CAIE P3 2020 March — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionMarch
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 (sum and power rules) to form a quadratic equation. While it involves multiple steps and algebraic manipulation, it follows a predictable pattern with no conceptual surprises, making it slightly easier than average for A-level.
Spec1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|

2 Solve the equation \(\ln 3 + \ln ( 2 x + 5 ) = 2 \ln ( x + 2 )\). Give your answer in a simplified exact form.

Question 2:
AnswerMarks
Use law of logarithm of a power and sum, remove logarithmsM1
Obtain correct equation e.g. \(3(2x+5)=(x+2)^2\)A1
Use correct method to solve a 3-term quadratic, obtaining at least one rootM1
Obtain final answer \(x = 1+2\sqrt{3}\) or \(1+\sqrt{12}\) onlyA1
## Question 2:

| Use law of logarithm of a power and sum, remove logarithms | M1 | |
| Obtain correct equation e.g. $3(2x+5)=(x+2)^2$ | A1 | |
| Use correct method to solve a 3-term quadratic, obtaining at least one root | M1 | |
| Obtain final answer $x = 1+2\sqrt{3}$ or $1+\sqrt{12}$ only | A1 | |

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2 Solve the equation $\ln 3 + \ln ( 2 x + 5 ) = 2 \ln ( x + 2 )$. Give your answer in a simplified exact form.\\

\hfill \mbox{\textit{CAIE P3 2020 Q2 [4]}}