O-LevelAdditional MathematicsTrigonometry4037/12 · May/June 2018 · Q88 Marks
Solve 3 cos²θ + 4 sinθ = 4 for 0° ≤ θ ≤ 180°.
- (a)Solve 3 cos²θ + 4 sinθ = 4 for 0° ≤ θ ≤ 180°.[4]
- (b)Solve sin2φ = √3 cos 2φ for -π/2 ≤ φ ≤ π/2 radians.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- M1 use of correct identity 3(1-sin²θ)+4sin θ = 4
- M1 For attempt to solve a 3 term quadratic equation in sinθ to obtain sin θ = (3sinθ-1)(sinθ-1) = 0 sin θ = 1/3, sinθ=1
- A1 θ=19.5°, 160.5°
- A1 90°
- M1 obtaining an equation in tan 2φ and correct attempt to solve for one solution to reach 2φ = k tan 2φ = √3
- A1 2φ = π/3
- M1 for attempt at a second solution
- A1 for a correct second solution and no other solutions within the range φ = π/6, -π/3 or -1.05
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 →