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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 38

Figure 1 below shows the region RRR, which is bounded by the curve with equation y=2x+1y = \sqrt{2^x + 1}y=2x+1​, the xxx-axis and the lines x=0x = 0x=0 and x=3x = 3x=3.

Figure for question 5

a.

Complete the table below, giving the missing values of 2x+1 \sqrt{2^x + 1}\,2x+1​ to three decimal places.

xxx: 0, 0.5, 1, 1.5, 2, 2.5, 3 2x+1\sqrt{2^x + 1}2x+1​: 1.414, 1.554, 1.732, 1.957, ..., ..., ...

[2]
b.

Use the trapezium rule with all the values from the table to find an approximation for the area of RRR, giving your answer to four significant figures.

[4]
c.

State, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of RRR.

[2]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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