Chapter 10 II Region Equalities ENHANCE

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CHAPTER 10 : REGION FOR INEQUALITIES

Define The Inequalities Area

The regions representing inequalities in two variables:

Skills Important NotesTo shade the region which satisfies the

inequalities of the form:

x > h, x < h,

x h and x h

x h is equivalent to x > h and x = h

x h is equivalent to x < h and x = h

x > h : region on the right and

x < h : region on the left of the line x = h

Region

Skills Important Notes

To shade the region which satisfies the

inequalities of the form :

y > k, y < ky and y k

y > k : region above the line.

y < k : region below the line.

Region


To shade the region which satisfies

inequalities of the form :

y > ax + b

y < ax + b

y ax + b and

y ax + b

y > ax + b : region above the line

y < ax + b : region below the line

The line y = ax + b is shown as a dotted line for region

satisfying y > ax + b or y < ax + b

Above, solid line

Below, solid line

> Above, dotted line

< Below, dotted line

Region For Inequalities 1


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Region


To shade the region which satisfies two or

three inequalities.

Consider the inequality one by one.

If 2 inequalities are given, draw the 2 corresponding

lines, then determine the region that satisfies both theinequalities.

If 3 inequalities are given, you must draw 3 straight

lines. The region has 3 boundaries.

Region

x > 5 x < 6

y -2 y x

x + y 6

Common Errors

Student are not sure whether x = 3 is a horizontal or vertical line, likewise for y = 1.

Students are not able to differentiate between solid lines and dotted lines.

Students failed to identify the correct region.

Students are weak in drawing straight lines of the form y = mx + c or x + y = k.



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10.1 Shade the region which satisfies the respective inequality.

Example Region Exercise Region

1. x > 4

x = 4

x > -1

2. x < -2

x = -2

x < 3

3. y < 4

y = 4

y < -3

4. y > -4

y = -4

y > 2

5. x 2

x = 2

x -3



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Example Region Exercise Region

6. x

5

x = 5

x

-1

7. y 2 y = 2 y -2

8. y 4 y -2

9. 1 < x 6

-3 > x > 2

10. 1 4y -2 2y



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10.2 Shade the region which satisfies the respective inequalities.

INEQUALITIES SHADED AREA INEQUALITIES SHADED AREA

Example 1

y 1 x,

y x,

x < 1

Example 2

y x + 3,

y -2x,

x -3

Exercises

y x + 5

y 5

y 1

y x + 5

y 5

x -5

y x + 7

y 9

y -x + 7

y x + 7

y -x + 7

x 7

y 5x + 5

y x + 3

y x + 5

y -5x

y x + 1

y x + 5

y x + 1

y x + 6

x 0

y x + 1

y x + 6

y 1



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Questions Based on the Examination Format.

On the graph provided, shade the region which satisfies the three inequalities.

1. y

2x 4, y

-x + 4 y -1

9. y 2x + 6, y x and y < 8

10. 2y x + 4 , y -x , x < 3



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PAST YEAR QUESTIONS

Nov 2003

On the graph provided, shaded the region which satisfies the three inequalities

y 2x + 8 , y x and y < 8

Nov 2005, Q3

On the graph in the answer space , shade the region which satisfies the three

inequalities y -2x + 10 , x < 5 and y 10.



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Nov 2007, Q1


inequalities y -x + 6 , y 2x 4 and x > 1

[ 3 marks ]

June 2008, Q1


inequalities y -x + 8, 2y x + 4 , and x < 8[ 3 marks ]


y

-4

8

8O

y

x

y = -x + 8

2y = x + 4

2


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ANSWERS

Chapter 10: Region for linear Inequalities

1.

2.

3.

4.



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5.

6.

8.

8.



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Nov 2007

June 2008


-4

8

8O

y

x

y = -x + 8

2y = x + 4

2

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Chapter 10 II Region Equalities ENHANCE