Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
41–50 of 108
Question 41
2 marks · Easy
Answer and see the solution →The velocity of a particle is given by , where is in seconds. Find the acceleration of the particle when .
Question 42
2 marks · Easy
Answer and see the solution →Consider the cubic function . A stationary point occurs when the gradient is zero.
(a)[2 marks]State why the gradient at a stationary point is zero.
Question 43
3 marks · Easy
Answer and see the solution →The table below gives the values of y for the curve at different points:
x y -1 -1 0 0 1 5 2 14 Use the table to estimate the gradient (rate of change) between the points where and . Give your answer in simplest form.
Question 44
1 mark · Easy
Answer and see the solution →What is the value of the gradient at a stationary point of a curve?
Question 45
2 marks · Normal
Answer and see the solution →Differentiate with respect to . Give your answer in terms of .
Question 46
3 marks · Normal
Answer and see the solution →The curve has stationary points.
Find the coordinates of the stationary points and determine whether each is a maximum or a minimum.
Question 47
3 marks · Normal
Answer and see the solution →A particle moves along a straight line and its displacement from a fixed point at time seconds is given by .
Explain how you would find the velocity and acceleration of the particle at . Write down the values.
Question 48
4 marks · Normal
Answer and see the solution →Let .
(a)[1 mark]Expand to write it in the form .
(b)[1 mark]Differentiate your answer from part a with respect to .
(c)[2 marks]Calculate the gradient of the curve at .
Question 49
4 marks · Normal
Answer and see the solution →The graph below shows the curve .
(a)[2 marks]By considering , find the x-coordinates of any stationary points of the curve.
(b)[2 marks]Classify each stationary point as a maximum or minimum, giving a reason for your answer.
Question 50
2 marks · Normal
Answer and see the solution →If the velocity in m/s of a particle is given by , where is in seconds, find the acceleration of the particle.