OCR C4 2006 January — Question 1 3 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypeSimple Algebraic Fraction Simplification
DifficultyEasy -1.2 This is a straightforward algebraic fraction simplification requiring factorisation of numerator (x² common factor) and denominator (difference of two squares), then cancellation. It's a single-step problem testing basic factorisation skills with no problem-solving or novel insight required, making it easier than average.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division

1 Simplify \(\frac { x ^ { 3 } - 3 x ^ { 2 } } { x ^ { 2 } - 9 }\).

Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Attempt to factorise numerator and denominatorM1
num \(= xx(x-3)\) or denom \(= (x-3)(x+3)\)A1 Not num \(= x(x^2-3x)\)
Final answer \(= \frac{x^2}{x+3}\) [Not \(\frac{xx}{x+3}\)]A1 3 Do not ignore further cancellation
# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempt to factorise numerator and denominator | M1 | |
| num $= xx(x-3)$ or denom $= (x-3)(x+3)$ | A1 | Not num $= x(x^2-3x)$ |
| Final answer $= \frac{x^2}{x+3}$ [Not $\frac{xx}{x+3}$] | A1 | **3** Do not ignore further cancellation |
1 Simplify $\frac { x ^ { 3 } - 3 x ^ { 2 } } { x ^ { 2 } - 9 }$.

\hfill \mbox{\textit{OCR C4 2006 Q1 [3]}}