CAIE P3 2021 November — Question 3 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Functions
TypeSolve exponential equation using logarithms
DifficultyModerate -0.3 This is a straightforward exponential equation requiring factorization of 4^x terms and basic logarithm application. While it needs algebraic manipulation (factoring out 4^x and dividing by 4^2), it's a standard technique taught in P3 with no conceptual difficulty or novel insight required, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

3 Solve the equation \(4 ^ { x - 2 } = 4 ^ { x } - 4 ^ { 2 }\), giving your answer correct to 3 decimal places.

Question 3:
AnswerMarks Guidance
AnswerMark Guidance
Use laws of indices correctly and solve for \(4^x\)M1
Obtain correct solution in any form, e.g. \(4^x = \frac{256}{15}\)A1
Use a correct method for solving an equation of the form \(4^x = a\), where \(a > 0\)M1
Obtain answer \(2.047\)A1
## Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| Use laws of indices correctly and solve for $4^x$ | M1 | |
| Obtain correct solution in any form, e.g. $4^x = \frac{256}{15}$ | A1 | |
| Use a correct method for solving an equation of the form $4^x = a$, where $a > 0$ | M1 | |
| Obtain answer $2.047$ | A1 | |

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3 Solve the equation $4 ^ { x - 2 } = 4 ^ { x } - 4 ^ { 2 }$, giving your answer correct to 3 decimal places.\\

\hfill \mbox{\textit{CAIE P3 2021 Q3 [4]}}