OCR C4 Specimen — Question 1 4 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
SessionSpecimen
Marks4
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Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Quadratic Divisor
DifficultyModerate -0.8 This is a straightforward polynomial long division problem with no complications. The divisor and dividend have convenient forms, requiring only basic algebraic manipulation to find quotient x²-1 and remainder 2. It's easier than average as it tests only mechanical application of the division algorithm with minimal steps.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
1 Find the quotient and remainder when \(x ^ { 4 } + 1\) is divided by \(x ^ { 2 } + 1\).
AnswerMarks Guidance
\(\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}\)B1 For correct leading term \(x^2\) in quotient
\(\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}\)M1 For evidence of correct division process
\(\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}\)A1 For correct quotient \(x^2-1\)
\(\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}\)A1 For correct remainder 2
4 
$\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}$ | B1 | For correct leading term $x^2$ in quotient
$\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}$ | M1 | For evidence of correct division process
$\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}$ | A1 | For correct quotient $x^2-1$
$\frac{x^4+1}{x^2+1} = x^2 - 1 + \frac{2}{x^2+1}$ | A1 | For correct remainder 2
| **4** |
1 Find the quotient and remainder when $x ^ { 4 } + 1$ is divided by $x ^ { 2 } + 1$.

\hfill \mbox{\textit{OCR C4  Q1 [4]}}
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