AQA Paper 1 Specimen — Question 3 3 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
SessionSpecimen
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSmall angle approximation
TypeSimplify expression to polynomial form
DifficultyStandard +0.3 This is a straightforward small angle approximation question requiring standard substitutions (cos x ≈ 1 - x²/2, sin x ≈ x) and basic algebraic manipulation. While it involves the compound angle 3θ and 2θ, the technique is routine and commonly practiced, making it slightly easier than average for A-level.
Spec1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x

When \(\theta\) is small, find an approximation for \(\cos 3\theta + \theta \sin 2\theta\), giving your answer in the form \(a + b\theta^2\) [3 marks]

Question 3:
AnswerMarks
31
Uses either cosx1 x2 or
2
AnswerMarks Guidance
sinx  x (PI)AO1.2 B1
cos3sin21 2
2
5
(cid:3406) 1 2
2
Substitutes 2and 3 into ‘their’
AnswerMarks Guidance
expressionAO1.1a M1
Obtains correct answerAO1.1b A1
Total3
QMarking Instructions AO
Question 3:
3 | 1
Uses either cosx1 x2 or
2
sinx  x (PI) | AO1.2 | B1 | 32
cos3sin21 2
2
5
(cid:3406) 1 2
2
Substitutes 2and 3 into ‘their’
expression | AO1.1a | M1
Obtains correct answer | AO1.1b | A1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
When $\theta$ is small, find an approximation for $\cos 3\theta + \theta \sin 2\theta$, giving your answer in the form $a + b\theta^2$
[3 marks]

\hfill \mbox{\textit{AQA Paper 1  Q3 [3]}}