OCR MEI C4 2008 January — Question 5 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2008
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with quadratic in denominator
DifficultyModerate -0.8 This is a straightforward partial fractions question with a standard form (linear factor times irreducible quadratic). It requires only routine application of the cover-up method and algebraic manipulation to find constants A, B, and C in the form A/x + (Bx+C)/(x²+4), with no problem-solving or novel insight needed.
Spec4.05c Partial fractions: extended to quadratic denominators
5 Express \(\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }\) in partial fractions.
AnswerMarks
(i) Gradients: \(-\frac{1}{\phi}\) and \(\frac{1}{\phi - 1}\)B1 B1
(ii) Product of gradients: \(-\frac{1}{\phi} \times \frac{1}{\phi - 1} = -\frac{1}{\phi^2 - \phi}\)M1 E1
\(= -\frac{1}{1} = -1\) 
(i) Gradients: $-\frac{1}{\phi}$ and $\frac{1}{\phi - 1}$ | B1 B1 |

(ii) Product of gradients: $-\frac{1}{\phi} \times \frac{1}{\phi - 1} = -\frac{1}{\phi^2 - \phi}$ | M1 E1 |

$= -\frac{1}{1} = -1$ |
5 Express $\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }$ in partial fractions.

\hfill \mbox{\textit{OCR MEI C4 2008 Q5 [6]}}
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Q1 7 Q2 8 Q3 5 Q4 7 Q5 6 Q6 3 Q7 18 Q8 18