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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
Skills Important Notes
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
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Region
Skills Important Notes
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
On the graph in the answer space , shade the region which satisfies the three
inequalities y -x + 6 , y 2x 4 and x > 1
[ 3 marks ]
June 2008, Q1
On the graph in the answer space , shade the region which satisfies the three
inequalities y -x + 8, 2y x + 4 , and x < 8[ 3 marks ]
Region For Inequalities 10
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
Region For Inequalities 14
-4
8
8O
y
x
y = -x + 8
2y = x + 4
2