AQA AS Paper 1 2024 June — Question 6 4 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
Year2024
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve quadratic inequality
DifficultyModerate -0.3 This is a straightforward quadratic inequality requiring rearrangement to standard form, factorization of 3x² + 2x - 6, and identification of critical points. While it involves multiple steps (rearrange, factor/solve, test regions, write in set notation), these are all standard AS-level techniques with no conceptual challenges or novel insights required, making it slightly easier than average.
Spec1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation
Determine the set of values of \(x\) which satisfy the inequality $$3x^2 + 3x > x + 6$$ Give your answer in exact form using set notation. [4 marks]
Question 6:
AnswerMarks
6Simplifies to a three term
quadratic > 0 or < 0
AnswerMarks Guidance
(Condone = 0)1.1a M1
−1+ 19
x >
3
−1− 19
x <
3
−1− 19 −1+ 19
{x: x < }∪{x: x > }
3 3
Obtains the correct two critical
values ACF
−1± 19
Accept OE
AnswerMarks Guidance
31.1b A1
Chooses the outer regions for
AnswerMarks Guidance
their two critical values1.1a M1
Expresses the correct
inequalities in set notation
Accept
 −1− 19 −1+ 19 
−∞, ∪ ,∞
   
AnswerMarks Guidance
 3   3 2.5 R1
Question 6 Total4
QMarking instructions AO 
Question 6:
6 | Simplifies to a three term
quadratic > 0 or < 0
(Condone = 0) | 1.1a | M1 | 3x2 + 2x – 6 > 0
−1+ 19
x >
3
−1− 19
x <
3
−1− 19 −1+ 19
{x: x < }∪{x: x > }
3 3
Obtains the correct two critical
values ACF
−1± 19
Accept OE
3 | 1.1b | A1
Chooses the outer regions for
their two critical values | 1.1a | M1
Expresses the correct
inequalities in set notation
Accept
 −1− 19 −1+ 19 
−∞, ∪ ,∞
   
 3   3  | 2.5 | R1
Question 6 Total | 4
Q | Marking instructions | AO | Marks | Typical solution
Determine the set of values of $x$ which satisfy the inequality
$$3x^2 + 3x > x + 6$$

Give your answer in exact form using set notation.
[4 marks]

\hfill \mbox{\textit{AQA AS Paper 1 2024 Q6 [4]}}
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Q1 1 Q2 1 Q3 4 Q4 7 Q5 3 Q6 4 Q7 5 Q8 6 Q9 5 Q10 6 Q11 5 Q12 6 Q13 1 Q14 1 Q15 4 Q16 3 Q17 4 Q18 6 Q19 8