CAIE P2 2017 March — Question 1 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionMarch
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyStandard +0.3 This is a straightforward logarithm equation requiring application of power and subtraction laws to combine terms, then solving the resulting quadratic. It's slightly above average difficulty due to the algebraic manipulation needed, but follows a standard template with no novel insight required.
Spec1.06f Laws of logarithms: addition, subtraction, power rules
1 Solve the equation \(2 \ln ( 2 x ) - \ln ( x + 3 ) = \ln ( 3 x + 5 )\).
Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Use \(2\ln(2x) = \ln(2x)^2\)\*M1
Use addition or subtraction property of logarithms\*M1
Obtain \(4x^2 = (x+3)(3x+5)\) or equivalent without logarithmsA1
Solve 3-term quadratic equationDM1 dep \*M \*M
Conclude with \(x = 15\) onlyA1 
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| Use $2\ln(2x) = \ln(2x)^2$ | \*M1 | |
| Use addition or subtraction property of logarithms | \*M1 | |
| Obtain $4x^2 = (x+3)(3x+5)$ or equivalent without logarithms | A1 | |
| Solve 3-term quadratic equation | DM1 | dep \*M \*M |
| Conclude with $x = 15$ only | A1 | |

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1 Solve the equation $2 \ln ( 2 x ) - \ln ( x + 3 ) = \ln ( 3 x + 5 )$.\\

\hfill \mbox{\textit{CAIE P2 2017 Q1 [5]}}
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Q1 5 Q2 5 Q3 6 Q4 6 Q5 8 Q6 10