| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions showing coefficient is zero |
| Difficulty | Standard +0.3 This is a standard C4 partial fractions question with a routine twist of showing one coefficient is zero, followed by straightforward binomial expansions. The techniques are well-practiced (cover-up method, substitution), and part (ii) involves direct application of the binomial theorem with simple indices. Slightly above average due to the two-part structure and algebraic manipulation required, but no novel insight needed. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Linear model: \(R = mt + c\) identified/used | M1 | Using linear model from article |
| Setting \(R = 0\) and solving for \(t\) | M1 | |
| Converting \(t\) value to calendar year | M1 | |
| Correct year stated (approx 2636) | A1 | ft from their linear equation |
# Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Linear model: $R = mt + c$ identified/used | M1 | Using linear model from article |
| Setting $R = 0$ and solving for $t$ | M1 | |
| Converting $t$ value to calendar year | M1 | |
| Correct year stated (approx 2636) | A1 | ft from their linear equation |
---2 (i) Given that
$$\frac { 3 + 2 x ^ { 2 } } { ( 1 + x ) ^ { 2 } ( 1 - 4 x ) } = \frac { A } { 1 + x } + \frac { B } { ( 1 + x ) ^ { 2 } } + \frac { C } { 1 - 4 x } ,$$
where $A , B$ and $C$ are constants, find $B$ and $C$, and show that $A = 0$.\\
(ii) Given that $x$ is sufficiently small, find the first three terms of the binomial expansions of $( 1 + x ) ^ { - 2 }$ and $( 1 - 4 x ) ^ { - 1 }$.
Hence find the first three terms of the expansion of $\frac { 3 + 2 x ^ { 2 } } { ( 1 + x ) ^ { 2 } ( 1 - 4 x ) }$.
\hfill \mbox{\textit{OCR MEI C4 2006 Q2 [11]}}