CAIE P2 Specimen — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
SessionSpecimen
Marks4
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Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward application of logarithms to solve an exponential equation with a single unknown. It requires only taking logs of both sides, expanding using log laws, collecting terms in x, and calculator work—all standard techniques with no problem-solving insight needed. Easier than average but not trivial since it involves algebraic manipulation.
Spec1.06g Equations with exponentials: solve a^x = b
1 Use logarithms to solve the equation $$5 ^ { x + 3 } = 7 ^ { x - 1 }$$ giving the answer correct to 3 significant figures.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Introduce logarithms and use power law twiceM1*
Obtain \((x+3)\log 5 = (x-1)\log 7\) or equivalentA1
Solve linear equation for \(x\)DM1
Obtain \(20.1\)A1
Total: 4 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Introduce logarithms and use power law twice | M1* | |
| Obtain $(x+3)\log 5 = (x-1)\log 7$ or equivalent | A1 | |
| Solve linear equation for $x$ | DM1 | |
| Obtain $20.1$ | A1 | |
| **Total: 4** | | |

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1 Use logarithms to solve the equation

$$5 ^ { x + 3 } = 7 ^ { x - 1 }$$

giving the answer correct to 3 significant figures.\\

\hfill \mbox{\textit{CAIE P2  Q1 [4]}}
This paper (6 questions)
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Q1 4 Q2 5 Q3 7 Q4 7 Q6 9 Q7 11