Question 4 - A-Level Maths

AQA FP1 2006 June — Question 4 5 marks

Exam Board	AQA
Module	FP1 (Further Pure Mathematics 1)
Year	2006
Session	June
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Standard trigonometric equations
Type	General solution — find all solutions
Difficulty	Moderate -0.5 This is a straightforward application of solving a trigonometric equation for the general solution. While it requires knowledge of the general solution formula and recognizing that cos θ = √3/2 gives θ = ±π/6, it's a direct single-step problem with no complications or multi-step reasoning, making it slightly easier than average.
Spec	1.05g Exact trigonometric values: for standard angles 1.05o Trigonometric equations: solve in given intervals

4 Find, in radians, the general solution of the equation $$\cos 3 x = \frac { \sqrt { 3 } } { 2 }$$ giving your answers in terms of $\pi$.

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Question 4:

Answer	Marks	Guidance
Working	Marks	Guidance
$\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}$ stated or used	B1	Condone decimals and/or degrees until final mark
Appropriate use of $\pm$	B1
Introduction of $2n\pi$	M1
Division by 3	M1	Of $\alpha + kn\pi$ or $\pm\alpha + kn\pi$
$x = \pm\frac{\pi}{18} + \frac{2}{3}n\pi$	A1 (5)

## Question 4:
| Working | Marks | Guidance |
|---------|-------|----------|
| $\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}$ stated or used | B1 | Condone decimals and/or degrees until final mark |
| Appropriate use of $\pm$ | B1 | |
| Introduction of $2n\pi$ | M1 | |
| Division by 3 | M1 | Of $\alpha + kn\pi$ or $\pm\alpha + kn\pi$ |
| $x = \pm\frac{\pi}{18} + \frac{2}{3}n\pi$ | A1 (5) | |

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4 Find, in radians, the general solution of the equation

$$\cos 3 x = \frac { \sqrt { 3 } } { 2 }$$

giving your answers in terms of $\pi$.

\hfill \mbox{\textit{AQA FP1 2006 Q4 [5]}}

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Q1 9 Q2 6 Q3 4 Q4 5 Q5 9 Q6 7 Q7 6 Q8 10 Q9 16