CAIE P3 2018 November — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Functions
TypeSolve rational exponential equation
DifficultyModerate -0.3 This is a straightforward exponential equation requiring standard algebraic manipulation (multiplying through, collecting terms, substituting y=e^x to get a quadratic) followed by taking logarithms. While it involves multiple steps, the technique is routine for P3 level with no conceptual challenges or novel insights required, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b
2 Showing all necessary working, solve the equation \(\frac { 2 \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } } { \mathrm { e } ^ { x } - \mathrm { e } ^ { - x } } = 4\), giving your answer correct to 2 decimal places.
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
Rearrange the equation in the form \(ae^{2x} = b\) or \(ae^x = be^{-x}\)M1
Obtain correct equation in either form with \(a = 2\) and \(b = 5\)A1
Use correct method to solve for \(x\)M1
Obtain answer \(x = 0.46\)A1 
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| Rearrange the equation in the form $ae^{2x} = b$ or $ae^x = be^{-x}$ | M1 | |
| Obtain correct equation in either form with $a = 2$ and $b = 5$ | A1 | |
| Use correct method to solve for $x$ | M1 | |
| Obtain answer $x = 0.46$ | A1 | |

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2 Showing all necessary working, solve the equation $\frac { 2 \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } } { \mathrm { e } ^ { x } - \mathrm { e } ^ { - x } } = 4$, giving your answer correct to 2 decimal places.\\

\hfill \mbox{\textit{CAIE P3 2018 Q2 [4]}}
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