Solving & Graphing Inequalities | Cambridge O Level Maths All Questions 2025

1a

3 marks

q8-paper4-spec-2025-cie-igcse-further-maths

On the grid, draw the lines $y = x$ and $x + y = 7$ .

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1b

1 mark

Region R satisfies the three inequalities $y ⩾ 0$ , $y ⩽ x$ and $x + y ⩾ 7$ .
On the grid, label 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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1c

5 marks

On the grid, draw three straight lines and shade the unwanted regions to show these inequalities.

cie-igcse-2020-may-june-p4-tz1-q6

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Solving & Graphing Inequalities (Cambridge O Level Maths)

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