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Mathematics for IGCSE & O level - Inequalities (Section 2)

1
When representing the solution graphically on a number line, what is implied by the use of an open circle?
Answer
(B)
The solution excludes that number
2
What are the key steps to represent regions satisfying more than one inequality?
Answer
A
B
D
3
Which of the following inequalities does the shaded region represent?
Answer
(A)
y > 2
4
Which of the following is correct?
Answer
A
C
D
5
Which of the following points, when substituted into the inequality, would determine the direction of the inequality?
Answer
(A)
(0, 0)
6
Given the inequalities x + y < 4, x >= -1, and y >= 0, what is the shape of the region defined by these inequalities?
Answer
(A)
Triangle
7
What is the integer value of x that satisfies -2 ≤ x < 3?
Answer
(B)
-2, -1, 0, 1, 2
8
Which inequality matches the graph showing y ≥ 2x - 1?
Answer
(A)
A solid line sloping upwards with shading above.
9
The solution to the inequality 3x + 2 < 8 is represented by which of the following?
Answer
(A)
x < 2
10
If you multiply or divide an inequality by a negative number, you must:
Answer
(A)
Reverse the inequality sign.
11
What is the solution set for the inequality 2x - 3 > 5?
Answer
(B)
x > 4
12
Which of the following inequalities does the shaded region represent?
Answer
(A)
y > -x + 2
13
Which of these inequalities is represented by a graph with an open circle at -1 and shading to the right?
Answer
(B)
x > -1
14
Which compound inequality is represented by the graph showing the values of x between -1 and 4, including -1 but not 4?
Answer
(B)
-1 ≤ x < 4
15
The inequality that describes the region on a graph bounded by the line y = 2x - 3 is:
Answer
(D)
y ≥ 2x - 3
16
Which of the following best describes the graph of y < x?
Answer
(A)
A dashed line, with shading below.
17
When graphing an inequality, what does a dashed line indicate?
Answer
(B)
The inequality does not include the 'equal to' condition.
18
What is the range of values for x that satisfies both x > 2 and x < 5?
Answer
(B)
2 < x < 5
19
Which inequality describes the shaded region?
Answer
(B)
y>x
20
Which inequalities define the shaded region in the given diagram?
Answer
A
D
21
What is the inequality that defines the shaded region in the first diagram?
Answer
(D)
y ≥ 3
22
In an inequality graph, what does a solid line represent?
Answer
(A)
The solution includes the equal to condition
23
Solve the inequality: -2x + 1 ≤ 5.
Answer
(B)
x ≥ -2
24
Which phrase represents the inequality x - 5 < 10?
Answer
(A)
A number minus 5 is less than 10.
25
Which are the inequalities that define the shaded region in the graph?
Answer
A
B
26
Which of the following inequalities is correctly represented by the graph?
Answer
(B)
y > x - 3
27
When plotting the line 3x + 4y = 12, choosing x=0 and then y=0 give the points?
Answer
(C)
(0, 4) and (3,0)
28
Which inequality represents the phrase: "A number is greater than or equal to -2"?
Answer
(D)
x ≥ -2
29
Which of the following is the correct way to represent the graph of the inequality x ≥ 3 on a number line?
Answer
(C)
A closed circle on 3 and a line shading to the right.
30
The inequality x + 3 < 7 is true when:
Answer
(A)
x < 4
31
Which number line correctly represents the solution to the inequality x < 4?
Answer
(D)
A number line with an open circle at 4, and shading to the left.
32
Solve for x: 4x - 1 < 7 and represent on a number line.
Answer
(A)
x < 2, open circle at 2, and shading to the left.
33
What do you do when solving an inequality and multiply or divide by a negative number?
Answer
(B)
Reverse the inequality sign.
34
Which of the following correctly describes the solution of the inequality -3x > 12?
Answer
(A)
x < -4
35
Given the following inequalities: y ≤ x + 5, y ≥ -x - 5, y ≥ 0, which of the following point is a solution of these inequalities?
Answer
(D)
(6, 0)
36
The graph of which inequality is a solid line with shading above the line?
Answer
(D)
y ≥ 2x + 1
37
Consider the inequalities: y < -x + 5, y > 3, x > 0. The region defined by these inequalities is a:
Answer
(A)
Triangle