CAIE P3 2015 June — Question 1 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2015
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyModerate -0.3 This is a straightforward logarithm equation requiring application of standard log laws (power law and addition law) to simplify, then solving the resulting quadratic. It's slightly easier than average as it follows a standard template with no conceptual surprises, though it does require multiple steps and careful algebraic manipulation.
Spec1.06g Equations with exponentials: solve a^x = b

1 Solve the equation \(\ln ( x + 4 ) = 2 \ln x + \ln 4\), giving your answer correct to 3 significant figures.

AnswerMarks Guidance
Use law for the logarithm of a product, quotient or powerM1
Obtain a correct equation free of logarithms, e.g. \(\frac{x+4}{x^2} = 4\)A1
Solve a 3-term quadratic obtaining at least one rootM1
Obtain final answer \(x = 1.13\) onlyA1 4
Use law for the logarithm of a product, quotient or power | M1 |

Obtain a correct equation free of logarithms, e.g. $\frac{x+4}{x^2} = 4$ | A1 |

Solve a 3-term quadratic obtaining at least one root | M1 |

Obtain final answer $x = 1.13$ only | A1 | 4 |
1 Solve the equation $\ln ( x + 4 ) = 2 \ln x + \ln 4$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P3 2015 Q1 [4]}}