AQA Paper 2 2023 June — Question 1 1 marks

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2023
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve quadratic inequality
DifficultyEasy -1.8 This is a straightforward reading-from-graph question requiring only visual interpretation of where a parabola is above the x-axis. No algebraic manipulation or problem-solving is needed—students simply identify that y > 0 between the roots, making it significantly easier than average A-level questions.
Spec1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation

1 The graph of \(y = a x ^ { 2 } + b x + c\) has roots \(x = 2\) and \(x = 5\), as shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_905_963_717_625} State the set of values of \(x\) which satisfy $$a x ^ { 2 } + b x + c > 0$$ Tick ( \(\checkmark\) ) one box. $$\begin{aligned} & \{ x : x < 2 \} \cup \{ x : x > 5 \} \\ & \{ x : 0 < x < 2 \} \cap \{ x : x > 5 \} \\ & \{ x : 2 < x < 5 \} \\ & \{ x : 2 > x > 5 \} \end{aligned}$$ \includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_118_115_1950_1087}


Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(\{x: x < 2\} \cup \{x: x > 5\}\)B1 Ticks correct box
Total: 1 AO 2.5
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\{x: x < 2\} \cup \{x: x > 5\}$ | B1 | Ticks correct box |
| **Total: 1** | | AO 2.5 |

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1 The graph of $y = a x ^ { 2 } + b x + c$ has roots $x = 2$ and $x = 5$, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_905_963_717_625}

State the set of values of $x$ which satisfy

$$a x ^ { 2 } + b x + c > 0$$

Tick ( $\checkmark$ ) one box.

$$\begin{aligned}
& \{ x : x < 2 \} \cup \{ x : x > 5 \} \\
& \{ x : 0 < x < 2 \} \cap \{ x : x > 5 \} \\
& \{ x : 2 < x < 5 \} \\
& \{ x : 2 > x > 5 \}
\end{aligned}$$

\includegraphics[max width=\textwidth, alt={}, center]{de8a7d38-a665-4feb-854e-ac83f413d133-02_118_115_1950_1087}\\
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\hfill \mbox{\textit{AQA Paper 2 2023 Q1 [1]}}