O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2015 · Q1012 Marks
Solve 4 sin x = cosec x for 0° ≤ x ≤ 360°.
- (a)Solve 4 sin x = cosec x for 0° ≤ x ≤ 360°.[3]
- (b)Solve tan²3y – 2 sec 3y - 2 = 0 for 0° ≤ y ≤ 180°.[6]
- (c)Solve tan(z – π/3) = √3 for 0 ≤ z ≤ 2π radians.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [M1] using cosecx = 1/sinx and obtaining sin x = ...
- [A1,A1] A1 for one correct pair, Al for another correct pair with no extra solutions
- [M1] use of the correct identity
- [M1] attempt to obtain a 3 term quadratic equation in sec 3y and attempt to solve
- [M1] dealing with sec and 3y correctly
- [A1,A1] A1 for a correct pair, Al for a second correct pair, Al for correct 5th solution and no other within the range
- [M1] correct order of operations
- [A1,A1] Al for a correct solution Al for a second correct solution and no other within the range
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