Solving & Graphing Inequalities | CIE IGCSE Maths: Extended Paper 2 & Paper 4 2023

1a

5 marks

cie-igcse-2020-mary-jun-p2-tz2-q23

By drawing suitable lines and shading unwanted regions, find the region, $R$ , where

$x \geq 2$ , $y \geq x$ and $2 x + y \leq 8$ .

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1b

1 mark

Find the largest value of $x + y$ in the region $R$ .

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1

2 marks

cie-igcse-2020-oct-nov-p2-tz1-q11

The diagram shows a rectangle with a line of symmetry at $x = 2$ .
Two vertices of the rectangle are at $(- 1, 1)$ and $(- 1, 4)$ .

The shaded region is defined by the inequalities $a \leq x \leq b$ and $c \leq y \leq d$ .
Find the values of $a, b, c$ and $d$ .

$a =$ ................................................

$b =$ ................................................

$c =$ ................................................

$d =$ ................................................

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1a

1 mark

Raheem makes baskets and mats.
Each week he makes $x$ baskets and $y$ mats.

He makes fewer than 10 mats.
The number of mats he makes is greater than or equal to the number of baskets he makes.

One of the inequalities that shows this information is $y < 10$ .

Write down the other inequality.

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1b

2 marks

Raheem takes $2 \frac{1}{4}$ hours to make a basket and $1 \frac{1}{2}$ hours to make a mat.
Each week he works for a maximum of 22.5 hours.

Show that $3 x + 2 y \leq 30$ .

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