Mathematics for IGCSE & O level - Inequalities (Section 1)
1
Which symbol represents 'is greater than or equal to'?
2
What is the purpose of a solid line on an inequality graph?
3
If a < b, what does the expression a > b mean?
Απάντηση(D)
It's not a valid expression
4
What type of line is used to represent the inequality y ≤ 2x - 1?
5
If an equation includes y < 2, what is the rule regarding the shaded area?
6
What does 'a ≤ b' signify?
Απάντηση(B)
a is less than or equal to b
7
What is the key process for shading the correct region for an inequality on a graph?
Απάντηση(C)
Choosing a test point, and checking if it meets the inequality
8
How can you determine which side of the line to shade on a graph for an inequality?
Απάντηση(B)
By substituting values of x, y to test for true statement.
9
What do we call expressions involving the signs <, >, ≤, and ≥?
10
What is the general rule for what you can do to inequalities without changing the solution?
Απάντηση(B)
Do the same thing to both sides.
11
If y > 2x - 3, what should be done in the graph?
Απάντηση(A)
Draw a dashed line and shade above it.
12
What does the solid line tell us about the set of solutions?
Απάντηση(A)
The line is included in the solution
13
What is the mathematical meaning of the symbol ≤?
14
When multiplying or dividing an inequality by a negative number, what must you do?
Απάντηση(B)
Reverse the inequality sign.
15
What does a dashed line on a graph of an inequality represent?
Απάντηση(B)
The boundary is excluded from the solution.
16
What are some of the key points to remember when representing regions satisfying more than one inequality?
17
What is the difference between 'a < b' and 'a ≤ b'?
Απάντηση(B)
'a ≤ b' includes the possibility that a equals b.
18
In the graph of y < 2x-3, which type of line represents the boundary?
19
What does 'is less than' mean in mathematical terms?
20
What is the core rule about what can be done to both sides of an inequality?
Απάντηση(B)
You must do the same thing to both sides.
21
What is the definition of 'a < b'?
22
In the question about A's age, if A's age is greater than 11 and less than or equal to 15, what is the maximum age possible for A?
23
Based on the image of a graph, what inequality is represented by a dashed line?
24
If A's age is greater than 11 years, and less than or equal to 15 years, what can we say about A?
25
What is represented by the region above a dashed line when graphing inequalities?
Απάντηση(B)
The solutions to the inequality
26
In the definition of inequalities, what type of expressions are used?
Απάντηση(B)
Expressions using comparison symbols
27
What is the general rule when performing operations on both sides of an inequality?
Απάντηση(C)
Do the same thing to both sides.
28
In the provided image with graph, what inequality is defined by the dashed line in the top-left corner?
29
What is the first step in solving for x in the inequality 3x + 4 < 10?
30
What type of line is used to represent an inequality that involves a > or < sign on a graph?
31
For the inequality y ≤ 4, which type of line would be used on the graph?
32
In the context of inequalities, which sign is associated with a solid line on a graph?
33
In a graph of a given inequality, how can you find what side to shade?
34
In the context of solving inequalities, what does the phrase "show the solution as a number line" instruct you to do?
Απάντηση(B)
Represent the solution graphically on a number line.
35
When graphing an inequality, where should you shade to represent y > 2?
36
If we are to shade regions that don't satisfy the inequality, what does the graph show?
37
What is represented by a solid line in an inequality graph?
Απάντηση(B)
The boundary is included.
38
If the perimeter of a rectangle is greater than 28cm, what is true about its perimeter (P)?
39
Which key factor defines a solution for a question when there are multiple inequalities?
40
What range of values is represented by 'x ≥ -3'?
Απάντηση(C)
All values greater than or equal to -3
41
What does a solid line on the graph represent in the context of inequalities?
42
In the general rule for solving inequalities, what happens when you multiply or divide by a negative number?
Απάντηση(C)
The inequality symbol reverses.
43
In the example x ≥ -3, what does the number line representation look like?
Απάντηση(D)
Closed circle at -3, with the line going to the right.
44
Which expression requires reversing the inequality sign when solving?
Απάντηση(D)
Multiplying by a negative number on both sides.
45
If A is older than 11 and less than or equal to 15, which option represents all possible ages of A?
46
What do we do to both sides of the equation to keep the equation true, which is also the same for inequalities?
Απάντηση(D)
Do the same thing to both sides.
47
What does the symbol '<' represent?
48
What is the result of adding or subtracting a constant from both sides of an inequality?
Απάντηση(B)
The inequality remains the same.
49
In the inequality 2x < 11, what is the last step to isolate x?
50
What is the meaning of a > b?
