CAIE P2 2022 November — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2022
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeMixed exponential and e terms
DifficultyStandard +0.3 This is a straightforward logarithmic equation requiring students to take logarithms of both sides, apply log laws to bring down the exponents, collect terms in x, and solve. It's a standard textbook exercise with clear methodology and no conceptual surprises, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

2 Use logarithms to solve the equation \(14 \mathrm { e } ^ { - 2 x } = 5 ^ { x + 1 }\), giving your answer correct to 3 significant figures. [4]

Question 2:
AnswerMarks Guidance
AnswerMark Guidance
Apply logarithms correctly to both sides and apply power law at least once\*M1
Obtain \(\ln 14 - 2x = (x+1)\ln 5\)A1 OE with \(x\) no longer part of a power
Attempt solution of linear equationDM1 Must have \(\ln 14 - \ln 5 = x(2 + \ln 5)\)
Obtain \(0.285\)A1
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms correctly to both sides and apply power law at least once | \*M1 | |
| Obtain $\ln 14 - 2x = (x+1)\ln 5$ | A1 | OE with $x$ no longer part of a power |
| Attempt solution of linear equation | DM1 | Must have $\ln 14 - \ln 5 = x(2 + \ln 5)$ |
| Obtain $0.285$ | A1 | |

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2 Use logarithms to solve the equation $14 \mathrm { e } ^ { - 2 x } = 5 ^ { x + 1 }$, giving your answer correct to 3 significant figures. [4]\\

\hfill \mbox{\textit{CAIE P2 2022 Q2 [4]}}