CAIE P1 2015 November — Question 3 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeInverse trigonometric function equations
DifficultyStandard +0.3 This is a straightforward inverse trig equation requiring students to apply the definition of arcsin, leading to a quadratic in x². The algebraic manipulation is routine (quadratic formula or factoring) and the domain restriction of arcsin ensures validity. Slightly above average due to the nested substitution, but still a standard textbook exercise with no novel insight required.
Spec1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs
3 Solve the equation \(\sin ^ { - 1 } \left( 4 x ^ { 4 } + x ^ { 2 } \right) = \frac { 1 } { 6 } \pi\).
Question 3:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(4x^2 + x^2 = 1/2\) soiB1
Solve as quadratic in \(x^2\)M1 E.g. \((4x^2-1)(2x^2+1)\) or \(x^2 = \text{formula}\)
\(x^2 = 1/4\)A1 Ignore other solution
\(x = \pm 1/2\)A1 [4] 
## Question 3:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $4x^2 + x^2 = 1/2$ soi | B1 | |
| Solve as quadratic in $x^2$ | M1 | E.g. $(4x^2-1)(2x^2+1)$ or $x^2 = \text{formula}$ |
| $x^2 = 1/4$ | A1 | Ignore other solution |
| $x = \pm 1/2$ | A1 [4] | |

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3 Solve the equation $\sin ^ { - 1 } \left( 4 x ^ { 4 } + x ^ { 2 } \right) = \frac { 1 } { 6 } \pi$.

\hfill \mbox{\textit{CAIE P1 2015 Q3 [4]}}
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Q1 3 Q2 3 Q3 4 Q4 6 Q5 8 Q6 7 Q7 7 Q8 8 Q9 8 Q10 9 Q11 12