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1 Unit 1: Pure Mathematics A

The diagram shows the curve $C\,$ with equation $y = x^2 - 4x + 3$ and the line $l\,$ with equation $y = 2 x - 2$ .

Figure for question 8

On the diagram, shade and label the region $R\,$ that is satisfied by the inequalities $\geqslant x^2 - 4x + 3$ and $\leqslant 2x - 2$

[2]

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

[3]

Determine whether the point $(2, 1)$ lies in $R$ , fully justifying your answer.

[2]

1 Unit 1: Pure Mathematics A Questions

The diagram shows the curve $C\,$ with equation $y = x^2 - 4x + 3$ and the line $l\,$ with equation $y = 2 x - 2$ .

Figure for question 8

On the diagram, shade and label the region $R\,$ that is satisfied by the inequalities $\geqslant x^2 - 4x + 3$ and $\leqslant 2x - 2$

[2]

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

[3]

Determine whether the point $(2, 1)$ lies in $R$ , fully justifying your answer.

[2]