CAIE IGCSE Mathematics Extended E2.6 Inequalities

Covered syllabus points

E2.6.1 Represent and interpret inequalities, including on a number line.E2.6.2 Construct, solve and interpret linear inequalities.E2.6.3 Represent and interpret linear inequalities in two variables E2.6.4 List inequalities that define a given region E2.6.5 Linear programming problems are not included.

[Maximum number: 6]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

Write down the inequality shown by the number line.

[ 1 ]

$-2<x\leqslant4$ oe

(b)

$-3\leqslant2x+3<9$

[ 5 ]

(i)

Solve the inequality.

[ 3 ]

$-3\leqslant x<3$ final answer
M2 for correct intermediate inequality;
SC1 for one side correct

(ii)

Write down all the integer values of x that satisfy the inequality.

[ 2 ]

[Maximum number: 1]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

Region R satisfies the three inequalities $y \geqslant 0, y \leqslant x$ and $x+y \geqslant 7$ . On the grid, label the region R .

[Maximum number: 4]

Figure for Question 3 — CAIE IGCSE Mathematics Extended

Write down all the inequalities that define the region R.

$\begin{aligned}x&\leqslant2.5\\y&>3\\y&\leqslant4\\y&\leqslant2x\end{aligned}$

B3 for answer $x<2.5,\ y\geqslant3,\ y<4,\ y<2x$
OR B1 for each
If 0 or 1 scored, instead award SC2 for recognition of x=2.5,y=3,y=4,y=2x. If 0 scored, SC1 for recognition of y=2x

[Maximum number: 1]

Figure for Question 4 — CAIE IGCSE Mathematics Extended

Write down the inequality shown by the number line.

$-2<x\leqslant4$ oe

[Maximum number: 2]

Solve.

6 x+14>6

$x>-\frac43$ or $x>-1\frac13$ final answer
M1 for 6x>6-14 or $x+\frac{14}{6}>1$

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CAIE IGCSE Mathematics Extended E2.6 Inequalities Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question 2

Question 3

Question 4

Question 5