A-LevelMathematicsDifferentiation9709/22 · Feb/Mar 2025 · Q46 Marks
A curve has equation y = 4 sinx / (3 + cos 2x) for values of x such that 0 ≤ x ≤ 2π.
- (a)Find dy/dx.[4]
- (b)Hence find the coordinates of the stationary points of the curve.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.
- [*M1] Attempt use of quotient rule or equivalent
- [A1] Obtain (4 cos x(3 + cos 2x) + 8 sin x sin 2x) / (3 + cos 2x)²
- [DM1] Equate first derivative to zero and attempt to express numerator in terms of cos x
- [A1] Obtain 24 cos x – 8 cos³ x = 0 OE
- [M1] Attempt solution to find coordinates of at least one stationary point From equation involving two powers of cos x.
- [A1] Obtain (½π, 2) and (³⁄₂π, –2) and no others
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