WorksheetsAlgebra 2 1st semester Final exam review
Total questions: 133
Worksheet time: 7hrs 37mins
Name
Class
Date
1.
What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)
a)
(1, 2) (3, 8) (-3, 6)
b)
(1, 2) (8, 3) (-3, 6)
c)
(-1, -2) (-3, -8) (3, -6)
d)
(2, 1) (8, 3) (6, -3)
2.
Find the inverse of f(x) = -4x - 12
a)
f-1(x) = 4x - 3
b)
f-1(x) = -1/4x - 3
c)
f-1(x) = 1/4x + 3
d)
f-1(x) = -4x - 3
3.
are these inverse functions?
a)
no
b)
yes
c)
no way to tell
4.
Are the following inverses of each other?
a)
True
b)
False
5.
Are these the graphs of two inverse functions?
a)
Yes
b)
No
c)
No way to tell
6.
a)
TRUE
b)
FALSE
7.
If f and g are inverse functions, and
f(2) = -1 g(1) = -2 f(1) = -2,
then which of the following MUST be true?
f(2) = -1 g(1) = -2 f(1) = -2,
then which of the following MUST be true?
a)
g(-2) = -1
b)
g(2) = 1
c)
g(-2) = 1
d)
g(1) = 2
8.
Will the inverse of this function, be a function?
a)
No
b)
Yes
c)
No way to tell
9.
What is g-1(1)?
a)
1
b)
-1
c)
3
d)
-3
10.
Was the inverse function found correctly?
a)
no,
b)
yes
11.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
12.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
g(x) = x - 2
Find f(g(0))
a)
16
b)
4
c)
-4
d)
None of these.
13.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(x))
g(x) = x - 2
Find f(g(x))
a)
3x2 - 2
b)
3x + 8
c)
3x + 4
d)
None of these.
14.
Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of f(g(4)).
a)
182
b)
40
c)
61
d)
None of the Above
15.
Given
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
a)
11x2 - 1
b)
5x4 + 6x2 - 1
c)
5x2 + 6x - 1
d)
5x2 + 8x - 1
16.
Given f(x) = -x + 4 and g(x) = 6x + 3, find (f - g)(x).
a)
-7x + 1
b)
5x +1
c)
-5x -1
d)
5x + 1
17.
When f(x) = x2 -9
and g(x) = x+3 ,
find (f/g)(x).
and g(x) = x+3 ,
find (f/g)(x).
a)
x-3
b)
x+3
c)
x-12
d)
x-6
18.
f(x)=2x + 4
g(x)=3x2 - 1
Find f(x)*g(x)
a)
6x4 + 12x3 - 4x2 - 8x
b)
-6x3 + 12x2 + 2x - 4
c)
6x3 + 12x2 - 2x - 4
d)
5x2 - 18x + 20
19.
If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?
a)
(1, 4) and (4, 6)
b)
(-4, -1) and (-6, -4)
c)
(-1, -4) and (-4, -6)
d)
(4, 1) and (6, 4)
20.
f(x) = {(3, 7), (4, -2), (5, -1), (8, 7)}
Is f-1(x) a function?
Is f-1(x) a function?
a)
Yes
b)
No
c)
No way to tell
21.
Find the inverse of
f(x) = 1/4x - 7
f(x) = 1/4x - 7
a)
f-1(x) = 4x + 7
b)
f-1(x) = -4x + 28
c)
f-1(x) = -4x - 7
d)
f-1(x) = 4x + 28
22.
Find the inverse of f(x) = x2 - 5
a)
f-1(x) = √(x) + 5
b)
f-1(x) = ∛(x-5)
c)
f-1(x) =√(x+5)
d)
f-1(x) = x2 - 5
23.
Will the inverse of this function, be a function?
a)
no
b)
yes
c)
no way to tell
24.
What are the transformations for the graph of
the parent function f(x) = √x to the function above
the parent function f(x) = √x to the function above
a)
Vertical Stretch by a factor of 2; translated down 5 units
b)
Shifted right 2 units and down 5 units
c)
Vertical stretch by a factor of 2; translated left 5 units
d)
Vertical stretch by a factor of 2; translated right one unit
25.
Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.
Hint: Use a scratch graph to help you visualize things.
a)
Domain: (-∞, ∞) Range: [-∞, 4]
b)
Domain: [1, ∞) Range: (-∞, 4]
c)
Domain: [-1. ∞) Range: [4, ∞)
d)
Domain: [4, ∞) Range: [-1,∞)
26.
Create a square root function with the following characteristics using the following graph:
a)
y = .5√(x + 1) - 2
b)
y = 2√(x - 1) + 2
c)
y = .5√(x - 1) - 2
d)
y = √(x + 1) - 2
27.
Describe the transformation.
a)
Left 1, Reflect over x-axis, up 2
b)
Left 1, Reflect over y-axis, down 2
c)
Right 1, Reflect over x-axis, up 2
d)
Right 1, Reflect over y-axis, uo 2
28.
What is the domain of this function?
f(x) = √(x-2) + 4
f(x) = √(x-2) + 4
a)
[2,∞)
b)
(-∞,2]
c)
(∞,2]
d)
[4,∞)
29.
What is the range of this function?
f(x) = √(x-2) + 4
f(x) = √(x-2) + 4
a)
(-∞,4]
b)
(-∞,2]
c)
(∞,4]
d)
[4,∞)
30.
What is the equation of the graph?
a)
y = √(x - 3)
b)
y = √(x) + 3
c)
y = √(x - 5) + 4
d)
y = √(x + 5) + 4
31.
Simplify: √36x³y⁴
a)
6y²x√x
b)
3y²√2x
c)
3y√x
d)
6x√3y
32.
Simplify:
∛45x2y8
∛45x2y8
a)
3xy4 ∛5
b)
y2 ∛45x2y2
c)
y2 √45x2y2
d)
3xy4 √5
33.
Simplify
a)
3x²y²z√3yz
b)
3xyz√xy²
c)
3xyz
d)
Can't Simplify
34.
IDENTIFY THE SIMPLEST EQUIVALENT EXPRESSION
a)
2m2n ⁶√m3n2
b)
8m9n2
c)
641/6m15/6n8/6
d)
2m3n2 √m2n
35.
Write a polynomial in factored form with zeros at x = 1, x = -1 x = 0
a)
(x - 1)(x + 1)
b)
x(x - 1)(x + 1)
c)
x2(x - 1)(x + 1)
d)
x(x - 1)(x - 1)
36.
Write the polynomial with the given zeros
a)
A
b)
B
c)
C
d)
D
37.
If polynomial P(x) is divided by ( 2x - 5 ), with a remainder of -2, is ( 2x - 5 ) a factor of P(x)?
a)
yes
b)
no
38.
Find all zeros for the polynomial function P(x) = x3 -3x2-5x+15
a)
3, √5
b)
3, √5, -√5
c)
-3, √5, -√5
d)
-3, 5i, -5i
39.
Find a polynomial function of degree 3 with zeros 3i and -2.
a)
P(x) = x3+2x2+9x+11
b)
P(x) = x3-2x2+9x+18
c)
P(x) = x3+2x2+9x+18
d)
P(x) = x2-3ix+2x-6i
40.
a)
A. (x + 3)(x - 4)
b)
B. (x - 3)(x + 4)
c)
C. (x + 3)(x + 4)
d)
D. (x - 3)(x - 4)
41.
a)
A. (x + 6)(2x - 7)
b)
B. (2x + 5)(x - 6)
c)
C. (x - 6)(2x - 5)
d)
D. (x + 6)(2x + 7)
42.
A Polynomial of Degree 6 CAN have the following number of imaginary roots:
a)
1
b)
4
c)
3
d)
8
43.
How many possible negatives solutions does the following polynomial have?
f(x) = x4 - 3x3 - 17x2 + 39x -20
a)
3 or 1
b)
3
c)
1
d)
2 or 0
44.
How many positive solutions does the following polynomial have?
f(x) =3x5 - x4 + 3x2 - 6x +11
a)
4, 2, or 0
b)
4
c)
3 or 1
d)
3
45.
How many possible negatives solutions does the following polynomial have?
f(x) = x4 - 3x3 - 17x2 + 39x -20
a)
3 or 1
b)
3
c)
1
d)
2 or 0
46.
Write a polynomial function of least degree with integral coefficients that has the given zeros.
a)
A
b)
B
c)
C
d)
D
47.
Which describes the number and type of roots of the equation x3+121x=0
a)
1 real, 2 imaginary
b)
2 real, 1 imaginary
c)
3 real
d)
3 imaginary
48.
State the possible number of imaginary zeros of
g(x)=x4+3x3+7x2-6x-13
a)
3 or 1
b)
2 or 0
c)
exactly 1
d)
exactly 3
49.
Factor: 27x3 + 8
a)
(3x + 2)(9x2 - 6x + 4)
b)
(9x + 2)(3x2 + 18x + 4)
c)
(3x2+4)(9x + 2)
d)
(27x + 8)(x2 - 216x + 64)
50.
125x3 - 64
a)
(5x - 4)(25x2 + 20x + 16)
b)
(5x + 2)(25x2 - 10x + 4)
c)
(3x - 1)(9x2 + 3x + 1)
d)
(4x - 3)(16x2 + 12x + 9)
51.
Solve b4+2b2-24=0
a)
b)
c)
d)
52.
Find all zeros
f(x)=x4-2x3+5x2-10x
a)
b)
c)
d)
53.
Solve x3-1=0
a)
b)
c)
d)
54.
a)
4a6
b)
4a5
c)
-4a6
d)
-4a5
55.
a)
7/ u3
b)
7u11
c)
7u1.75
d)
7u3
56.
a)
-12m6n9
b)
n9/ 64m6
c)
-12n9/ m6
d)
-64m6n9
57.
a)
-7 / (3abc7)
b)
1
c)
0
d)
What does the zero power do?
58.
a)
9a8 / 4b2
b)
9b2 / 4a8
c)
9a4b6 / 4
d)
9a4 / 4b2
59.
Simplify the expression.
a)
76
b)
7-5
c)
1/75
d)
75
60.
Evaluate f(x)=-2t2+ 1 for f(-3)
a)
19
b)
37
c)
-17
d)
-11
61.
Given
f(x)= 2x2 + 5x - 17, find f(-1).
f(x)= 2x2 + 5x - 17, find f(-1).
a)
f(-1) = -20
b)
f(-1) = -24
62.
Evaluate for f(1)
a)
0
b)
-3
c)
3
d)
2
63.
If f(x) = 2x – 4 find f(q + 1):
a)
2q + 4
b)
2q + 2
c)
2q - 6
d)
2q - 2
64.
Classify by degree of polynomial:
3x3 – 6x
3x3 – 6x
a)
Constant
b)
Linear
c)
Quadratic
d)
Cubic
65.
How many real zeros does the polynomial function
P(x) = x3+2x2+9x+18 have?
P(x) = x3+2x2+9x+18 have?
a)
0
b)
1
c)
2
d)
3
66.
What is the leading coefficient of the following polynomial?
-4x + 7 - 3x3 + 12x2
-4x + 7 - 3x3 + 12x2
a)
-4
b)
7
c)
-3
d)
12
67.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
68.
a)
5w 2 − 4w + 3
b)
12w 2 − 9w + 6
c)
12w 2 − 12w + 9
d)
5w 2 − 12w+ 9
69.
Divide:
(9x2 + 6x) ÷ 3x
(9x2 + 6x) ÷ 3x
a)
3x + 2
b)
3x2 + 2x
c)
5x2
d)
3x + 6
70.
a)
2x - 4
b)
x - 8
c)
x - 5
d)
x + 5
71.
The area of a rectangular pool table is: x2 + 14x +40.
The length is x+4. What is the width?
The length is x+4. What is the width?
a)
(x + 8)
b)
(x + 14)
c)
(x + 10)
d)
(x +4)
72.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
73.
Using the above graph what is the sign of the leading coefficient?
a)
Positive
b)
Negative
74.
Which function has this end behavior?
a)
-x4-3x3+3
b)
-2x7+2x4+4
c)
3x8+3x5-4x+7
d)
4x5-4x4+2x3-9
75.
Identify the degree of the polynomial and the sign of the leading coefficient
a)
Leading Coefficient Positive
Degree - Even
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
Degree - Odd
76.
What is the degree of the polynomial:
f(x) = -4x + 5x3 - 2x2
f(x) = -4x + 5x3 - 2x2
a)
Degree 2
b)
Degree 3
c)
Degree 4
d)
Degree 5
77.
What is the end behavior as x → -∞ f(x)→ ?
a)
-∞
b)
∞
78.
Determine the end behavior of the graph of
f(x) = 3x4 + 2x - 5
f(x) = 3x4 + 2x - 5
a)
As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.
As x→-∞, f(x) →-∞.
b)
As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.
As x→-∞, f(x) →∞.
c)
As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.
As x→-∞, f(x) →∞.
d)
As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.
As x→-∞, f(x) →-∞.
79.
What is the degree?
a)
Positive
b)
Negative
c)
Odd
d)
Even
80.
a)
The end behavior of the graph is x →∞, f(x)→∞ and x→-∞, f(x)→⁻∞
b)
The end behavior of the graph is x →∞, f(x)→-∞ and x→⁻∞, f(x)→-∞
c)
The end behavior of the graph is x →∞, f(x)→∞ and x→⁻∞, f(x)→∞
d)
The end behavior of the graph is The end behavior of the graph is x →∞,f(x)→⁻∞ and x→-∞, f(x)→∞
81.
How many extrema (maxes and mins) are in the picture?
a)
2
b)
3
c)
4
d)
5
82.
This graph shows a/an ...
a)
Relative max
b)
Relative min
c)
Absolute max
d)
Absolute min
83.
What is the relative maximum value?
a)
y = 4
b)
y = 2
c)
y = 1
d)
y = -1
84.
Where do you find relative minimums and relative maximums?
a)
zeros
b)
y-intercepts
c)
turning points
d)
by degree
85.
There is a relative maximum at:
a)
x = -1
b)
x = 3
c)
x = -0.5
d)
x = 1.5
86.
What is the maximum number of roots for
8x7 - 6x5 + 4x3 + 2x + 1 = 0
8x7 - 6x5 + 4x3 + 2x + 1 = 0
a)
4
b)
6
c)
7
d)
16
87.
What are the zeros of the function?
a)
4,1
b)
3,1,-2,-5
c)
-3, -1, 2, 5
d)
-2,4
88.
Select all statements that apply to this graphed polynomial...
a)
The domain is (-∞,+∞)
b)
The range is (-∞,+∞)
c)
The range is [-4,+∞)
d)
There are 1 relative minimum, 1 absolute minimum and 1 relative maximum
89.
What is the range of the graph?
a)
-15 < y < ∞
b)
(-∞, ∞)
c)
(-15, ∞)
d)
[-15, ∞)
90.
What interval is the function DECREASING over?
a)
-3 < x < -1
b)
-3 < x < -2
c)
-2 < x < 0
d)
2 < x < 3
91.
What is the absolute maximum?
a)
None
b)
(0, 9)
c)
(9,0)
d)
(-1,0) (1,0)
92.
Which of the following points are zeros of this function?
a)
(0,9)
b)
(0,-1) (0,1)
c)
(-3,0) (3,0)
d)
(9,0)
93.
What is the vertex of the equation:
f(x) = (x-2)2 + 4
f(x) = (x-2)2 + 4
a)
(-2, 4)
b)
(4, 2)
c)
(2, 4)
d)
(-4, 2)
94.
Write a quadratic equation in vertex form with the given values:
a=2, h=-3, k=-7
a=2, h=-3, k=-7
a)
f(x) = 2(x - 3)2 -7
b)
f(x) = -3(x + 2)2 -7
c)
f(x) = 2(x + 3)2 +7
d)
f(x) = 2(x + 3)2 -7
95.
Does this parabola have a maximum or a minimum:
-3(x - 5)2 + 1
-3(x - 5)2 + 1
a)
Maximum
b)
Minimum
96.
Rewrite this expression as a perfect square:
x2 - 10x + 25
x2 - 10x + 25
a)
(x - 5)2
b)
(x + 5)2
c)
(x + 10)2
d)
(x - 10)2
97.
Rewrite this expression as a perfect square:
x2 + 7x + 49/4
x2 + 7x + 49/4
a)
(x - 49/4)2
b)
(x + 7)2
c)
(x + 7/2)2
d)
(x - 7/2)2
98.
Rewrite in vertex form by completing the square:
f(x) = x2 - 12x +11
f(x) = x2 - 12x +11
a)
f(x) = (x + 6)2 - 25
b)
f(x) = (x - 6)2 - 25
c)
f(x) = (x - 6)2 + 11
d)
f(x) = (x - 6)2 + 47
99.
Solve for x:
(x + 2)2 - 16 = 0
(x + 2)2 - 16 = 0
a)
x = 2 & x = -6
b)
x = 2
c)
x = -6
d)
x = -2 & x = 6
100.
What is the y-intercept of:
f(x) = (x + 3)2 + 3
f(x) = (x + 3)2 + 3
a)
(3, -3)
b)
(-3, 3)
c)
(0, 12)
d)
(0, 9)
101.
What best describes the shifts of the graph:
f(x) = (x + 7)2 -1
f(x) = (x + 7)2 -1
a)
Down 7, Left 1
b)
Up 7, Right 1
c)
Right 7, Down 1
d)
Left 7, Down 1
102.
What value of "a" will make the parabola wider?
a)
a = negative
b)
0 < a < 1
c)
a > 1
d)
a = positive
103.
What value is needed to "complete the square"
(x2 + 14x + ____) - _____ + 3
(x2 + 14x + ____) - _____ + 3
a)
9
b)
14
c)
7
d)
49
104.
What did I forget when completing the square:
x2 + 10x + 3
(x2 + 10x + 25) + 3
(x + 5)2 + 3
x2 + 10x + 3
(x2 + 10x + 25) + 3
(x + 5)2 + 3
a)
Should be: (x + 25)2 + 3
b)
Need to square the 3
c)
Subtract 25
d)
Forgot to solve for x
105.
Find the coordinates of the minimum point on the graph:
x2 - 2x - 5
x2 - 2x - 5
a)
(5, -2)
b)
(-2, -5)
c)
(-1, 6)
d)
(1, -6)
106.
Simplify √-4
a)
2i
b)
-2i
c)
2
d)
4i
107.
What does i2 = ?
a)
1
b)
-1
c)
√-1
d)
√1
108.
Simplify √-45
a)
3i√5
b)
-3i√5
c)
-i√45
d)
45i
109.
x2+141=20
a)
-11i, 11i
b)
-11i
c)
11i
d)
no solution
110.
-5x2=200
a)
-10i√2,10i√2
b)
2i√10
c)
-2i√10
d)
-2i√10,2i√10
111.
When asked to find when a ball hits the ground or when business will have no profit you should...
a)
Convert to standard form and find the y-intercept
b)
Solve for the zeros
c)
Find the max or min
d)
Complete the square and find the vertex
112.
The following quadratic has how many and what type of solution(s).
a)
Two real solutions
b)
Two complex solutions
c)
One real solution
d)
One complex solution
113.
Solve by completing the square.
x2 +12x = 5
x2 +12x = 5
a)
X = 6 + √41 or 6 − √41
b)
X= 35 or 47
c)
X = −6 + √41 or −6 − √41
d)
X = √35 or √47
114.
2x2 – 6x + 5 = 0
a)
x=3/2±i/2
b)
x=3 ± i/2
c)
x=3/2 ± i
d)
x=3±i
115.
____________
For the function above, is the discriminant positive, negative, or zero?
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
116.
What does the discriminant tell us?
a)
The maximum or minimum
b)
The y-intercept
c)
The number and type of solutions
d)
The axis of symmetry
117.
What is the domain of the graph?
a)
y≥1
b)
x ≥ 1
c)
All real numbers
d)
none of these
118.
What is the range?
a)
-4 < x ≤ 5
b)
-4 ≤ x < 5
c)
-3 < y < 3
d)
-3 ≤ y ≤ 3
119.
What is the range?
a)
-3 < y ≤ 3
b)
-4 ≤ y < 5
c)
-4 ≤ y ≤ 5
d)
-3 < y ≤ 3
120.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
a)
D: {1, -3, -4,}
R: {0, 1, 2, -4}
R: {0, 1, 2, -4}
b)
D: {-4, 0, 1, 2}
R:{-4, -3, 1}
R:{-4, -3, 1}
c)
D: {0, 1, 2, 3, 4}
R:{1, -3, -4}
R:{1, -3, -4}
d)
D: {0, 1, 2, -4}
R: {1, -3, -4, 1}
R: {1, -3, -4, 1}
121.
What is the range?
a)
-7≤x≤6
b)
-7<x<6
c)
-8<y<2
d)
-8≤y≤2
122.
What is the domain?
a)
-3 < y ≤ 3
b)
-4 ≤ y ≤ 5
c)
-4 ≤ x ≤ 5
d)
-3 < x ≤ 3
123.
What is the range of the function?
a)
0≤h≤3
b)
0≤h≤36
c)
h<3
d)
t≤36
124.
a)
F
b)
G
c)
H
d)
J
125.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
126.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
127.
Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?
a)
3x + 2y = 315
2x + 4y = 450
2x + 4y = 450
b)
3x + 2y = 450
2x + 4y = 315
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
3x + 4y = 450
128.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
129.
What equation can be used to solve for x?
a)
Sin(40°)= x/40
b)
Sin(40º)=x/19
c)
Cos(40º)=x/19
d)
Tan(40°)=19/x
130.
Find x round to the nearest tenth.
a)
46.1
b)
4.9
c)
16.4
d)
26.9
131.
Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.
a)
63 ft
b)
65 ft
c)
74 ft
d)
87 ft
132.
a)
18/30
b)
24/30
c)
18/24
d)
24/18
133.
Find the measurement of the missing side indicated
a)
4.98
b)
5.98
c)
3.20
d)
4.18
100 %
