Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx
GCSE: Inequalities – Shading
Regions
Dr J Frost ([email protected])
www.drfrostmaths.com
}
~
Last modified: 31st August 2015
RECAP: Inequalities on a Number Line
This is known as a
‘strict’ inequality.
x>3
Means: x is (strictly) greater
? than 3.
0
1
2
3
4
x < -1
Means: x is (strictly) less?than -1.
5
-3
-2
-1
?
4
5
?
2
x≤5
Means: x is greater than?or equal to 4.
3
1
?
x≥4
2
0
6
7
Means: x is less than or ?
equal to 4.
2
3
4
5
?
6
7
STARTER: Solving Inequalities
(On your worksheet)
? 𝟏, 𝟐, 𝟑
−𝟐, −𝟏, 𝟎,
𝒙 < 𝟒?
?
𝒙 < −𝟒
?
𝟔<𝒙≤𝟗
Sketch the
region
representing
𝑥>2
-10
-8
-6
-4
8
Think: How are the values of x constrained, and
how are the values of y constrained?
6
4
2
-2
2
-2
-4can be
𝒙 can be any number greater than 2, but 𝒚
ANY value because it is not constrained.
The dotted line indicates that 𝒙 can’t be 2.-6
4
6
8
10
8
-4 < y ≤ -2
6
4
2
-10
-8
-6
-4
-2
2
-2
-4
-6
4
6
8
10
8
y≥x
6
4
2
-10
-8
-6
-4
-2
2
4
6
8
-2
How can we tell which way
round the inequality is?
-4
Just try a point on one side, e.g. (0, 4).
Is y ≥ x? Yes, so we’re on the right
-6
side.
10
Quickfire Regions
Bro Tip: An easier way to see if the region is on the correct side is to see whether 𝑦 is
on the smaller side of the inequality or the greater side. If the greater, we’re above.
Is the region on the correct side of the line?
y>x+2
y>1-x
2
Fail

y–x>1
Win

1
1
Win

Fail

x > 2y - 3
x+y>1
Win

y > -x
1.5
1
Fail

Fail

Win

Fail

Win

Fail

Win

Combining Inequalities
8
y ≤ x + 1 and x ≤ 66 and y > 2
4
2
-10
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
Bro Tip: In GCSE exam questions, the
region you want is almost always the
region enclosed by your 3 lines.
10
Question 4
Worksheet Answers

 

Click to Sketch >
Question 5
Worksheet Answers

 
Click to Sketch >
Question 6
Worksheet Answers
Click to Sketch >
R
𝟐, 𝟐 , 𝟐, 𝟑 , 𝟐, 𝟒 , (𝟑, 𝟑)
?
Question 7
Worksheet Answers

 
  
Click to Sketch >
Question 8
Worksheet Answers
Click to Sketch >

 

3
?
2?
Question 9
Worksheet Answers
R
𝟓 𝟓
−? 𝒙
𝟐 𝟔
𝟐𝟎?
Click to Sketch >
1
?1