CAIE P2 2010 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2010
SessionJune
Marks3
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Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeExponential to linear form proof
DifficultyModerate -0.8 This is a straightforward logarithm manipulation requiring students to take logs of both sides and rearrange to isolate y/x. It's a standard textbook exercise testing basic log laws with no problem-solving insight needed, making it easier than average but not trivial since it requires correct algebraic manipulation.
Spec1.06d Natural logarithm: ln(x) function and properties1.06f Laws of logarithms: addition, subtraction, power rules
1 Given that \(13 ^ { x } = ( 2.8 ) ^ { y }\), use logarithms to show that \(y = k x\) and find the value of \(k\) correct to 3 significant figures.
AnswerMarks Guidance
State or imply \(y \log 2.8 = x \log 13\)B1
Rearrange into form \(y = \frac{\log 13}{\log 2.8}\) or equivalentB1
Obtain answer \(k = 2.49\)B1 [3] 
State or imply $y \log 2.8 = x \log 13$ | B1 |

Rearrange into form $y = \frac{\log 13}{\log 2.8}$ or equivalent | B1 |

Obtain answer $k = 2.49$ | B1 | [3]
1 Given that $13 ^ { x } = ( 2.8 ) ^ { y }$, use logarithms to show that $y = k x$ and find the value of $k$ correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2010 Q1 [3]}}
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