CAIE P3 2016 November — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Functions
TypeSolve rational exponential equation
DifficultyModerate -0.5 This is a straightforward algebraic manipulation question requiring cross-multiplication, collecting terms, and taking logarithms. While it involves exponential functions, the technique is routine for P3 level with no conceptual difficulty or multi-step problem-solving required. Slightly easier than average due to its direct approach.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
1 Solve the equation \(\frac { 3 ^ { x } + 2 } { 3 ^ { x } - 2 } = 8\), giving your answer correct to 3 decimal places.
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Solve for \(3^x\) and obtain \(3^x = \frac{18}{7}\)B1
Use correct method for solving equation of form \(3^x = a\), where \(a > 0\)M1
Obtain answer \(x = 0.860\)A1 3 d.p. only 
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Solve for $3^x$ and obtain $3^x = \frac{18}{7}$ | B1 | |
| Use correct method for solving equation of form $3^x = a$, where $a > 0$ | M1 | |
| Obtain answer $x = 0.860$ | A1 | 3 d.p. only |

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1 Solve the equation $\frac { 3 ^ { x } + 2 } { 3 ^ { x } - 2 } = 8$, giving your answer correct to 3 decimal places.

\hfill \mbox{\textit{CAIE P3 2016 Q1 [3]}}
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