CAIE P2 2004 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2004
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeExponential to linear form proof
DifficultyEasy -1.2 This is a straightforward application of logarithms to solve an exponential equation. It requires taking logs of both sides and using log laws (log a^n = n log a), then simple algebraic manipulation to find x/y. This is a standard textbook exercise testing basic logarithm rules with no problem-solving insight needed, making it easier than average.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
1 Given that \(2 ^ { x } = 5 ^ { y }\), use logarithms to find the value of \(\frac { x } { y }\) correct to 3 significant figures.
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Use logarithms to linearise an equationM1
Obtain \(\frac{x}{y} = \frac{\ln 5}{\ln 2}\) or equivalentA1
Obtain answer 2.32A1 Total: 3 
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use logarithms to linearise an equation | M1 | |
| Obtain $\frac{x}{y} = \frac{\ln 5}{\ln 2}$ or equivalent | A1 | |
| Obtain answer 2.32 | A1 | **Total: 3** |

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1 Given that $2 ^ { x } = 5 ^ { y }$, use logarithms to find the value of $\frac { x } { y }$ correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2004 Q1 [3]}}
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