CAIE P3 2013 June — Question 3 5 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2013
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with quadratic in denominator
DifficultyModerate -0.5 This is a standard partial fractions decomposition with a linear factor and an irreducible quadratic factor. The setup is straightforward (A/x + (Bx+C)/(x²+1)), requiring only routine algebraic manipulation to find coefficients. While it involves more steps than the simplest partial fractions problems, it's a textbook exercise with no conceptual challenges beyond applying the standard method.
Spec1.02y Partial fractions: decompose rational functions

3 Express \(\frac { 7 x ^ { 2 } - 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

Question 3:
AnswerMarks Guidance
Answer/WorkingMark Guidance
State or imply correct form \(\frac{A}{x} + \frac{Bx+C}{x^2+1}\)B1
Use any relevant method to find at least one constantM1
Obtain \(A = 2\)A1
Obtain \(B = 5\)A1
Obtain \(C = -3\)A1 [5]
## Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| State or imply correct form $\frac{A}{x} + \frac{Bx+C}{x^2+1}$ | B1 | |
| Use any relevant method to find at least one constant | M1 | |
| Obtain $A = 2$ | A1 | |
| Obtain $B = 5$ | A1 | |
| Obtain $C = -3$ | A1 | [5] |

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3 Express $\frac { 7 x ^ { 2 } - 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }$ in partial fractions.

\hfill \mbox{\textit{CAIE P3 2013 Q3 [5]}}