CAIE P1 2010 November — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2010
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeIntegrate after expanding or multiplying out
DifficultyEasy -1.2 This requires expanding a simple binomial (x + 1/x)² to get x² + 2 + 1/x², then integrating term-by-term using standard power rules. It's a straightforward algebraic manipulation followed by routine integration with no problem-solving required, making it easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 Find \(\int \left( x + \frac { 1 } { x } \right) ^ { 2 } \mathrm {~d} x\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\int\left(x+\frac{1}{x}\right)^2 dx = \frac{x^3}{3} - \frac{1}{x} + 2x + (c)\)\(B1 \times 3\) Omission of middle term of expansion can still get 2/3 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int\left(x+\frac{1}{x}\right)^2 dx = \frac{x^3}{3} - \frac{1}{x} + 2x + (c)$ | $B1 \times 3$ | Omission of middle term of expansion can still get 2/3 |

---
1 Find $\int \left( x + \frac { 1 } { x } \right) ^ { 2 } \mathrm {~d} x$.

\hfill \mbox{\textit{CAIE P1 2010 Q1 [3]}}
This paper (11 questions)
View full paper
Q1 3 Q2 4 Q3 5 Q4 6 Q5 6 Q6 7 Q7 7 Q8 8 Q9 8 Q10 10 Q11 11