A-LevelMathematicsTrigonometry9709/12 · May/June 2015 · Q66 Marks

A tourist attraction in a city centre is a big vertical wheel on which passengers can ride. The wheel turns in such a way that the height, h m, of a passenger above the ground is given by the formula h = 60(1 – cos kt). In this formula, k is a constant, t is the time in minutes that has elapsed since the passenger started the ride at ground level and kt is measured in radians.

(i)Find the greatest height of the passenger above the ground.[1]
(ii)One complete revolution of the wheel takes 30 minutes. Show that k = π/15.[2]
(iii)Find the time for which the passenger is above a height of 90 m.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[B1] (i) Max h when cos = -1 → 120 Co
[M1] (ii) h = 0 and t = 30, or h = 120 and t = 15 Substituting a correct pair of values into the equation.
[A1] (ii) → k = 2π/30 = π/15 co ag
[B1] (iii) 90 = 60(1 - cos kt) → cos kt = 90/60 = -0.5 co - but there must be evidence of correct subtraction.
[B1] (iii) → kt = 2π/3 or → kt = 4π/3
[B1] (iii) → Either t = 10 or 20 or both → t = 10 minutes

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