O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2010 · Q1011 Marks
Solve
- (i)4 sinx = cosx for 0° <x<360°,[3]
- (ii)3 + siny = 3 cos²y for 0° <y<360°,[5]
- (iii)sec (z/3) = 4 for 0<z< 5 radians.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [3] (i) M1 for use of tan x = (1/4); A1 for x = 14.0°; A1 for x = 194.0° (Ft on 14.0°)
- [5] (ii) M1 for use of correct identity (cos²y = 1 - sin²y) and attempt to simplify; DM1 for attempt to solve quadratic; B1 for y = 180°; A1 for y = 199.5°; A1 for y = 340.5° (Ft on 199.5°)
- [3] (iii) B1 for cos (z/3) = 1/4 or equivalent in terms of cos; M1 for a correct order of operations (solving for z/3 then multiplying, allow π for decimals); A1 for z = 3.95 (Allow 3.96, 1.25π, 1.26π)
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