Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
51–60 of 108
Question 51
3 marks · Normal
Answer and see the solution →Differentiate the function with respect to and find the value of the gradient at .
Question 52
3 marks · Normal
Answer and see the solution →Explain how you can use the second derivative to classify stationary points of a cubic function.
Illustrate your answer by referring to the function .
Question 53
2 marks · Hard
Answer and see the solution →Differentiate the function with respect to , and state the value of the gradient when .
Question 54
4 marks · Hard
Answer and see the solution →(a)[2 marks]Find the coordinates of the stationary points of the curve .
(b)[2 marks]Determine the nature (maximum or minimum) of each stationary point.
Question 55
4 marks · Hard
Answer and see the solution →A particle moves along a straight line such that its displacement after t seconds is given by , where s is in metres.
(a)[2 marks]Find the times when the particle is at rest.
(b)[2 marks]Explain how you would determine whether the particle is speeding up or slowing down at seconds.
Question 56
1 mark · Easy
Answer and see the solution →Write down the formula for the area of a triangle when two sides are of length and and the included angle is .
Question 57
2 marks · Easy
Answer and see the solution →Calculate the value of .
Question 58
2 marks · Easy
Answer and see the solution →In triangle XYZ, sides XY = 9 cm, XZ = 7 cm, and YZ = 12 cm. Angle YXZ is opposite side YZ. Can you use the sine rule to find angle YXZ? Explain your answer.
Question 59
3 marks · Easy
Answer and see the solution →The triangle below has sides PQ = 5.0 cm and QR = 6.0 cm, and angle PQR = 60°.
Triangle PQR (not to scale) (a)[1 mark]Write down the lengths of the two sides and the angle needed to calculate the area of triangle PQR using trigonometry.
(b)[2 marks]Calculate the area of triangle PQR, giving your answer to 2 decimal places.
Question 60
3 marks · Easy
Answer and see the solution →The table below gives values for the function . Complete the missing values for and .
Values for \( y = \sin \theta \) (degrees) 0 90 180 270 360