A-LevelMathematicsNumerical methods9709/23 · May/June 2022 · Q46 Marks
Use the trapezium rule with three intervals to show that the value of S 4م In 12. In x dx is approximately [4]
- (a)Use the trapezium rule with three intervals to show that the value of S 4م In 12. In x dx is approximately [4][4]
- (b)Use a graph of y = ln x to show that In 12 is an under-estimate of the true value of off Inxdx. [2][2]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] Use y-values [ln1], ln2, ln3, ln4 but not their decimal equivalents
- [M1] Use correct formula, or equivalent, with h = 1. Allow with decimal equivalents
- [M1] Use both relevant logarithm properties correctly
- [A1] Obtain ½[ln1+2ln2+2ln3+ln4] and hence ln12 AG - necessary detail needed
- [B1] Sketch correct graph of y = ln x for at least y ≥ 0
- [DB1] Indicate that top of each trapezium is below curve or clear equivalent. but B0 if only one chord shown from (1, 0) to (4, ln 4) allow 'concave down'
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