CAIE P3 2018 November — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeRational exponential equation
DifficultyModerate -0.3 This is a straightforward exponential equation requiring multiplication to clear the fraction, rearrangement into a quadratic in e^x, and solving. The technique is standard for P3 level with no conceptual difficulty beyond recognizing the substitution method, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

Showing all necessary working, solve the equation \(\frac{2e^x + e^{-x}}{e^x - e^{-x}} = 4\), giving your answer correct to 2 decimal places. [4]

Question 2:
AnswerMarks Guidance
2Rearrange the equation in the form ae2x =b or aex =be−x M1
Obtain correct equation in either form with a = 2 and b = 5A1
Use correct method to solve for xM1
Obtain answer x = 0.46A1
4
AnswerMarks Guidance
QuestionAnswer Marks
Question 2:
2 | Rearrange the equation in the form ae2x =b or aex =be−x | M1
Obtain correct equation in either form with a = 2 and b = 5 | A1
Use correct method to solve for x | M1
Obtain answer x = 0.46 | A1
4
Question | Answer | Marks | Guidance
Showing all necessary working, solve the equation $\frac{2e^x + e^{-x}}{e^x - e^{-x}} = 4$, giving your answer correct to 2 decimal places. [4]

\hfill \mbox{\textit{CAIE P3 2018 Q2 [4]}}