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A-LevelMathematicsNumerical methods9709/33 · May/June 2017 · Q78 Marks

The diagram shows a sketch of the curve y = e^(½x) / x for x > 0, and its minimum point M. [Figure 7.1]

  1. (i)Find the x-coordinate of M.[4]
  2. (ii)Use the trapezium rule with two intervals to estimate the value of ∫(from 1 to 3) e^(½x) / x dx, giving your answer correct to 2 decimal places.[3]
  3. (iii)The estimate found in part (ii) is denoted by E. Explain, without further calculation, whether another estimate found using the trapezium rule with four intervals would be greater than E or less than E.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [M1] Use correct quotient rule or product rule
  2. [A1] Obtain correct derivative in any form
  3. [M1] Equate derivative to zero and solve for x
  4. [A1] Obtain x = 2
  5. [B1] State or imply ordinates 1.6487..., 1.3591..., 1.4938...
  6. [M1] Use correct formula, or equivalent, with h = 1 and three ordinates
  7. [A1] Obtain answer 2.93 only
  8. [B1] Explain why the estimate would be less than E

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About this question

Topic
Numerical methods, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, May/June 2017 Paper 3 Variant 3, question 7.

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