About this Study Set
This study set covers Mathematics through
30 practice questions.
A comprehensive quiz covering the graphing, interval notation, and solution sets of quadratic inequalities and boundary conditions. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 30 questions from the
Quadratic Inequalities and Interval Notation study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
Which point satisfies x²+y≤16?
-
A
(3,4)
-
B
(2,5)
-
C
(4,4)
-
D
(3,8)
2
Which symbol indicates that endpoints are included in a number line solution?
-
A
Open circle
-
B
Closed circle
-
C
Dashed line
-
D
Arrow
3
Why does x²-4>0 produce two separate intervals?
-
A
Values between roots satisfy
-
B
Values beyond both roots satisfy
-
C
Endpoints are included
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D
None of the above
4
Why are brackets used in the interval [-3, 3]?
-
A
Endpoints are included
-
B
Endpoints are excluded
-
C
Only negative values are included
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D
The set is infinite
5
Which set-builder notation represents (-3,3)?
-
A
{x|x<-3 or x>3}
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B
{x|-3<x<3}
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C
{x|-3≤x≤3}
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D
{x|x<3}
6
Which interval represents the solution of x²-100<0?
-
A
(-10,10)
-
B
[-10,10]
-
C
(-10,10]
-
D
[-10,10)
7
Which solution set satisfies x²-9<0?
-
A
x<-3 or x>3
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B
-3<x<3
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C
x≤-3 or x≥3
-
D
-3≤x≤3
8
Which interval represents all values less than -2?
-
A
(-2, ∞)
-
B
(-∞, -2)
-
C
(-∞, -2]
-
D
[-2, ∞)
9
Why is the boundary dashed for x+y<9?
-
A
The graph is decreasing
-
B
The boundary is not included
-
C
The graph is a parabola
-
D
The values are positive
10
Which student uses the correct reasoning when graphing x²+y>16?
-
A
Boundary is solid
-
B
Boundary is dashed because equality is excluded
-
C
Boundary is dashed because it is a parabola
-
D
Boundary is solid because it is a circle
11
Which interval notation represents all values between -5 and 5 without including endpoints?
-
A
[-5, 5]
-
B
(-5, 5)
-
C
(-5, 5]
-
D
[-5, 5)
12
A drone may fly where x²+y<18. Which point is permitted?
-
A
(4,4)
-
B
(3,8)
-
C
(5,0)
-
D
(2,15)
13
Why does x²+4<0 have no real solution?
-
A
Square values cannot be negative
-
B
Critical values are roots
-
C
The parabola opens downward
-
D
The graph does not exist
14
Which inequality has the solution set (-4, 4)?
-
A
x²-16<0
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B
x²-16>0
-
C
x²+16<0
-
D
x²+16>0
15
Which symbol indicates that endpoints are excluded from a number line solution?
-
A
Closed circle
-
B
Open circle
-
C
Brackets
-
D
Solid line
16
Which interval solves x²-49<0?
-
A
(-7, 7)
-
B
(-∞, -7) U (7, ∞)
-
C
[-7, 7]
-
D
(-∞, -7] U [7, ∞)
17
Which notation is commonly used to describe solution sets of inequalities?
-
A
Scientific Notation
-
B
Interval notation
-
C
Roman numerals
-
D
Binary code
18
Which notation represents all real numbers greater than 3?
-
A
(3, ∞)
-
B
[3, ∞)
-
C
(-∞, 3)
-
D
(-∞, 3]
19
What are the solutions of x²-64≥0?
-
A
(-8, 8)
-
B
(-∞, -8] U [8, ∞)
-
C
[-8, 8]
-
D
(-∞, -8) U (8, ∞)
20
Why should a test point be substituted into an inequality?
-
A
To identify the correct shaded region
-
B
To calculate the vertex
-
C
To find the roots
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D
To draw the axis
21
Which method is most appropriate for verifying if a point satisfies a quadratic inequality?
-
A
Measure coordinates
-
B
Substitute coordinates into inequality
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C
Guessing
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D
Visual estimation
22
A park allows locations satisfying x²+y≤20. Which point meets the condition?
-
A
(4,4)
-
B
(2,18)
-
C
(5,1)
-
D
(3,12)
23
Which point does not satisfy x²+y<9?
-
A
(1,2)
-
B
(0,1)
-
C
(2,4)
-
D
(1,1)
24
How are critical values related to solution intervals?
-
A
They are midpoints
-
B
They are boundaries
-
C
They are always zero
-
D
They are always negative
25
Which explanation correctly identifies the solution region of x²+y>25?
-
A
Region below the curve
-
B
Region above the curve
-
C
Region on the curve
-
D
No region
26
Which student uses the correct reasoning to solve x²-81>0?
-
A
Solution between values
-
B
Solution outside critical values
-
C
Solution is the root
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D
Solution is empty
27
What are the solutions of the quadratic inequality x²+x-6<0?
-
A
x≤-3 or x≥2
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B
-3<x<2
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C
x<-3 or x>2
-
D
x≤-3
28
Which quadratic inequality has the point (2, 5) as a solution?
-
A
x²+y>12
-
B
x²+y≤10
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C
x²+y<5
-
D
x²+y>20
29
Which solution set satisfies x²-1>0?
-
A
(-∞, -1) U (1, ∞)
-
B
(-1, 1)
-
C
(-∞, -1] U [1, ∞)
-
D
[-1, 1]
30
Which observation correctly compares x²+y<16 and x²+y≤16?
-
A
Only one graph changes the axis
-
B
Only one graph includes the boundary
-
C
They are identical
-
D
They have different roots
