| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Combining Algebraic Fractions |
| Difficulty | Moderate -0.8 This question tests routine algebraic manipulation skills. Part (i) requires factorising a difference of squares and finding a common denominator—standard techniques. Part (ii) involves recognising and factorising a difference of cubes and a quadratic, then cancelling common factors. Both parts are straightforward applications of well-practiced methods with no problem-solving or novel insight required, making this easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
4. (i) Express
$$\frac { 4 x } { x ^ { 2 } - 9 } - \frac { 2 } { x + 3 }$$
as a single fraction in its simplest form.\\
(ii) Simplify
$$\frac { x ^ { 3 } - 8 } { 3 x ^ { 2 } - 8 x + 4 }$$
\hfill \mbox{\textit{OCR C4 Q4 [8]}}