AQA Paper 1 Specimen — Question 13 3 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
SessionSpecimen
Marks3
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Mark schemeDownload PDF ↗
TopicTrig Proofs
TypeProve trigonometric identity
DifficultyModerate -0.8 This is a straightforward trigonometric identity proof requiring only basic manipulation of standard identities (cot θ = cos θ/sin θ) and algebraic factoring. With 3 marks and a clear path from LHS to RHS using routine techniques, it's easier than average but not trivial, as students must recognize the factoring step.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2
Prove the identity \(\cot^2 \theta - \cos^2 \theta = \cot^2 \theta \cos^2 \theta\) [3 marks]
Question 13:
AnswerMarks
13Recalls a correct trig identity,
which could lead to a correct
AnswerMarks Guidance
answerAO1.2 B1
cot2cos2
cos2
 cos2
sin2
 1 
cos2 1
sin2 
cos2  cosec21 
cos2cot2
(RHS)
(AG)
Performs some correct
algebraic manipulation and
uses second identity to
commence proof (at least two
AnswerMarks Guidance
lines of argument)AO2.1 R1
Concludes a rigorous
mathematical argument to
prove given identity AG
Must start with one side and
through clear logical steps
arrive at the other side. In
order to be sufficiently clear,
each line should be a single
step, unless clear further
AnswerMarks Guidance
explanation is given.AO2.1 R1
Total3
QMarking Instructions AO 
Question 13:
13 | Recalls a correct trig identity,
which could lead to a correct
answer | AO1.2 | B1 | (LHS)
cot2cos2
cos2
 cos2
sin2
 1 
cos2 1

sin2 
cos2  cosec21 
cos2cot2
(RHS)
(AG)
Performs some correct
algebraic manipulation and
uses second identity to
commence proof (at least two
lines of argument) | AO2.1 | R1
Concludes a rigorous
mathematical argument to
prove given identity AG
Must start with one side and
through clear logical steps
arrive at the other side. In
order to be sufficiently clear,
each line should be a single
step, unless clear further
explanation is given. | AO2.1 | R1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
Prove the identity $\cot^2 \theta - \cos^2 \theta = \cot^2 \theta \cos^2 \theta$
[3 marks]

\hfill \mbox{\textit{AQA Paper 1  Q13 [3]}}
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