Question 3 - A-Level Maths

AQA FP1 2010 January — Question 3 4 marks

Exam Board	AQA
Module	FP1 (Further Pure Mathematics 1)
Year	2010
Session	January
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Standard trigonometric equations
Type	General solution — find all solutions
Difficulty	Easy -1.2 This is a straightforward trig equation requiring only knowledge that sin θ = 1 when θ = π/2 + 2πn. Students set 4x + π/4 = π/2 + 2πn and solve for x. Despite being FP1, this is a routine single-step question with no problem-solving required, making it easier than average.
Spec	1.05o Trigonometric equations: solve in given intervals

3 Find the general solution of the equation $$\sin \left( 4 x + \frac { \pi } { 4 } \right) = 1$$

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Answer	Marks	Guidance
$\sin \frac{\pi}{2} = 1$ stated or used	B1	Deg/dec penalised in 4th mark
Introduction of $2n\pi$	M1	(or $n\pi$) at any stage
Going from $4x + \frac{\pi}{4}$ to $x$	m1	incl division of all terms by 4
$x = \frac{\pi}{16} + \frac{1}{2}n\pi$	A1	4 marks
Total for Q3	4 marks

| $\sin \frac{\pi}{2} = 1$ stated or used | B1 | Deg/dec penalised in 4th mark |
| Introduction of $2n\pi$ | M1 | (or $n\pi$) at any stage |
| Going from $4x + \frac{\pi}{4}$ to $x$ | m1 | incl division of all terms by 4 |
| $x = \frac{\pi}{16} + \frac{1}{2}n\pi$ | A1 | 4 marks | or equivalent unsimplified form |

| **Total for Q3** | **4 marks** |

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3 Find the general solution of the equation

$$\sin \left( 4 x + \frac { \pi } { 4 } \right) = 1$$

\hfill \mbox{\textit{AQA FP1 2010 Q3 [4]}}

This paper (9 questions)

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Q1 9 Q2 6 Q3 4 Q4 7 Q5 7 Q6 8 Q7 9 Q8 9 Q9 16

Answer	Marks	Guidance
\(\sin \frac{\pi}{2} = 1\) stated or used	B1	Deg/dec penalised in 4th mark
Introduction of \(2n\pi\)	M1	(or \(n\pi\)) at any stage
Going from \(4x + \frac{\pi}{4}\) to \(x\)	m1	incl division of all terms by 4
\(x = \frac{\pi}{16} + \frac{1}{2}n\pi\)	A1	4 marks
Total for Q3	4 marks