CAIE IGCSE Additional Math 4.5 Solve Cubic Inequalities Graphically Questions

Practise Cambridge IGCSE Additional Mathematics by solving polynomial inequalities from sign intervals and graph positions.

Exam points

Solve polynomial inequalities using roots, sign intervals and graph information.
Use a graph to identify where a polynomial lies above or below a stated level.
Include or exclude boundary roots correctly according to the inequality symbol.

[Maximum number: 3]

The diagram shows the graph of $y=\mathrm{f}(x)$ , where $\mathrm{f}(x)=2(x+1)^2(x-1)$ .
Use the graph to solve the inequality $\mathrm{f}(x)\leqslant -1$ .

Figure for Question CAIE IGCSE Additional Math 4.5 Solve Cubic Inequalities Graphically Questions question 1 — CAIE IGCSE Additional Math

Finds three correct critical values:
-1.5 to -1.4 inclusive,
-0.4,
0.8 to 0.9 inclusive. B1

Correct pair of inequalities:
$x\leqslant -1.45$ and $-0.4\leqslant x\leqslant 0.85$ . B2
B1 for either inequality correct.

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CAIE IGCSE Additional Math 4.5 Solve Cubic Inequalities Graphically Questions question 1