CAIE P1 2014 November — Question 2 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeInverse trigonometric function equations
DifficultyStandard +0.8 This question requires understanding of inverse trigonometric functions and the ability to construct a right-angled triangle to evaluate tan^(-1)(3), then use this to find sin of that angle via Pythagoras, finally solving for x. It goes beyond routine manipulation and requires geometric insight linking different inverse trig functions, making it moderately harder than average but still within standard A-level scope.
Spec1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs
2 Find the value of \(x\) satisfying the equation \(\sin ^ { - 1 } ( x - 1 ) = \tan ^ { - 1 } ( 3 )\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\tan^{-1}(3) = 1.249\) or \(71.565°\)M1 Attempt at \(\tan^{-1}3\) or right angle triangle with attempt at hypotenuse \(= \sqrt{10}\)
\(\sin 1.25\) or \(\sin 71.6\) or \(0.949\)M1 Attempt at \(\sin\tan^{-1}3\)
\((x =) 1.95\) cao, accept \(1 + \frac{3}{\sqrt{10}}\)A1 Answer only B3 
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\tan^{-1}(3) = 1.249$ or $71.565°$ | **M1** | Attempt at $\tan^{-1}3$ or right angle triangle with attempt at hypotenuse $= \sqrt{10}$ |
| $\sin 1.25$ or $\sin 71.6$ or $0.949$ | **M1** | Attempt at $\sin\tan^{-1}3$ |
| $(x =) 1.95$ cao, accept $1 + \frac{3}{\sqrt{10}}$ | **A1** | Answer only **B3** |

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2 Find the value of $x$ satisfying the equation $\sin ^ { - 1 } ( x - 1 ) = \tan ^ { - 1 } ( 3 )$.

\hfill \mbox{\textit{CAIE P1 2014 Q2 [3]}}
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