Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
21–30 of 49 · Normal
Question 21
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 22
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 23
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 24
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 25
3 marks · Normal
Answer and see the solution →Differentiate the function with respect to and find the value of the gradient at .
Question 26
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 27
2 marks · Normal
Answer and see the solution →Write down the maximum and minimum values of the function for .
Question 28
3 marks · Normal
Answer and see the solution →In triangle PQR, cm, cm, and . Calculate the length of QR. Give your answer correct to 3 significant figures.
Question 29
3 marks · Normal
Answer and see the solution →Explain why the area of a triangle with sides of lengths and , and included angle , can be written as .
Question 30
4 marks · Normal
Answer and see the solution →The function is plotted for angles from to .
(a)[2 marks]On the axes below, sketch the graph of for .
Axes for \( y = \cos \theta \) graph. Sketch with labelled key points. (b)[1 mark]Write down the value of between and for which is at its minimum.
(c)[1 mark]State the period of the function in degrees.