CAIE P2 2004 November — Question 2 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2004
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeSolve power equations
DifficultyModerate -0.8 This is a straightforward power equation requiring only basic index law manipulation: dividing both sides by x^3.2 gives x^0.7 = 11, then taking the (1/0.7)th power. It's a single-step algebraic technique with no conceptual difficulty, making it easier than average but not trivial since students must recognize the approach.
Spec1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b
2 Solve the equation \(x ^ { 3.9 } = 11 x ^ { 3.2 }\), where \(x \neq 0\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Use logarithms to obtain an equation in \(\ln x\)M1
Obtain \(\ln x = \frac{\ln 11}{(3.9-3.2)}\), or equivalentA1
Obtain answer \(x = 31\) (accept 30.7, 30.74)A1 Total: 3 
## Question 2:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Use logarithms to obtain an equation in $\ln x$ | M1 | |
| Obtain $\ln x = \frac{\ln 11}{(3.9-3.2)}$, or equivalent | A1 | |
| Obtain answer $x = 31$ (accept 30.7, 30.74) | A1 | **Total: 3** |

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2 Solve the equation $x ^ { 3.9 } = 11 x ^ { 3.2 }$, where $x \neq 0$.

\hfill \mbox{\textit{CAIE P2 2004 Q2 [3]}}
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Q1 3 Q2 3 Q3 4 Q4 5 Q5 6 Q6 8 Q7 11 Q8 10