OCR C4 — Question 4 8 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypeCombining Algebraic Fractions
DifficultyModerate -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.
Spec1.02j 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 $$\frac { x ^ { 3 } - 8 } { 3 x ^ { 2 } - 8 x + 4 }$$

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]}}