Solving & Graphing Inequalities (CIE IGCSE Maths: Extended)

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

,      and   .

Find the largest value of  in the region .

Write down the three inequalities that define the region .

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

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

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

There are four inequalities that define the region R.
One of these is .

Find the other three inequalities.

Find the two inequalities that define the region on the grid that is not shaded.

Find the three inequalities that define the region .

Find the point , with integer co-ordinates, inside the region such that .

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

Raheem makes baskets and mats.
Each week he makes baskets and 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  .

Write down the other inequality.

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

Show that  .

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

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.

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

A car hire company has small cars and 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 and/or , to show this information.

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 .

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

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

[2]

Klaus buys  silver balloons and 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  and/or , to show this information.
 

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

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

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

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

Given that and are integers such that

find all the possible values of .

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

Mark this region with the letter R.

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

Label the region R.

Here are two inequalities.

and are integers.

Work out the greatest possible value of