CAIE P2 2020 November — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using subtraction law
DifficultyModerate -0.5 This is a straightforward application of the logarithm subtraction law (ln a - ln b = ln(a/b)) followed by exponentiating both sides and solving a linear equation. It requires fewer steps than a typical multi-part question and involves only routine algebraic manipulation with no problem-solving insight needed.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
1 Given that $$\ln ( 2 x + 1 ) - \ln ( x - 3 ) = 2$$ find \(x\) in terms of e.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Use correct logarithm property to simplify left-hand sideM1 Or equivalent method
Use correct process to obtain equation without logarithmsM1
Obtain \(\dfrac{2x+1}{x-3} = e^2\)A1 OE
Obtain \(x = \dfrac{3e^2+1}{e^2-2}\)A1 OE
Total4 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use correct logarithm property to simplify left-hand side | M1 | Or equivalent method |
| Use correct process to obtain equation without logarithms | M1 | |
| Obtain $\dfrac{2x+1}{x-3} = e^2$ | A1 | OE |
| Obtain $x = \dfrac{3e^2+1}{e^2-2}$ | A1 | OE |
| **Total** | **4** | |

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1 Given that

$$\ln ( 2 x + 1 ) - \ln ( x - 3 ) = 2$$

find $x$ in terms of e.\\

\hfill \mbox{\textit{CAIE P2 2020 Q1 [4]}}
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