CAIE P2 2020 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeExponential to linear form proof
DifficultyModerate -0.8 This is a straightforward logarithm application requiring students to take logs of both sides and use basic log laws (log of a power). It's a standard textbook exercise with a clear method and minimal steps, making it easier than average but not trivial since it requires correct manipulation of logarithmic properties.
Spec1.06g Equations with exponentials: solve a^x = b

1 Given that \(2 ^ { y } = 9 ^ { 3 x }\), use logarithms to show that \(y = k x\) and find the value of \(k\) correct to 3 significant figures.

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Apply logarithms to both sides and apply power law at least onceM1
Rearrange to the form \(y = \dfrac{3\ln 9}{\ln 2}x\)A1 OE
Obtain \(k = 9.51\)A1
Total3
**Question 1:**

| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms to both sides and apply power law at least once | M1 | |
| Rearrange to the form $y = \dfrac{3\ln 9}{\ln 2}x$ | A1 | OE |
| Obtain $k = 9.51$ | A1 | |
| **Total** | **3** | |

---
1 Given that $2 ^ { y } = 9 ^ { 3 x }$, use logarithms to show that $y = k x$ and find the value of $k$ correct to 3 significant figures.\\

\hfill \mbox{\textit{CAIE P2 2020 Q1 [3]}}