A-LevelMathematicsTrigonometry9709/21 · Oct/Nov 2020 · Q710 Marks
A curve is defined by the parametric equations x = 3t - 2 sin t, y = 5t + 4 cos t, where 0 ≤ t ≤ 2π. At each of the points P and Q on the curve, the gradient of the curve is 5/2.
- (a)Show that the values of t at P and Q satisfy the equation 10 cos t - 8 sin t = 5.[3]
- (b)Express 10 cos t – 8 sin t in the form Rcos(t + α), where R > 0 and 0 < α < ½π. Give the exact value of R and the value of α correct to 3 significant figures.[3]
- (c)Hence find the values of t at the points P and Q.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] Obtain dx/dt = 3-2cos t and dy/dt = 5-4sin t
- [M1] Equate expression for dy/dx to 5/2
- [A1] Obtain 10cos t - 8sin t = 5 AG - sufficient working to be shown.
- [B1] State R = √164 or exact equivalent
- [M1] Use appropriate trigonometry to find α
- [A1] Obtain 0.675 with no errors seen
- [M1] Must be using the result from (b)
- [A1] Obtain 0.495 AWRT
- [M1] Carry out correct method to find second value of t
- [A1] Obtain 4.44 AWRT
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