)[1 mark]Which class has the most even spread of scores? Give a reason for your answer.
Question 32
2 marks · Easy
Answer and see the solution →Two histograms represent the test marks for two different science groups, P and Q. The modal class for Group P is 30–50 marks and for Group Q is 70–90 marks.
Which group performed better overall? Write the modal class of the better performing group and explain why it shows better overall performance.
Question 33
8 marks · Easy
Answer and see the solution →A function is defined by the curve . The diagram below shows part of this curve.
(a)The curve \( y = x^2 \) and two highlighted points. Find the gradient of the curve at the point A.
(i)[3 marks]Draw a tangent at point A and estimate its gradient. Show your working.
(b)A cuboid has an edge OA of 6 cm and OB of 8 cm. OC is perpendicular to both OA and OB and has a length of 5 cm. O, A, B, and C are adjacent vertices joining at one corner.
Use Pythagoras’ theorem in 3D to find the length of the diagonal OC.
(i)[2 marks]Calculate the length OC, giving your answer correct to one decimal place.
(c)[3 marks]Explain how the ideas of gradient (from part a) and using Pythagoras’ theorem in three dimensions (from part b) are similar when working with curves and 3D shapes.
Question 34
8 marks · Easy
Answer and see the solution →The graph of for is sketched below.
(a)[2 marks]Graph sketch of \( y = f(x) \) Write down the equation of the graph reflected in the x-axis.
(b)[2 marks]A right-angled triangle has sides AB = 4 cm, BC = 3 cm and the right angle is at B. The triangle is a face on a cuboid.
Calculate the length AC.
(c)[2 marks]The cuboid from part b has a height BD = 8 cm, perpendicular to triangle ABC. Find the length from A to D.
(d)[2 marks]Describe how the transformation in part a and the 3D length calculation in part c both involve symmetry or distance.
Question 35
7 marks · Easy
Answer and see the solution →A function is defined by . The graph of is shown below.
Graph of \( y = x^2 \ ) (a)[2 marks]Write down the equation of the curve obtained when the graph of is reflected in the y-axis.
(b)[2 marks]The point on has coordinates (2, 4). The point is the image of under a stretch, scale factor 3, parallel to the y-axis.
Work out the coordinates of point after this transformation.
(c)[3 marks]A cuboid has length 5 cm, width 2 cm, and height 4 cm. One diagonal passes from one vertex (corner) to the opposite vertex through the interior of the cuboid.
Using Pythagoras' theorem in 3D, calculate the length of this diagonal.
Question 36
7 marks · Easy
Answer and see the solution →A straight road runs up a hill and is shown on a diagram below from the side. The road runs from point A at (0, 1) to point B at (5, 7), where the coordinates are given in metres.
(a)[2 marks]Find the gradient of the road from A to B.
(b)[5 marks]A signpost is placed vertically at B and is 3 m tall. Calculate the angle between the signpost at B and the sloping road AB. Give your answer in degrees to 1 decimal place.
Question 37
8 marks · Easy
Answer and see the solution →A box is in the shape of a cuboid with dimensions 12 cm by 5 cm by 9 cm. It is used to store packets whose heights (in cm) are given below.
Packet height distribution Height, h (cm) Frequency 6 < h ≤ 7 5 7 < h ≤ 8 7 8 < h ≤ 9 4 (a)[3 marks]Work out the length of the diagonal from one corner of the cuboid to the opposite corner. Give your answer correct to 3 significant figures.
(b)[3 marks]Draw a histogram to show the distribution of packet heights. You must calculate the frequency density for each class.
(c)[2 marks]State which class interval has the highest frequency density and what this means about the distribution of packet heights.
Question 38
8 marks · Easy
Answer and see the solution →A regular square-based pyramid stands on ABCD, where each side of the base is 10 cm. The vertex, V, is 14 cm above the centre of the base. The masses (in g) of stones used to make several pyramids are grouped into classes as shown.
Masses of stone pyramids Mass, m (g) Frequency 200 < m ≤ 300 4 300 < m ≤ 500 9 500 < m ≤ 800 7 (a)[3 marks]Calculate the slant height of the pyramid (from the centre of one base edge to the vertex). Give your answer to 3 significant figures.
(b)[2 marks]Calculate the frequency density for each class in the mass table.
(c)[3 marks]Estimate the proportion of pyramids with mass greater than 500 g.
Question 39
8 marks · Easy
Answer and see the solution →A solid cuboid has sides 15 cm, 8 cm, and 6 cm. Its dimensions are measured to the nearest cm. A shop packs chocolates of two sizes. The company checks the distributions of their box heights with histograms, shown below.
Cuboid ABCDEFGH with AB = 15, BC = 8, BF = 6 Histogram showing heights of Small and Large boxes (frequency densities in arbitrary units) (a)[2 marks]Using the cuboid shown, explain how you would find the length of the main body diagonal from one corner to the farthest corner. State the formula in terms of the side lengths.
(b)[2 marks]Calculate the length of the body diagonal of the cuboid. Give your answer to 3 significant figures.
(c)[4 marks]Interpret the histogram above. Compare the number and spread of shorter versus taller boxes. What does the distribution tell you about the two products?