AQA Paper 3 2019 June — Question 4 3 marks

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2019
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeGraph feasible region from inequalities
DifficultyModerate -0.8 This is a straightforward linear programming/inequalities question requiring sketching a parabola and a line, then shading the correct region. It involves routine techniques (finding intercepts, vertex) with no problem-solving or novel insight required, making it easier than average but not trivial since students must correctly interpret both inequalities and identify the intersection region.
Spec1.02g Inequalities: linear and quadratic in single variable1.02i Represent inequalities: graphically on coordinate plane

Sketch the region defined by the inequalities $$y \leq (1 - 2x)(x + 3) \text{ and } y - x \leq 3$$ Clearly indicate your region by shading it in and labelling it \(R\). [3 marks] \includegraphics{figure_4}

Question 4:
AnswerMarks
4Draws quadratic curve in the
correct orientation eg vertex
above x-axis and two
AnswerMarks Guidance
intersections on the x-axis1.1a M1
Labels all correct points of
intersection for the correct
quadratic curve with vertex
clearly in the 2nd quadrant
AnswerMarks Guidance
Must see −3, 0.5 and 31.1b A1
Draws correct straight line
passing through (−3, 0) and (0,
3) or straight line which intersects
their quadratic curve on the
negative x-axis and positive y-
axis and shades corresponding
region for their quadratic curve
FT their quadratic
All lines must be solid
AnswerMarks Guidance
Condone missing label R2.2a A1F
Total3
QMarking instructions AO
Question 4:
4 | Draws quadratic curve in the
correct orientation eg vertex
above x-axis and two
intersections on the x-axis | 1.1a | M1
Labels all correct points of
intersection for the correct
quadratic curve with vertex
clearly in the 2nd quadrant
Must see −3, 0.5 and 3 | 1.1b | A1
Draws correct straight line
passing through (−3, 0) and (0,
3) or straight line which intersects
their quadratic curve on the
negative x-axis and positive y-
axis and shades corresponding
region for their quadratic curve
FT their quadratic
All lines must be solid
Condone missing label R | 2.2a | A1F
Total | 3
Q | Marking instructions | AO | Mark | Typical solution
Sketch the region defined by the inequalities

$$y \leq (1 - 2x)(x + 3) \text{ and } y - x \leq 3$$

Clearly indicate your region by shading it in and labelling it $R$.
[3 marks]

\includegraphics{figure_4}

\hfill \mbox{\textit{AQA Paper 3 2019 Q4 [3]}}