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1 Unit 1: Pure Mathematics A

The diagram shows the curve $C\,$ with equation $y = 3 + 2x - x^2$ and the line $l\,$ with equation $x + y = 3$ .

Figure for question 7

On the diagram, shade and label the region $R\,$ that is satisfied by the inequalities $\leqslant y \leqslant 3 + 2x - x^2$ and $\geqslant 3$

[2]

Find the coordinates of the two points where $C\,$ and $l\,$ intersect.

[3]

1 Unit 1: Pure Mathematics A Questions

The diagram shows the curve $C\,$ with equation $y = 3 + 2x - x^2$ and the line $l\,$ with equation $x + y = 3$ .

Figure for question 7

On the diagram, shade and label the region $R\,$ that is satisfied by the inequalities $\leqslant y \leqslant 3 + 2x - x^2$ and $\geqslant 3$

[2]

Find the coordinates of the two points where $C\,$ and $l\,$ intersect.

[3]