CAIE P3 2021 November — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Quadratic Divisor
DifficultyModerate -0.5 This is a straightforward polynomial long division problem with no complications. The dividend and divisor are given explicitly, and the task is purely mechanical application of the division algorithm. It requires fewer steps than average A-level questions and involves no problem-solving or conceptual insight beyond executing a standard procedure.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
1 Find the quotient and remainder when \(2 x ^ { 4 } + 1\) is divided by \(x ^ { 2 } - x + 2\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Commence division and reach partial quotient of the form \(2x^2 + kx\)M1
Obtain quotient \(2x^2 + 2x - 2\)A1
Obtain remainder \(-6x + 5\)A1
Total3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Commence division and reach partial quotient of the form $2x^2 + kx$ | M1 | |
| Obtain quotient $2x^2 + 2x - 2$ | A1 | |
| Obtain remainder $-6x + 5$ | A1 | |
| **Total** | **3** | |

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1 Find the quotient and remainder when $2 x ^ { 4 } + 1$ is divided by $x ^ { 2 } - x + 2$.\\

\hfill \mbox{\textit{CAIE P3 2021 Q1 [3]}}
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