HARD

Upper Secondary: IGCSE

IMPORTANT

Earn 100

Draw graph to show the solution sets of the inequalities: $y ⩽ 4$ , $y ⩾ x + 2$ and $3 x + y ⩾ 4$ . Write down the integer co-ordinates $(x, y)$ that satisfies all the inequalities in this case.

Important Questions on Further Solving of Equations and Inequalities

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 1

In the diagram, the unshaded region represents the set of inequalities $x ⩽ 6$ , $0 ⩽ y ⩽ 6$ and $x + y ⩾ 4$ . Find the greatest and least possible values of $3 x + 2 y$ subject to these inequalities.

Question Image

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 2

On a grid, shade the unwanted regions to indicate the region satisfying all the inequalities

y ⩽ x, x + y ⩽ 6

and

y ⩾ 0

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 2

In the diagram the unshaded region represents the set of inequalities $x + 2 y ⩾ 6$ , $y ⩽ x$ and $x < 4$ . Find the greatest possible value of $2 x + y$ if $x$ and $y$ satisfies all these inequalities?

Question Image

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 3

The whole numbers

x

and

y

satisfy all the inequalities

y ⩾ 1

y ⩽ x + 3

and

3 x + y ⩽ 6

. find the greatest and least possible values of the expression

x + y

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 4

An IGCSE class is making school flags and T-shirts to sell to raise funds for the school. Due to time constraints, the class is able to make at most

150

flags and

120

T-shirts. The fabric is donated and they have enough to make

200

items in total. A flag sells for

$ 2

and T-shirt sells for

$ 5

. How many of each item should they make to maximize their income from sales?

HARD

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.7>Q 5

A school principal wants to buy some book cases for the school library. She can choose two types of book case. Type A costs

$ 10

and it requires

0.6 m^{2}

of floor space and holds

0.8 m^{3}

of books. Type B costs

$ 20

and it requires

0.8 m^{2}

of floor space and holds

1.2 m^{3}

of books. The maximum floor space available is

7.2 m^{3}

and the budget is

$ 140

(But the school would prefer to spend less). What number and type of book cases should the principal buy to get the largest possible storage space for books?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.8>Q 1

Write the given expression in the form of ${(x + a)}^{2} + b$ :

$x^{2} + 6 x + 14$

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 14 - Further Solving of Equations and Inequalities>Exercise 14.8>Q 1

Write the given expression in the form of ${(x + a)}^{2} + b$ :

$x^{2} + 8 x + 1$

Draw graph to show the solution sets of the inequalities: y⩽4, y⩾x+2 and 3x+y⩾4. Write down the integer co-ordinatesx,y that satisfies all the inequalities in this case.

Important Questions on Further Solving of Equations and Inequalities

Learn and Prepare for any exam you want !

Draw graph to show the solution sets of the inequalities: $y ⩽ 4$ , $y ⩾ x + 2$ and $3 x + y ⩾ 4$ . Write down the integer co-ordinates $(x, y)$ that satisfies all the inequalities in this case.