A-LevelMathematicsDifferentiation9709/21 · May/June 2018 · Q57 Marks
The parametric equations of a curve are x = 2 cos 2θ + 3 sin θ, y = 3 cos θ for 0 < θ < ½π.
- (i)Find the gradient of the curve at the point for which θ = 1 radian.[4]
- (ii)Find the value of sin θ at the point on the curve where the tangent is parallel to the y-axis.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] Obtain dx/dθ = -4sin 2θ + 3cos θ
- [M1] Use dy/dx = (dy/dθ) / (dx/dθ) in terms of θ or with 1 already substituted
- [A1] Obtain or imply dy/dx = (-3 sin θ) / (-4 sin 2θ + 3 cos θ)
- [A1] Substitute 1 to obtain 1.25
- [M1] Equate denominator of first derivative to zero
- [A1] Use sin 2θ = 2 sin θ cos θ
- [A1] Obtain sin θ = 1/4
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →