A-LevelFurther MathematicsDifferentiation9231/12 · Oct/Nov 2015 · Q14 Marks
The curve C is defined parametrically by x = 2 cos³t and y = 2 sin³t, for 0 < t < π. Show that, at the point with parameter t, d²y/dx² = ¹⁄₆ sec⁴t cosect.
- (a)Show that, at the point with parameter t, d²y/dx² = ¹⁄₆ sec⁴t cosect.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [B1] dy/dx = −tan t (OE)
- [B1] d(dy/dx)/dt = −sec²t
- [M1] d²y/dx² = d(dy/dx)/dt / dx/dt
- [A1] = ¹⁄₆ sec⁴t cosect AG
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