Syllabus Edition

First teaching 2021

Last exams 2024

|

Solving & Graphing Inequalities (CIE IGCSE Maths: Extended)

Exam Questions

2 hours20 questions
1
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2 marks

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

The diagram shows a rectangle with a line of symmetry at x space equals space 2.
Two vertices of the rectangle are at left parenthesis negative 1 comma space 1 right parenthesis and left parenthesis negative 1 comma space 4 right parenthesis.

The shaded region is defined by the inequalities a less or equal than space x less or equal than space b and c less or equal than space y less or equal than space d .
Find the values of a comma space b comma space c and d.


a space equals ................................................ 

b space equals ................................................ 

c space equals ................................................ 

d space equals ................................................ 

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2
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2 marks

Solve the inequality.

x over 2 minus 13 greater than 12 plus 3 x

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3
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2 marks

Solve the inequality.

3 n minus 5 greater than 17 plus 8 n

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4
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2 marks

Solve the inequality.

3 x space plus space 12 space less than space 5 x space minus space 3

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5
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5 marks

cie-igcse-2019-may-jun-p2-tz3-q24

By shading the unwanted regions of the grid, draw and label the region R which satisfies the following three inequalities.

y less or equal than 2 x less than 3 y less or equal than x plus 4

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6
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3 marks

cie-igcse-2018-oct-nov-p2-tz2-q14
 

By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities.

x less or equal than 3 space space space space space space space space space space x greater or equal than 2 space space space space space space space space space space y less or equal than 2 x plus 1 space space space space space space space space space space y greater or equal than 4 minus x

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1a
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5 marks

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

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

x greater or equal than 2 y greater or equal than x   and   2 x plus y less or equal than 8.

1b
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1 mark

Find the largest value of space x plus y space in the region R.

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2
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4 marks

cie-igcse-2020-mary-jun-p2-tz3-q13

Write down the three inequalities that define the region R.

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3
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4 marks

cie-igcse-2019-oct-nov-p2-tz2-q16

By shading the unwanted regions of the grid, find and label the region R that satisfies the following inequalities

y less or equal than 5 space space space space space space space space space space 2 x plus y greater or equal than 6 space space space space space space space space space space y greater or equal than x plus 1

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4
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4 marks

cie-igcse-2019-oct-nov-p2-tz3-q17

By shading the unwanted regions on the grid, draw and label the region R that satisfies the following inequalities.

negative 2 less than x less or equal than 3 space space space space space space space space space space y less or equal than x plus 3

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5a
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2 marks

cie-igcse-2019-may-jun-p2-tz2-q16
y less or equal than negative 1 half x plus 6    y greater or equal than 3 x minus 4    x plus y greater or equal than 5

By shading the unwanted regions of the grid, find and label the region R that satisfies the three inequalities.

5b
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1 mark

Find the largest value of x plus y in the region R, where x and y are integers. 

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6
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4 marks

cie-igcse-2018-may-jun-1-p2-q21
There are four inequalities that define the region R.
One of these is y less or equal than x plus 1.

Find the other three inequalities.

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7
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3 marks

cie-igcse-2018-may-jun-2-p2-q19
Find the two inequalities that define the region on the grid that is not shaded.

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8a
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4 marks

cie-igcse-2018-may-jun-3-p4-q9b

Find the three inequalities that define the region R.

8b
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2 marks

Find the point left parenthesis x comma space y right parenthesis, with integer co-ordinates, inside the region R such that 3 x plus 5 y equals 35.

( .............. , .............. )

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1a
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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 less than 10.

Write down the other inequality.

1b
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2 marks

Raheem takes 2 1 fourth hours to make a basket and 1 1 half hours to make a mat.
Each week he works for a maximum of 22.5 hours.

Show that  3 x plus 2 y less or equal than 30.

1c
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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

1d
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2 marks

Raheem makes $40 profit on each basket he sells and $28 profit on each mat he sells.

Calculate the maximum profit he can make each week.

$ ................................................

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2a
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3 marks

A car hire company has x small cars and y large cars.
The company has at least 6 cars in total.
The number of large cars is less than or equal to the number of small cars.
The largest number of small cars is 8.

Write down three inequalities, in terms of x and/or y, to show this information.

2b
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1 mark

A small car can carry 4 people and a large car can carry 6 people.
One day, the largest number of people to be carried is 60.

Show that 2 x plus 3 y less or equal than 30.

2c
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6 marks

cie-igcse-2019-oct-nov-p4-tz1-q9c

By shading the unwanted regions on the grid, show and label the region R that satisfies all four inequalities.

2d
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3 marks
i)
Find the number of small cars and the number of large cars needed to carry exactly 60 people.

.........small cars, .........large cars [1]

ii)
When the company uses 7 cars, find the largest number of people that can be carried.

[2]

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3a
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4 marks

Klaus buys x silver balloons and y gold balloons for a party.
 
He buys

  • more gold balloons than silver balloons
  • at least 15 silver balloons
  • less than 50 gold balloons
  • a total of no more than 70 balloons.

Write down four inequalities, in terms of x and/or y, to show this information.
 

.................................................
.................................................
.................................................
.................................................

3b
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5 marks

On the grid, show the information from part (a) by drawing four straight lines and shading the unwanted regions.

cie-igcse-2018-march-p4-q6b

3c
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2 marks

Silver balloons cost $2 and gold balloons cost $3. 
 
Calculate the most that Klaus could spend.
 

$ ...............................................

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4a
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2 marks

Given that x and y are integers such that

space space space space space space space space 3 space less than space x space less than space 7 space
space space space space space space space space 4 space less than space y space less than space 9
and space space x space plus space y space equals space 13

find all the possible values of x.

4b
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4 marks

On the grid below show, by shading, the region defined by the inequalities

y space greater-than or slanted equal to space minus 1 space space space space space space space space space space space space space space space space y space less-than or slanted equal to space 4 space minus space x space space space space space space space space space space space space space space space space y space less-than or slanted equal to space 3 x space minus space 1

Mark this region with the letter R.

q4b-2-16-very-hard-cie-igcse-maths-extended

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5
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4 marks

On the grid, shade the region that satisfies all these inequalities.

x space plus space y space less than space 4 space space space space space space space space space space space space space space space space y space greater than space x space minus 1 space space space space space space space space space space space space space space space space space space y space less than space 3 x

Label the region R.

q5-2-16-very-hard-cie-igcse-maths-extended

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6
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3 marks

Here are two inequalities.

– 2 space less-than or slanted equal to space x space less-than or slanted equal to space 3
9 space less-than or slanted equal to space x space plus space y space less-than or slanted equal to space 11

x and y are integers.

Work out the greatest possible value of y space – space x

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