Author: Stewart Gale

Inequalities GCSE Exam Questions

Q1.
For her maths homework, Helen answered the following question.
Shade the region that is defined by all these inequalities.
x + y ≤ 6                  y ≥ 0                  y ≤ x + 2
Here is Helen's answer.

Helen made some mistakes when she answered the question.
Write down two mistakes Helen made.
 1 ...................................................................................................................................... 
 2 ......................................................................................................................................
 
(Total for question = 2 marks)
 Q2.
 The shaded region shown on the grid is bounded by four straight lines.

Find the four inequalities that define the shaded region.

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

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

 ........................................................... 
 
(Total for question = 4 marks)
Q3.
On the grid show, by shading, the region that satisfies all of these inequalities.
2y + 4 < x          x < 3          y < 6 – 3x
Label the region R.

(Total for question = 3 marks)

Q4.
 
On the grid below, show by shading, the region defined by the inequalities
x + y < 6                               x > − 1                               y > 2
Mark this region with the letter R.

(Total for Question is 4 marks)

Q5.
 On the grid, shade the region that satisfies all these inequalities.
x + y < 4           y > x − 1           y < 3x
Label the region R.

 
(Total for question is 4 marks)

Q6.
(a) Given that x and y are integers such that

find all the possible values of x.

...........................................................
(2)
(b)  On the grid below show, by shading, the region defined by the inequalities

Mark this region with the letter R.

(4)
 
(Total for question = 6 marks)
 Q7.
 On the grid show, by shading, the region defined by the inequalities

Label the region R.

 
(Total for question = 3 marks)

Q8.

Write down the three inequalities that define the shaded region.

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

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

 ........................................................... 
 
(Total for question = 4 marks)