CAIE P3 2020 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Quadratic Divisor
DifficultyModerate -0.5 This is a straightforward polynomial long division question requiring systematic application of the division algorithm. While it involves a quartic divided by a quadratic (requiring multiple steps), the technique is mechanical and well-practiced at A-level, with no conceptual challenges or problem-solving insight needed beyond careful arithmetic.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

1 Find the quotient and remainder when \(6 x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + 5 x - 6\) is divided by \(2 x ^ { 2 } - x + 1\).

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Commence division and reach partial quotient \(3x^2 + kx\)M1
Obtain quotient \(3x^2 + 2x - 1\)A1
Obtain remainder \(2x - 5\)A1
4
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| Commence division and reach partial quotient $3x^2 + kx$ | M1 | |
| Obtain quotient $3x^2 + 2x - 1$ | A1 | |
| Obtain remainder $2x - 5$ | A1 | |
| | **4** | |

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1 Find the quotient and remainder when $6 x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + 5 x - 6$ is divided by $2 x ^ { 2 } - x + 1$.\\

\hfill \mbox{\textit{CAIE P3 2020 Q1 [3]}}