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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 11

The area under y=ln⁡xy=\ln xy=lnx from x=1x=1x=1 to x=2x=2x=2 is bounded using eight rectangles of equal width.

a.

Explain why left-hand endpoints give a lower bound and right-hand endpoints give an upper bound.

[2]
b.

Write down expressions for the two bounds as finite sums.

[2]
c.

Evaluate both bounds to four decimal places.

[2]
d.

Verify that the exact area lies between the bounds.

[2]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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