CAIE P2 2017 November — Question 2 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve equation with sin2x/cos2x by substitution
DifficultyStandard +0.3 This question requires applying the double angle formula cos 2θ = 2cos²θ - 1, then solving a quadratic equation in cos θ, followed by finding angles in the given range. While it involves multiple steps, each step is standard technique from the syllabus with no novel insight required, making it slightly easier than average.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

2 Solve the equation \(5 \cos \theta ( 1 + \cos 2 \theta ) = 4\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Use \(\cos 2\theta = 2\cos^2\theta - 1\)B1
Obtain \(10\cos^3\theta = 4\) or equivalentB1
Use correct process to find at least one value of \(\theta\) from equation of form \(k_1\cos^3\theta = k_2\)M1
Obtain \(42.5\)A1
Obtain \(317.5\) and no others between \(0\) and \(360\)A1
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use $\cos 2\theta = 2\cos^2\theta - 1$ | B1 | |
| Obtain $10\cos^3\theta = 4$ or equivalent | B1 | |
| Use correct process to find at least one value of $\theta$ from equation of form $k_1\cos^3\theta = k_2$ | M1 | |
| Obtain $42.5$ | A1 | |
| Obtain $317.5$ and no others between $0$ and $360$ | A1 | |

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2 Solve the equation $5 \cos \theta ( 1 + \cos 2 \theta ) = 4$ for $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$.\\

\hfill \mbox{\textit{CAIE P2 2017 Q2 [5]}}