OCR C4 2007 January — Question 1 3 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2007
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypeSimple Algebraic Fraction Simplification
DifficultyModerate -0.8 This is a straightforward algebraic simplification requiring factorisation of both numerator and denominator, then cancelling common factors. It's a routine C4 skill with no problem-solving element—students either recognise the factorisation or they don't. Below average difficulty due to being purely procedural with clear method.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division

It is given that $$f(x) = \frac{x^2 + 2x - 24}{x^2 - 4x} \quad \text{for } x \neq 0, x \neq 4.$$ Express \(f(x)\) in its simplest form. [3]

AnswerMarks Guidance
Factorise numerator and denominator: \(\text{Num} = (x+6)(x-4)\) or \(\text{denom} = x(x-4)\)M1
Final answer \(= \frac{x+6}{x}\) or \(1 + \frac{6}{x}\)A1 3 marks
Factorise numerator and denominator: $\text{Num} = (x+6)(x-4)$ or $\text{denom} = x(x-4)$ | M1 |

Final answer $= \frac{x+6}{x}$ or $1 + \frac{6}{x}$ | A1 | 3 marks |

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It is given that
$$f(x) = \frac{x^2 + 2x - 24}{x^2 - 4x} \quad \text{for } x \neq 0, x \neq 4.$$

Express $f(x)$ in its simplest form. [3]

\hfill \mbox{\textit{OCR C4 2007 Q1 [3]}}