| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions for differential equations |
| Difficulty | Standard +0.3 This is a straightforward two-part question combining routine partial fractions decomposition with separation of variables for a differential equation. Part (i) is standard textbook practice, and part (ii) follows a predictable method (separate variables, integrate using the partial fractions result, apply initial condition). The 'show that' format removes problem-solving challenge since students know the target answer. Slightly above average difficulty only due to the multi-step integration and algebraic manipulation required. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08k Separable differential equations: dy/dx = f(x)g(y)1.08l Interpret differential equation solutions: in context |
(i) Express $\frac{1}{(2x-1)(x-1)}$ in partial fractions. [3]
(ii) A curve passes through the point $(0, 2)$ and satisfies the differential equation
$$\frac{dy}{dx} = \frac{y}{(2x-1)(x-1)}$$
Show by integration that $y = \frac{4x-2}{x-1}$. [5]6 (i) Express $\frac { 1 } { ( 2 x + 1 ) ( x + 1 ) }$ in partial fractions.\\
(ii) A curve passes through the point $( 0,2 )$ and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y } { ( 2 x + 1 ) ( x + 1 ) }$$
Show by integration that $y = \frac { 4 x + 2 } { x + 1 }$.
Section B (36 marks)\\
\hfill \mbox{\textit{OCR MEI C4 2007 Q6 [8]}}