The roots of any quadratic equation can NEVER be...

one rational and one irrational

To determine which x-values make a rational function undefined, you first...

Set the denominator equal to zero and then solve for roots

Imaginary numbers are used when...

You're taking the square root of a negative number

What does the variable x represent in the problem shown?

the number of visits per week in thousands

What is one fact we know about the focus point, vertex point, and the point on the directrix?

They all have the same x-values

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Algebra 2 - Fall Review

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This #algebra2 quiz is to help review all of the topics from September through December.

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Questions 85

Answers

1
The formula used to determine the discriminant of a quadratic equation is...?
b2 + 4ac
b2 - 4ac
y = mx + b
a2 + b2 = c2
2
What is the first step to typing in a logarithmic equation on the calculator?
Math --> Frac --> Enter twice
2nd --> Table
2nd --> TRACE --> Intersect
Math --> logBASE --> Enter
3
When solving for the solutions of any radical equation, you always check to see if they're?
even numbers
real solutions
extraneous solutions
imaginary solutions
4
The roots of any quadratic equation can NEVER be...
both imaginary
one rational and one irrational
one positive and one negative
both real
5
To determine which x-values make a rational function undefined, you first...
Set the equation equal to zero
Plug in random x-values
Plug zero into the denominator
Set the denominator equal to zero and then solve for roots
6
Determine the correct answer for the problem shown.
x
x1/6
x5/6
x1/3
7
Determine the correct answer for the problem shown.
x = -4
x = 4
x = 3
x = -1
8
A function is odd when they reflect...?
over the x-axis
over the y-axis
through the origin
9
The rate of an exponential function can...
be either positive or negative
only be an imaginary number
only be negative
only be positive
10
When you express an answer in a + bi form, that form is known as...
an exponential equation
a real number
a complex number
a quadratic equation
11
Create an equation that can represent Jonesville based on the table shown.
y = 1240(1.06)t
y = 1240(1.11)t
y = 890(1.06)t
y = 890(0.89)t
12
How many weeks are in a year?
52
54
53
51
13
Rounding to the nearest ten thousandth, what does log(3) equal to?
0.4772
0.4771
0.5
0.48
14
Which formula represents the power rule?
xa / xb = xa - b
(xa)b = xab
x0 = 1
xa ⋅ xb = xa + b
15
Determine the correct answer.
-102
-6
6
102
16
Which equation represents the vertex form of a quadratic equation?
ax2 + bx + c = y
(x - h)2 = 4p(y - k)
y = a(x - h)2 + k
b2 - 4ac
17
In the equation shown, which part represents the initial value?
2560
0.017185
e
t
18
Cosine from SOHCAHTOA is equal to...?
hypotenuse / adjacent
opposite / hypotenuse
adjacent / hypotenuse
opposite / adjacent
19
When two angles sum to 180 degrees, they're called...? (Hint: Remember from Geometry)
Vertical angles
Supplementary angles
Complementary angles
Corresponding angles
20
A parabola has its focus at (1, 2) and its directrix is y = -2. Determine the vertex point.
(0, 1)
(1, 4)
(1, 0)
(-1, 0)
21
In the equation y = 3x² + 5x + 2, the parabola opens...?
to the left
down
to the right
up
22
Determine the correct answer.
1
2
3
4
23
Which formula represents the quotient rule?
x0 = 1
xa ⋅ xb = xa + b
(xa)b = xab
xa / xb = xa - b
24
Imaginary numbers are used when...
You can't think of a number
You're taking the cube root of a negative number
You're taking the square root of a negative number
25
Which formula proves that a function is odd?
When f(x) = f(x)
When f(-x) = -f(x)
When f(x) = f(-x)
26
What formula is used for the phrase "rate of change"?
distance formula
vertex form of a quadratic equation
slope formula
pythagorean theorem
27
Which function represents exponential decay?
3
2
4
1
28
Which equation represents the focal-length form of a quadratic equation?
(x - h)2 = 4p(y - k)
y = a(x - h)2 + k
y = mx + b
ax2 + bx + c = y
29
Based on the problem shown, which is the correct answer choice?
I, only
II, only
neither I nor II
both I and II
30
To the nearest tenth, the value of x that satisfies 2^x = -2x + 11 is...? (Hint: Use calculator)
5.9
5.8
2.5
2.6
31
Sine from SOHCAHTOA is equal to...?
opposite / hypotenuse
opposite / adjacent
adjacent / hypotenuse
hypotenuse / adjacent
32
Determine the correct answer. (Hint: Use the table of values)
1
4
2
3
33
What does the variable x represent in the problem shown?
the website's popularity
the ranking of the website
the number of visits per week in thousands
34
The domain of any function pertains to its...?
x-values
y-values
both x- and y-values
35
The focus of any parabola is always...
a point outside of the parabola
a point inside of the parabola
a line inside of the parabola
a line outside of the parabola
36
The value of "e" is also known as the...?
Pi
Mathematical constant
Avogadro number
Distance formula
37
Which is an example of a binomial?
-11
6x2 + 2x - 11
3a + 5
0.5x + 11y - 6z + 15
38
What is one fact we know about the focus point, vertex point, and the point on the directrix?
The vertex point is not in between the FP and D
The directrix intersects with the parabola
They all have the same x-values
The focus point is outside of the parabola
39
What is the base value of the equation shown?
t
100
-0.023
e
40
If the vertex point is (0,4) & the focal length is -2, what is the focus point?
(0, 2)
(0, 6)
(2, 4)
(-2, 4)
41
Which formula proves that a function is even?
When f(x) = f(x)
When f(-x) = -f(x)
When f(x) = f(-x)
42
How do you turn a decimal into a fraction on the calculator?
Math --> logBASE --> Enter
2nd --> TRACE --> Intersect
Math --> Frac --> Enter twice
Math --> Num --> Abs(
43
How many days are in a year?
366
364
363
365
44
Solve the following system of equations.
x = 28, x = 192
x = 12, x = 16
x = -12, x = -16
x = 56, x = 384
45
Determine the average rate of change btwn one car traveling @ 50 mph & one traveling @ 70 mph.
0.133
-7.5
-0.133
7.5
46
Determine the vertex point of the quadratic equation (x - 3)² = 4(y + 2).
(2, -3)
(-2, 3)
(-3, 2)
(3, -2)
47
Which function is the inverse of y = e^x ?
y = log(x)
x = log(y)
x = ln(x)
y = ln(x)
48
What is √(-9)?
-3
3i
-3i
49
A function is even when they reflect...?
over the x-axis
through the origin
over the y-axis
50
How many years are in two decades?
100
10
50
20
51
Determine the correct answer.
1
3
4
2
52
How many seconds are in a day?
24 hours / day
1440 seconds / day
60 seconds / day
24 seconds / day
53
To the nearest hundredth, what is 10log(5/11) equal to?
-3.424
-3.4
-3
-3.42
54
The following system contains which types of equations?
two linear equations
two quadratic equations
linear equation and a quadratic equation
linear equation and a circle equation
55
When g(x) is divided by x + 4, the remainder is 0. What does this tell you about x + 4?
That x = 4 is one of the zeroes for g(x)
Absolutely nothing
That x + 4 is not a factor of g(x) b/c the remainder is 0.
That x + 4 is a factor of g(x) b/c the remainder is 0.
56
How many seconds in a year?
7 days / week
525600 seconds / year
24 hours / day
365 days / year
57
Which formula represents the product rule?
xa / xb = xa - b
xa ⋅ xb = xa + b
x0 = 1
(xa)b = xab
58
Which statement is true about the equation shown?
100 is the initial value and 1/2 is the base
100 is the base and 1/2 is the initial value
I is the initial value and 100 is the final value
d is represented in years
59
Which equation represents the standard form of a quadratic equation?
b2 - 4ac
a2 + b2 = c2
y = mx + b
ax2 + bx + c = y
60
What does SOHCAHTOA stand for?
sin = opp/hyp; cos = adj/hyp; tan = opp/adj
Absolutely nothing
sin = adj/hyp; cos = opp/hyp; tan = opp/adj
61
Which equation represents a parabola w/ the focus at (0, -1) and the directrix of y = 1?
x2 = 4y
x2 = -8y
x2 = 8y
x2 = -4y
62
The range of any function pertains to its...?
x-values
both x- and y-values
y-values
63
Trigonometry is used to solve for missing sides and angles of which shape only?
Trapezoids
Right triangles
Hexagons
Circles
64
Determine the answer.
(2, 0)
(0, 0)
(1, 0)
(3, 0)
65
Simplify xi(i - 7i)² , where i is the imaginary unit.
36x
36xi
-36xi
-36x
66
The value of i²= ?
1
-1
i
-i
67
The directrix of the parabola 12(y + 3) = (x - 4)² is y = -2. Determine the vertex point.
(-4, 3)
(3, -4)
(4, -3)
(-3, 4)
68
What does "f(x) = g(x)" mean?
That both graphs never intersect
Both graphs came to a mutual agreement on a serious decision
f(x) = g(x) when they have the same y-value for a specific x
69
Determine the correct answer to the problem shown.
3
2
4
1
70
If R(t) = -33t² + 360t and C(t) = 700 + 5t, determine C(t) - R(t).
33t2 - 355t + 700
-33t2 + 355t + 700
-33t2 - 355t - 700
33t2 + 355t - 700
71
Which formula represents the zero power rule?
xa / xb = xa - b
x0 = 1
(xa)b = xab
xa ⋅ xb = xa + b
72
The real zeroes of any polynomial..?
Sometimes intersects the x-axis
Never intersects the x-axis
Always intersects the x-axis
73
The square root of -1 is equal to...?
θ
i
e
π
74
Tangent from SOHCAHTOA is equal to...?
opposite / adjacent
adjacent / hypotenuse
hypotenuse / adjacent
opposite / hypotenuse
75
Inverse functions are functions that reflected over which line?
Over the y = x line
Over the y = -x line
Over the y-axis
Over the x-axis
76
The non-real zeroes of any polynomial..?
Never intersects the x-axis
Always intersects the x-axis
Sometimes intersects the x-axis
77
When g(x) is divided by x + 4, the remainder is -13. What does this tell you about x + 4?
That x + 4 is a factor of g(x) b/c the remainder is -13.
Absolutely nothing
That x = -4 is one of the zeroes for g(x)
That x + 4 is not a factor of g(x) b/c the remainder is -13.
78
Which statement is true?
p(x) has three real roots and m(x) has four real roots.
p(x) has three real roots and m(x) has two real roots.
p(x) has one real root and m(x) has two real roots.
p(x) has two real roots and m(x) has three real roots.
79
Which of the following is an example of a pair of conjugates?
(a + 3) and (a - 3)
(k + 3) and (k + 3)
(g - 3) and (g - 3)
(a + 3) and (b - 3)
80
For the system shown below, what is the value of z?
5
6
2
4
81
When two angles sum to 90 degrees, they're called...? (Hint: Remember from Geometry)
Supplementary angles
Corresponding angles
Complementary angles
Vertical angles
82
The directrix of any parabola is always...?
a line outside of the parabola
a line inside of the parabola
a point inside of the parabola
a point outside of the parabola
83
What is the degree of the polynomial P(m) = (m² - 4)(m² + 1)?
1
4
3
2
84
The base of any exponential function can...
only be an imaginary number
only be positive
only be negative
be either positive or negative
85
Which terms are synonymous with "solutions"?
x-intercepts, y-intercepts
horizontal and vertical asymptote
focus, directrix
roots, zeros

Algebra 2 - Fall Review Flashcards | StudBud