| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions with validity range |
| Difficulty | Moderate -0.3 This is a standard two-part question combining partial fractions with binomial expansion. Part (i) is routine A-level algebra. Part (ii) requires applying the binomial theorem to each partial fraction term and collecting coefficients, which is a well-practiced C4 technique. The validity condition is straightforward (intersection of convergence radii). While it requires multiple steps and careful algebra, it follows a predictable template with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
| Answer | Marks |
|---|---|
| 1 | y degrees |
| Answer | Marks | Guidance |
|---|---|---|
| 80 –1 | 50 –1 | 20 –9 |
| –30 | 3 | 0 6 |
Question 1:
1 | y degrees
90
60
30
x degrees
–180 –150 –120 –90 –60 –30 0 30 60 90 120 150 180
–30
–60
–90
Fig. 4
90
60
30
80 –1 | 50 –1 | 20 –9 | 0 –6 | 0 –3 | 0 0
–30 | 3 | 0 6 | 0 9 | 0 1 | 20 15 | 0 1
–
60
–\begin{enumerate}[label=(\roman*)]
\item Express $\frac{x}{(1 + x)(1 - 2x)}$ in partial fractions. [3]
\item Hence use binomial expansions to show that $\frac{x}{(1 + x)(1 - 2x)} = ax + bx^2 + ...$, where $a$ and $b$ are constants to be determined.
State the set of values of $x$ for which the expansion is valid. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 2013 Q1 [8]}}