October 2021 Paper 3 Q1
1 Show in a sketch the region of the \(x\)-\(y\) plane within which all three of the following inequalities hold.
\(y \geqslant x^2,\quad x + y \leqslant 2,\quad x \geqslant 0.\)
You should indicate the region for which the inequalities hold by labelling the region \(R\). [3]
| Scheme | Marks | AO |
|---|---|---|
 | B1 B1 B1 | 1.1 1.1 2.2a |
| [3] |
Notes
B1: \(y = x^2\) drawn correctly – must pass through the origin and (roughly) symmetrically about the \(y\)-axis
B1: \(x + y = 2\) drawn correctly – must have positive \(y\)-intercept and negative gradient
Line need not intersect the \(x\)-axis and intercepts need not be labelled
B1: Correct identification of region (dependent on both previous B marks) – ignore shading if \(R\) correctly labelled
Condone dashed line/curve for full marks