Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 4
104 practice questions
Topics covered
Practice questions
51–60 of 104
Question 51
4 marks · Hard
Answer and see the solution →A rectangular field is to be enclosed on three sides with fencing. The fourth side is a hedge and requires no fence. The length of the field is metres and the width is metres. If 160 m of fencing is available, express the total area of the field in terms of , and find the value of that gives the maximum area.
(a)[1 mark]Show that .
(b)[3 marks]Calculate the value of that produces the largest field area, and find this maximum area.
Question 52
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 53
2 marks · Easy
Answer and see the solution →In the right-angled triangle shown, one side is 12 cm long and the other side (adjacent to the right angle) is 5 cm long. Calculate the length of the hypotenuse.
Question 54
1 mark · Easy
Answer and see the solution →State the sine ratio in a right-angled triangle in terms of the sides.
Question 55
2 marks · Easy
Answer and see the solution →A right-angled triangle has a hypotenuse of 15 cm. One of the other sides is 9 cm. Work out the length of the remaining side.
Question 56
2 marks · Easy
Answer and see the solution →Calculate the size of angle in a right-angled triangle where the side opposite is 7 m and the hypotenuse is 14 m. Give your answer correct to 3 significant figures.
Question 57
3 marks · Easy
Answer and see the solution →PQRS is a rectangle. PQ = 6 cm and QR = 8 cm.
(a)[2 marks]Calculate the length of the diagonal PS.
(b)[1 mark]Work out the perimeter of rectangle PQRS.
Question 58
1 mark · Easy
Answer and see the solution →Explain why the diagonals of a rectangle are always equal in length.
Question 59
2 marks · Easy
Answer and see the solution →A triangle has sides of length 3 cm, 4 cm, and 5 cm. Work out the area of the triangle.
Question 60
3 marks · Normal
Answer and see the solution →A ladder 4.5 m long leans against a vertical wall, making an angle of 68° with the ground. Calculate the height above the ground that the top of the ladder reaches.