CAIE P1 2023 November — Question 2 2 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionNovember
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeFunction properties and inverses
DifficultyStandard +0.3 This is a straightforward inverse trigonometry equation requiring students to isolate tan^{-1}(4x), evaluate the right-hand side using knowledge that cos^{-1}(√3/3) = π/6, then apply tan to both sides and solve for x. It's slightly above average difficulty due to the inverse function manipulation and exact value work, but follows a standard procedure with no novel insight required.
Spec1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs
Find the exact solution of the equation $$\frac{1}{6}\pi + \tan^{-1}(4x) = -\cos^{-1}(\frac{1}{3}\sqrt{3}).$$ [2]
Question 2:
AnswerMarks
2     
[tan−14x=] their−    tan−14x= , 1.047 or 0 
AnswerMarks Guidance
 6 6  3 M1 OE
 3 π
Evaluating −cos−1  in rad and adding or subtracting .
 
 2  6
Allow working with both angles in degrees.
3
4x=− 3, x=−
 
AnswerMarks Guidance
4A1 3
Note: answer of −0.43 or implies M1
4
2
AnswerMarks Guidance
QuestionAnswer Marks 
Question 2:
2 |      
[tan−14x=] their−    tan−14x= , 1.047 or 0 
 6 6  3  | M1 | OE
 3 π
Evaluating −cos−1  in rad and adding or subtracting .
 
 2  6
Allow working with both angles in degrees.
3
4x=− 3, x=−
 
4 | A1 | 3
Note: answer of −0.43 or implies M1
4
2
Question | Answer | Marks | Guidance
Find the exact solution of the equation
$$\frac{1}{6}\pi + \tan^{-1}(4x) = -\cos^{-1}(\frac{1}{3}\sqrt{3}).$$ [2]

\hfill \mbox{\textit{CAIE P1 2023 Q2 [2]}}
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Q1 4 Q2 2 Q3 6 Q4 6 Q5 6 Q6 8 Q7 9 Q8 8 Q9 9 Q10 7 Q11 10