CAIE P2 2011 June — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2011
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward exponential equation requiring a standard technique: take logarithms of both sides, apply log laws, and solve linearly for x. It's a single-step problem testing basic logarithm manipulation with no conceptual difficulty or problem-solving required, making it easier than the average A-level question.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
1 Use logarithms to solve the equation \(3 ^ { x } = 2 ^ { x + 2 }\), giving your answer correct to 3 significant figures.
AnswerMarks Guidance
Use power law for logarithms: \(x\log 3 = x\log 2 + 2\log 2\) or equivalentM1*
Obtain \(x\log 3 = x\log 2 + 2\log 2\) or equivalentA1
Attempt solution for \(x\) of linear equationM1 dep*
Obtain \(3.42\)A1 [4] 
Use power law for logarithms: $x\log 3 = x\log 2 + 2\log 2$ or equivalent | M1* |
Obtain $x\log 3 = x\log 2 + 2\log 2$ or equivalent | A1 |
Attempt solution for $x$ of linear equation | M1 dep* |
Obtain $3.42$ | A1 | [4]
1 Use logarithms to solve the equation $3 ^ { x } = 2 ^ { x + 2 }$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2011 Q1 [4]}}
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