Pure Mathematics Year 1 (AS) Unit Test 7: Integration
1 Find (5 marks)
2 The curve with equation y = h(x) passes through the point (4, 19).
Given that , find h(x). (6 marks)
3 a Given that , find the two possible values of a. (6 marks)
b Labelling all axes intercepts, sketch the graph of for (2 marks)
c With reference to the integral in part a and the sketch in part b, explain why the
larger value of a found in part a produces a solution for which the actual area under
the graph between a and 2a is not equal to 1 and state whether the area is greater
than 1 or smaller than 1. (2 marks)
4 The speed, v ms−1, of a rollercoaster at time t s is given by
The distance, s m, travelled by the rollercoaster in the first 20 s is given
by
Find the value of s, giving your answer to 3 significant figures. (5 marks)
5 The graph shows part of the curve C with equation
Figure 1
The curve C crosses the x-axis at the origin O and at points A and B.
a Using an appropriate algebraic method, find the coordinates of A and B. (3 marks)
b The finite region shown shaded is bounded by the curve C and the x-axis.
Use calculus to find the total area of the shaded region. (8 marks)
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1 Find (5 marks)
2 The curve with equation y = h(x) passes through the point (4, 19).
Given that , find h(x). (6 marks)
3 a Given that , find the two possible values of a. (6 marks)
b Labelling all axes intercepts, sketch the graph of for (2 marks)
c With reference to the integral in part a and the sketch in part b, explain why the
larger value of a found in part a produces a solution for which the actual area under
the graph between a and 2a is not equal to 1 and state whether the area is greater
than 1 or smaller than 1. (2 marks)
4 The speed, v ms−1, of a rollercoaster at time t s is given by
The distance, s m, travelled by the rollercoaster in the first 20 s is given
by
Find the value of s, giving your answer to 3 significant figures. (5 marks)
5 The graph shows part of the curve C with equation
Figure 1
The curve C crosses the x-axis at the origin O and at points A and B.
a Using an appropriate algebraic method, find the coordinates of A and B. (3 marks)
b The finite region shown shaded is bounded by the curve C and the x-axis.
Use calculus to find the total area of the shaded region. (8 marks)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
