A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2020 · Q47 Marks
The diagram shows the curve with equation y = x-2 x² + 8 and the lines x = 14 and y = 0. [Figure 4.1]
- (a)Find dy/dx and hence determine the exact x-coordinates of the stationary points.[4]
- (b)Use the trapezium rule with three intervals to find an approximation to the area of the shaded region. Give the answer correct to 2 significant figures.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [1] Differentiate using quotient rule (or product rule)
- [1] Obtain (x²+8)-2x(x-2) / (x²+8)²
- [1] Equate first derivative to zero and attempt solution to get x = ...
- [1] Obtain 2±√12 or exact equivalents
- [1] Use y values (0), 4/44, 8/108, 12/204 or decimal equivalents
- [1] Use correct formula, or equivalent, with h = 4
- [1] Obtain 2(0 + 2×4/44 + 2×8/108 + 12/204) or equivalent and hence 0.78
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