OCR C1 2012 June — Question 1 3 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2012
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Expansion and Simplification
DifficultyEasy -1.2 This is a straightforward algebraic expansion and simplification requiring only basic distributive property and combining like terms. It's routine C1 content with no problem-solving element—purely mechanical manipulation that's easier than average A-level questions.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

1 Simplify \(( x - 5 ) \left( x ^ { 2 } + 3 \right) - ( x + 4 ) ( x - 1 )\).

Question 1:
AnswerMarks Guidance
[answer/working][mark] [guidance]
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Mark Scheme Extraction
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(x^3 - 5x^2 + 3x - 15 - (x^2 + 4x - x - 4)\)M1 Attempt to expand both pairs of brackets. No more than one "missing term"
Expansion with at most one incorrect term (no missing terms)A1 Do not allow "invisible brackets" unless final answer correct. Allow one simplified incorrect term e.g. \((x^2 + 5x - 4)\)
\(= x^3 - 6x^2 - 11\)A1 [3] cao
Question 1:
[answer/working] | [mark] | [guidance]
```

# Mark Scheme Extraction

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## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $x^3 - 5x^2 + 3x - 15 - (x^2 + 4x - x - 4)$ | M1 | Attempt to expand both pairs of brackets. No more than one "missing term" |
| Expansion with at most one incorrect term (no missing terms) | A1 | Do not allow "invisible brackets" unless final answer correct. Allow one simplified incorrect term e.g. $(x^2 + 5x - 4)$ |
| $= x^3 - 6x^2 - 11$ | A1 [3] | cao |

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1 Simplify $( x - 5 ) \left( x ^ { 2 } + 3 \right) - ( x + 4 ) ( x - 1 )$.

\hfill \mbox{\textit{OCR C1 2012 Q1 [3]}}