Question 3 - A-Level Maths

AQA FP1 2008 January — Question 3 5 marks

Exam Board	AQA
Module	FP1 (Further Pure Mathematics 1)
Year	2008
Session	January
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Standard trigonometric equations
Type	General solution — find all solutions
Difficulty	Moderate -0.8 This is a straightforward trig equation requiring only a substitution and knowledge that tan θ = 1 when θ = π/4 + nπ. The question involves routine manipulation with no problem-solving insight needed, making it easier than average despite being Further Maths content.
Spec	1.05o Trigonometric equations: solve in given intervals

3 Find the general solution of the equation $$\tan 4 \left( x - \frac { \pi } { 8 } \right) = 1$$ giving your answer in terms of $\pi$.

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Question 3:

Answer	Marks	Guidance
Working/Answer	Marks	Guidance
Use of $\tan\frac{\pi}{4} = 1$	B1	Degrees or decimals penalised in last mark only
Introduction of $n\pi$	M1	or $kn$ at any stage
Division of all terms by 4	m1
Addition of $\frac{\pi}{8}$	m1	OE
GS $x = \frac{3\pi}{16} + \frac{n\pi}{4}$	A1	OE
Total	5

## Question 3:

| Working/Answer | Marks | Guidance |
|---|---|---|
| Use of $\tan\frac{\pi}{4} = 1$ | B1 | Degrees or decimals penalised in last mark only |
| Introduction of $n\pi$ | M1 | or $kn$ at any stage |
| Division of all terms by 4 | m1 | |
| Addition of $\frac{\pi}{8}$ | m1 | OE |
| GS $x = \frac{3\pi}{16} + \frac{n\pi}{4}$ | A1 | OE |
| **Total** | **5** | |

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3 Find the general solution of the equation

$$\tan 4 \left( x - \frac { \pi } { 8 } \right) = 1$$

giving your answer in terms of $\pi$.

\hfill \mbox{\textit{AQA FP1 2008 Q3 [5]}}

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Q1 4 Q2 5 Q3 5 Q4 7 Q5 8 Q6 10 Q7 12 Q8 12 Q9 12