Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Graphs 9
18 practice questions
Practice questions
11–18 of 18
Question 11
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 12
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 13
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.
Question 14
3 marks · Normal
Answer and see the solution →Differentiate the function with respect to and find the value of the gradient at .
Question 15
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 16
2 marks · Hard
Answer and see the solution →Differentiate the function with respect to , and state the value of the gradient when .
Question 17
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 18
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.