AQA AS Paper 1 2022 June — Question 5 3 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
Year2022
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFactor & Remainder Theorem
TypeExpress as product with specific form
DifficultyModerate -0.8 This is a straightforward polynomial division or factorization problem where one factor is given. Students simply need to perform algebraic long division or compare coefficients to find a, b, and c. It's routine manipulation requiring no problem-solving insight, making it easier than average, though not trivial since it involves cubic polynomials.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem
Express \(3x^3 + 5x^2 - 27x + 10\) in the form \((x - 2)(ax^2 + bx + c)\), where \(a\), \(b\) and \(c\) are integers. [3 marks]
Question 5:
AnswerMarks Guidance
5Obtains 3x2 or a = 3 1.1b
= 3x2 + 11x – 5
Obtains constant term of – 5 or
AnswerMarks Guidance
c = – 51.1b B1
Obtains 11x or b = 111.1b B1
Question 5 Total3
QMarking instructions AO 
Question 5:
5 | Obtains 3x2 or a = 3 | 1.1b | B1 | (x – 2) )3x3 + 5x2 – 27x +10
= 3x2 + 11x – 5
Obtains constant term of – 5 or
c = – 5 | 1.1b | B1
Obtains 11x or b = 11 | 1.1b | B1
Question 5 Total | 3
Q | Marking instructions | AO | Marks | Typical solution
Express $3x^3 + 5x^2 - 27x + 10$ in the form $(x - 2)(ax^2 + bx + c)$, where $a$, $b$ and $c$ are integers.

[3 marks]

\hfill \mbox{\textit{AQA AS Paper 1 2022 Q5 [3]}}
This paper (17 questions)
View full paper
Q1 1 Q2 1 Q3 3 Q4 5 Q5 3 Q6 9 Q7 6 Q8 11 Q9 5 Q10 9 Q11 1 Q12 1 Q13 3 Q14 3 Q15 5 Q16 6 Q17 8