CAIE P2 2016 March — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Linear Divisor
DifficultyEasy -1.2 This is a straightforward polynomial division problem requiring only the application of a standard algorithm (long division or synthetic division) with a linear divisor. It's a routine procedural question with no conceptual challenges, making it easier than average for A-level, though not trivial since it requires careful arithmetic with multiple terms.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

1 Find the quotient and the remainder when \(2 x ^ { 3 } + 3 x ^ { 2 } + 10\) is divided by \(( x + 2 )\).

AnswerMarks Guidance
Attempt division at least as far as quotient \(2x^2 + kx\)M1
Obtain quotient \(2x^2 - x + 2\)A1
Obtain remainder 6A1 [3]
Special case: Use of Remainder Theorem to give 6B1
Attempt division at least as far as quotient $2x^2 + kx$ | M1 |
Obtain quotient $2x^2 - x + 2$ | A1 |
Obtain remainder 6 | A1 | [3]
Special case: Use of Remainder Theorem to give 6 | B1 |
1 Find the quotient and the remainder when $2 x ^ { 3 } + 3 x ^ { 2 } + 10$ is divided by $( x + 2 )$.

\hfill \mbox{\textit{CAIE P2 2016 Q1 [3]}}