CAIE P2 2024 June — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2024
SessionJune
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, expand using log laws, collect terms in x, and solve. It's a standard textbook exercise with clear methodology and no conceptual challenges beyond applying familiar techniques, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

2 Use logarithms to solve the equation \(6 ^ { 2 x - 1 } = 5 \mathrm { e } ^ { 3 x + 2 }\). Give your answer correct to 4 significant figures. [4]

Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\((2x-1)\ln 6\)M1
\(\ln 5 + 3x + 2\)\*M1
Attempt solution of linear equationDM1
Obtain \(9.256\)A1 Or greater accuracy
Total: 4 marks
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| $(2x-1)\ln 6$ | **M1** | |
| $\ln 5 + 3x + 2$ | **\*M1** | |
| Attempt solution of linear equation | **DM1** | |
| Obtain $9.256$ | **A1** | Or greater accuracy |

**Total: 4 marks**
2 Use logarithms to solve the equation $6 ^ { 2 x - 1 } = 5 \mathrm { e } ^ { 3 x + 2 }$. Give your answer correct to 4 significant figures. [4]\\

\hfill \mbox{\textit{CAIE P2 2024 Q2 [4]}}