Edexcel A-Level Mathematics AS P1.1.8 Graphing Linear and Quadratic Inequalities Questions

Practise defining shaded regions with linear and quadratic inequalities, including boundary lines, curves and valid x- or y-ranges.

Exam points

write inequalities for a shaded region bounded by a line, curve and axis
choose strict or non-strict signs from the drawn boundaries and shading

[Maximum number: 2]

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Figure 2

Figure 2 shows a sketch of the curve C with equation $y=x^{2}-5 x+13$

The point M is the minimum point of C.

The straight line l passes through the origin O and intersects C at the points M and N as shown.

Find, showing your working,

Use inequalities to define the region R.

M1: States any two of $y<x^2-5x+13$ , y>2.7x, and $0\le x<b$ , where $2.5\le b\le5.2$ .
A1ft: States all three inequalities, following through on their line from part (b) and their boundary values.

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Edexcel A-Level Mathematics AS P1.1.8 Graphing Linear and Quadratic Inequalities Questions question 1