A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2021 · Q56 Marks
A curve has equation x² + 4x cos 3y = 6. Find the exact value of the gradient of the normal to the curve at the point (√2, π/12).
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [*M1] Use product rule to differentiate 4x cos 3y to obtain k₁ cos 3y + k₂x sin 3y dy/dx Where k₁k₂ ≠ 0
- [A1] Obtain 4 cos 3y – 12x sin 3y dy/dx Allow unsimplified.
- [A1] Obtain 2x + 4 cos 3y – 12x sin 3y dy/dx = 0 Allow unsimplified.
- [DM1] Substitute x- and y-values to find value of first derivative
- [M1] Apply –1 / (dy/dx) to find gradient of normal
- [A1] Obtain –1/√2 or –√2 or exact equivalent
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