Moderate -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.
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:
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]}}