AQA Paper 1 2023 June — Question 4 1 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
Year2023
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSmall angle approximation
TypeMultiple choice small angle formula
DifficultyModerate -0.8 This is a straightforward application of the small angle approximation cos θ ≈ 1 - θ²/2 to the double angle formula cos 2θ = 2cos²θ - 1. It requires only direct substitution and basic algebraic manipulation, making it easier than average but not trivial since students must recognize which formula to use.
Spec1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x1.05l Double angle formulae: and compound angle formulae
4 Given that \(\theta\) is a small angle, find an approximation for \(\cos 2 \theta\) Circle your answer. \(1 - \frac { \theta ^ { 2 } } { 2 }\) \(2 - 2 \theta ^ { 2 }\) \(1 - 2 \theta ^ { 2 }\) \(1 - \theta ^ { 2 }\)
Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
\(1 - 2\theta^2\)R1 Circles the correct answer 
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $1 - 2\theta^2$ | R1 | Circles the correct answer |
4 Given that $\theta$ is a small angle, find an approximation for $\cos 2 \theta$ Circle your answer.\\
$1 - \frac { \theta ^ { 2 } } { 2 }$\\
$2 - 2 \theta ^ { 2 }$\\
$1 - 2 \theta ^ { 2 }$\\
$1 - \theta ^ { 2 }$

\hfill \mbox{\textit{AQA Paper 1 2023 Q4 [1]}}
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Q1 1 Q2 1 Q3 1 Q4 1 Q5 4 Q6 5 Q7 4 Q8 6 Q9 9 Q10 8 Q11 9 Q12 8 Q13 9 Q14 13 Q15 9 Q16 14