OCR MEI Paper 1 2023 June — Question 2 4 marks

Exam BoardOCR MEI
ModulePaper 1 (Paper 1)
Year2023
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypeBasic partial fractions decomposition
DifficultyEasy -1.2 This is a straightforward partial fractions question requiring factorization of a quadratic denominator into linear factors, then solving for constants using standard methods (cover-up or equating coefficients). It's a routine textbook exercise with no complications like repeated factors or improper fractions, making it easier than average.
Spec1.02y Partial fractions: decompose rational functions

2 Express \(\frac { 5 x + 1 } { x ^ { 2 } - x - 12 }\) in partial fractions.

Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(x^2 - x - 12 = (x-4)(x+3)\)B1 Both factors seen
\(\frac{5x+1}{x^2-x-12} = \frac{A}{x-4} + \frac{B}{x+3}\)M1 Setting up partial fractions using their factors. May be implied by correct expression as final answer
\(5x+1 = A(x+3) + B(x-4)\)
Substitute \(x = -3\) giving \(B = 2\)M1 Method for finding either \(A\) or \(B\)
Substitute \(x = 4\) giving \(A = 3\)A1 Both \(A\) and \(B\) correct if clear which denominator they apply to. ISW if an error made only in the transcription to final answer
\(\frac{5x+1}{x^2-x-12} = \frac{3}{x-4} + \frac{2}{x+3}\)
Total: [4]
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x^2 - x - 12 = (x-4)(x+3)$ | B1 | Both factors seen |
| $\frac{5x+1}{x^2-x-12} = \frac{A}{x-4} + \frac{B}{x+3}$ | M1 | Setting up partial fractions using their factors. May be implied by correct expression as final answer |
| $5x+1 = A(x+3) + B(x-4)$ | | |
| Substitute $x = -3$ giving $B = 2$ | M1 | Method for finding either $A$ or $B$ |
| Substitute $x = 4$ giving $A = 3$ | A1 | Both $A$ and $B$ correct if clear which denominator they apply to. ISW if an error made only in the transcription to final answer |
| $\frac{5x+1}{x^2-x-12} = \frac{3}{x-4} + \frac{2}{x+3}$ | | |

**Total: [4]**

---
2 Express $\frac { 5 x + 1 } { x ^ { 2 } - x - 12 }$ in partial fractions.

\hfill \mbox{\textit{OCR MEI Paper 1 2023 Q2 [4]}}