Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
51–60 of 105
Question 51
2 marks · Hard
Answer and see the solution →The curve y = x^2 + 2x + 1 is shown below.
Graph of y = x^2 + 2x + 1 Estimate the gradient of the curve at the point where x = -1.
Question 52
4 marks · Hard
Answer and see the solution →The graph of y = f(x) is shown below.
(a)[2 marks]The graph is reflected in the x-axis and then translated by the vector . Write down the equation of the resulting graph in terms of f(x).
(b)[2 marks]If the original graph is y = , write down the equation of the final transformed graph.
Question 53
4 marks · Hard
Answer and see the solution →Below are functions f(x) and g(x):
Describe fully the sequence of transformations that map the graph of y = f(x) onto y = g(x), giving the algebraic form, and provide the order they are applied in.
Question 54
1 mark · Easy
Answer and check →In a cuboid, the length is 3 cm, the width is 4 cm, and the height is 5 cm. Work out the length of the space diagonal (the longest line from one corner to the opposite corner) to 1 decimal place.
Question 55
2 marks · Easy
Answer and see the solution →In a square-based pyramid, each base edge is 6 cm and the vertex is 8 cm vertically above the centre of the base. Calculate, to 3 significant figures, the length of the slope from a corner of the base to the vertex.
Question 56
2 marks · Easy
Answer and see the solution →Explain how to use Pythagoras’ theorem to calculate the direct distance from one corner of a cuboid to the opposite corner (the space diagonal).
Question 57
3 marks · Easy
Answer and see the solution →A triangular prism has a right-angled triangle as its cross-section with side lengths 5 cm, 12 cm and 13 cm. The prism is 8 cm long.
(a)[2 marks]Calculate the length of the diagonal joining one vertex at the base to the opposite vertex at the top, across the full length of the prism.
(b)[1 mark]Find, to 1 decimal place, the angle that this diagonal makes with the base of the prism.
Question 58
3 marks · Easy
Answer and see the solution →The table below shows the lengths (in cm) of the edges of three different cuboids.
Edge lengths of cuboids (in cm) Cuboid Length Width Height A 4 3 9 B 6 5 2 C 8 7 3 Work out the length of the longest space diagonal for each cuboid, giving your answers to 1 decimal place.
Question 59
2 marks · Normal
Answer and see the solution →The diagram below shows a cuboid ABCDEFGH with AB = 4 cm, BC = 5 cm, and BF = 12 cm.
Cuboid diagram for question 1. Work out the length of the space diagonal AE.
Question 60
3 marks · Normal
Answer and see the solution →A pyramid has a square base PQRS, with PQ = QR = 6 cm. The vertex T is vertically above the centre of the base TSQ. The height VT = 9 cm.
Calculate the length of the edge VP from the vertex to a base corner.