CAIE P1 Specimen — Question 3 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
SessionSpecimen
Marks4
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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, then solve a quadratic-in-x² equation. While it involves composition of functions, the steps are mechanical: evaluate sin(π/6), set up 4x⁴ + x² = 1/2, substitute u = x², solve the quadratic, then find x. No novel insight required, slightly easier than average due to its routine nature.
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
AnswerMarks Guidance
\(4x^2 + x^2 = \frac{1}{2}\) soiB1
Solve as quadratic in \(x^2\)M1 E.g. \((4x^2-1)(2x^2+1)\) or \(x^2 = \) formula
\(x^2 = \frac{1}{4}\)A1 Ignore other solution
\(x = \pm\frac{1}{2}\)A1
Total: 4 
## Question 3:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $4x^2 + x^2 = \frac{1}{2}$ soi | B1 | |
| Solve as quadratic in $x^2$ | M1 | E.g. $(4x^2-1)(2x^2+1)$ or $x^2 = $ formula |
| $x^2 = \frac{1}{4}$ | A1 | Ignore other solution |
| $x = \pm\frac{1}{2}$ | A1 | |
| **Total: 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  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