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WorksheetsAlgebra 2- Units 1 - 4 Review
Total questions: 90
Worksheet time: 6hrs 17mins
Name
Class
Date
1.
Solve |x – 12| - 3 = 11.
a)
-2, -26
b)
-2, 26
c)
3, 25
d)
4, -7
2.
3 | 2t - 3 | - 5 > 16
a)
No Solution
b)
All Real Numbers
c)
t < -2 or t > 5
d)
-2 < t < 5
3.
6i (-5 + 10i)
a)
-60 - 30i
b)
16 + 30i
c)
60 + 11i
d)
11 + 16i
4.
Find the conjugate of:
5 + 7i
5 + 7i
a)
5 − 7i
b)
-5 − 7i
c)
-5 + 7i
5.
i13
a)
-1
b)
1
c)
i
d)
-i
6.
Factor
n2 + 16n + 63
n2 + 16n + 63
a)
(n-7)(n+4)
b)
(n+7)(n-9)
c)
(n-3)(n-10)
d)
(n+7)(n+9)
7.
Factor
3v2 - 4v - 7
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
8.
Factor
81m2 - 1
81m2 - 1
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
9.
What are the x-intercepts for the function
f(x) = (x + 7)(x + 5)
f(x) = (x + 7)(x + 5)
a)
(7 , 0) and (5 , 0)
b)
(0 , 7) and (0 , 5)
c)
(-7 , 0) and (-5 , 0)
d)
(7 , 0) and (5 , 0)
10.
Simplify.
2x2 + (4x - 6x2) + 9 - (6x + 3)
2x2 + (4x - 6x2) + 9 - (6x + 3)
a)
-4x2 - 2x + 12
b)
4x2 + 2x - 6
c)
-4x2 - 2x + 6
d)
-4x2 + 10x + 12
11.
What is the slope of the line passing through the points (3,5) and (-1,7)?
a)
-1/2
b)
-1
c)
-2
d)
1/2
12.
What is the equation for the line that passes through the points (4,2) and (0,6)?
a)
y = x + 6
b)
y = -2x + 2
c)
y = -x - 6
d)
y = -x + 6
13.
What is the equation for the line with a slope of 7 and passes through (0,1)?
a)
y = -7x + 1
b)
y = 7x + 1
c)
y = -1/7x - 1
d)
y = -1/7x + 1
14.
Give the equation for the graph
a)
y = 5x - 3
b)
y = 4x + 2
c)
y =-2x + 5
d)
y = - 2x + 4
15.
What is the equation of this line?
a)
0
b)
undefined
c)
y = -2
d)
x = -2
16.
What is the equation of the line that has a slope of 5 and goes through the point (2,7)?
a)
y = 5x + 3
b)
y = 1/5x - 3
c)
y = 1/5x + 3
d)
y = 5x - 3
17.
What is the equation of the line in the graph?
a)
y = 3
b)
x = 3
c)
x = 0
18.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
19.
Is the relation a function? Why.
a)
Yes, because the x-value 11 has two y-values pair with it.
b)
Yes, because each x-value has only one y-value paired with it.
c)
No, because the x-value 11 has two y-values pair with it.
d)
No, because each x-value has only one y-value paired with it.
20.
a)
Function
b)
Not a Function
21.
a)
Function
b)
Not a Function
22.
a)
Function
b)
Not a Function
23.
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}
24.
Does the graph represent a function?
a)
Yes, because the vertical line test shows there are no repeating input values
b)
No, because the vertical line test shows there are repeating input values
25.
Is this relation a function?
a)
Function
b)
Not a Function
26.
Is this a function? Explain.
a)
Yes; it passes the horizontal line test.
b)
No; it is not a straight line.
c)
Yes; it passes the vertical line test.
d)
No; there is a line connecting the dots.
27.
The table of values are shown. What is the range of the relation? From least to greatest.
a)
(-4,-8,-3)
b)
(-3,2,6)
c)
(-8,-4,4)
d)
(6,2,-3)
28.
What is the domain of the graph?
a)
-3 ≤ x ≤ 3
b)
3 ≤ x ≤ -3
c)
-2 ≤ x ≤ 10
d)
-3 ≤ x ≤ 10
29.
What is the range of the graph?
a)
-2 < y < 10
b)
-3 < x < 3
c)
-2 ≤ y ≤ 10
d)
-3≤ x ≤ 3
30.
What is the domain of the graph?
a)
x≤0
b)
x≥0
c)
All real numbers
d)
y≥0
31.
What is the range of the graph?
a)
x≤0
b)
y≥0
c)
y≤0
d)
All real numbers
32.
What is the domain of the function?
a)
x>3
b)
x≥-3
c)
y≤4
d)
y<4
33.
What is the range of the graph?
a)
1 ≤ x ≤ 5
b)
1 < x < 5
c)
1 ≤ y ≤ 5
d)
1 < y < 5
34.
What is the range of the function given below?
a)
0 ≤ y ≤ 7
b)
-2 ≤ y ≤ 4
c)
.2 ≤ y ≤ 4
d)
All real numbers
35.
What is the domain of the graph?
a)
-7 ≤ x < 5
b)
-3 ≤ x < 1
c)
-3 ≤ y < 1
d)
-7 ≤ y < 5
36.
Solve the equation:
3(x - 1) = 2x + 9
3(x - 1) = 2x + 9
a)
x = 12
b)
no solution
c)
x = 10
d)
x = 6
37.
Solve the equation:
3x - x + 2 = 4(2x - 1)
3x - x + 2 = 4(2x - 1)
a)
infinite solutions
b)
x = 1
c)
x = -1
d)
no solution
38.
Describe the solution set:
2(x + 5) = 2x + 5
2(x + 5) = 2x + 5
a)
one solution
b)
no solution
c)
infinitely many solutions
d)
two solutions
39.
Solve the equation:
½ (2x + 6) = 3x + 13
½ (2x + 6) = 3x + 13
a)
no solution
b)
x = 8
c)
x = -5
d)
x = 7
40.
Solve:
3(3x - 6) = 18
3(3x - 6) = 18
a)
x = 4
b)
x = -4
c)
no solution
d)
infinite solutions
41.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
42.
Which answer choice describes y = -3x2 +7x - 2 accurately?
a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum
43.
.How many zeros does this parabola have?
a)
3
b)
2
c)
0
d)
1
44.
Find the y-intercept of f(x) = 2x2-2x + 1
a)
2
b)
-2
c)
1
d)
-1
45.
Find the vertex of
f(x) = -x2 - 4x + 12.
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
46.
Find the axis of symmetry for
f(x) = x2- 8x + 15.
f(x) = x2- 8x + 15.
a)
x = -4
b)
x = 4
c)
y = 4
d)
y = -4
47.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
48.
y=2x2-6x+1 is in what form?
a)
Vertex Form
b)
Factored form
c)
Standard Form
d)
Cannot be determined
49.
Is this a max or min?
a)
max
b)
min
c)
cannot be determined
50.
The solutions of a quadratic equation are known as the _____.
a)
Vertices
b)
Roots
c)
Squares
d)
Formulas
51.
What is the y intercept for the equation:
y = -8x2 + 3x - 7
y = -8x2 + 3x - 7
a)
(0, -8)
b)
(0, 3)
c)
(-8, -7)
d)
(0, -7)
52.
What is the equation for the axis of symmetry of
f(x)= (x +1)2 + 5
f(x)= (x +1)2 + 5
a)
x = 1
b)
x = -1
c)
x = -5
d)
x = 5
53.
What are the zeros for the function
f(x) = (x + 7)(x + 5)
f(x) = (x + 7)(x + 5)
a)
(7 , 0) and (5 , 0)
b)
(0 , 7) and (0 , 5)
c)
(-7 , 0) and (-5 , 0)
d)
(7 , 0) and (5 , 0)
54.
What is the vertex form of this quadratic?
a)
f(x) = -(x + 2)2 - 4
b)
f(x) = (x - 2)2 + 4
c)
f(x) = (x - 2)2 - 4
d)
f(x) = -(x - 2)2 - 4
55.
Solve by taking the Square Root:
16a2 - 9 = 0
a)
a = ± 3/4
b)
a = ± 4/3
c)
a = ± 9/16
d)
a = ± 16/9
56.
Solve by taking the Square Root:
4m2 - 100 = 0
a)
m = ± 25
b)
m = 96
c)
m = ± 5
d)
m = -96
57.
Solve for x by taking the Square Root:
(x+6)2 = 49
a)
x = 7 and 12
b)
x = ±7
c)
x = 1 and -13
d)
x = 43 and -55
58.
Solve the equation using square roots:
x2 = 121
a)
x = 60.5
b)
x = ± 11
c)
x = ± 12
d)
x= 11
59.
Solve by completing the square:
n2 - 2n - 3 = 0
a)
n = 3 and -1
b)
n = 4 and -4
c)
n = 5 and -3
d)
n = 8 and -7
60.
Solve by completing the square:
x2 + 10x = -9
a)
x = 1 and -12
b)
x = -1 and -9
c)
x = 1 and -9
d)
x = 1 and -1
61.
Solve by completing the square:
k2 − 12k + 20 = 0
a)
k = 10 and 2
b)
k = -6 and -6
c)
k = 22 and -10
d)
k = -2 and 6
62.
What is the vertex of the parabola: y=2(x-3)2+4
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
63.
Complete the Square and write in Vertex Form:
f(x) = x2 + 6x + 5
f(x) = x2 + 6x + 5
a)
(x + 3)2 - 4
b)
(x + 6)2 - 4
c)
(x + 3x)2 - 4
d)
(x + 3)2 + 9
64.
Complete the square and write in Vertex Form
f(x) = x2 + 4x + 9
f(x) = x2 + 4x + 9
a)
f(x) = (x+2)2 + 5
b)
f(x) = (x - 2)2 + 5
c)
f(x) = (x+4)2 + 5
d)
f(x) = (x+2)2 - 5
65.
Convert to vertex form.
y = 3x2 +6x - 5
y = 3x2 +6x - 5
a)
y=3(x+1)2 - 8
b)
y=3(x-1) 2 - 8
c)
y=3(x+2)2 - 8
d)
y=3(x-2)2 - 8
66.
If given the equation
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
67.
Complete the square and write in Vertex Form
f(x) = x2 + 6x + 12
a)
f(x)= (x+3)2 -3
b)
f(x)= (x+3)2 +3
c)
f(x)= (x+6)2+3
d)
f(x)= (x-3)2 -3
68.
(-7 + 9i) + (2 - 10i)
a)
-5 + i
b)
-5 - i
c)
-9 + 1
d)
9 - i
69.
(4 - 2i) - (3 + 6i)
a)
7 - 4i
b)
1 + 4i
c)
1 - 8i
d)
7 - 8i
70.
The expression (2 + 3i)2 is equal to
a)
-5
b)
-5 + 12i
c)
13
d)
13 + 12i
71.
(3 + 8i)(-2 - i)
a)
2-19i
b)
23-i
c)
34+5i
d)
23-i
72.
Simplify
a)
(-10+6i)/17
b)
(1+50i)/61
c)
(-23+36i)/25
d)
(-21+33i)/34
73.
√-36
a)
6
b)
-6
c)
-6i
d)
6i
74.
Simplify.
a)
b)
c)
d)
75.
Simplify i23
a)
i
b)
-1
c)
1
d)
-i
76.
√-4
a)
-2
b)
-2i
c)
2
d)
2i
77.
Which function shows horizontal translation and a vertical stretch?
a)
f(x) = -2|-x |
b)
f(x) = -3|x| - 7
c)
f(x) = -|-x + 1| + 4
d)
f(x) = 5|x - 4| - 1
78.
Which function is graphed?
a)
f(x) = 2|x + 2| -4
b)
f(x) = 2|x - 4| + 2
c)
f(x) = |x + 2| - 4
d)
f(x) = -2|x - 4|
79.
Which function is graphed?
a)
f(x) = -|2x - 3| + 5
b)
f(x) = -|x + 5| - 3
c)
f(x) = -|2x + 6| + 5
d)
f(x) = -2|x + 5| - 3
80.
Which function is graphed?
a)
f(x) = 2|x - 5|
b)
f(x) = |x - 5|
c)
f(x) = |x - 5| + 5
d)
f(x) = |x| + 5
81.
Which function is graphed?
a)
f(x) = -3|-x + 1| + 4
b)
f(x) = -|x - 1| + 4
c)
f(x) = -5|x + 1| + 4
d)
f(x) = -3|x - 4| + 1
82.
When x is less than or equal to 2, what equation is shown in the graph?
a)
f(x) = 3
b)
f(x) = x
c)
f(x) = | x |
d)
f(x) = | x - 1 |
83.
What is g(7) if:
a)
-17
b)
-13
c)
13
d)
17
84.
Using the pictured graph, what is f(-3)?
a)
-3
b)
-1
c)
1
d)
3
85.
7x+4y =12
x + 2y = -4
x + 2y = -4
a)
(-4,4)
b)
(4,4)
c)
(4,-4)
d)
(-4,-4)
86.
x + 2y = -4
x - 2y = 8
x - 2y = 8
a)
(2,5)
b)
(2,-3)
c)
(2,-2)
d)
(-3,2)
87.
7x - 2y = 6
x - 2y = -6
x - 2y = -6
a)
(2,4)
b)
(3,-2)
c)
(1,2)
d)
(-2,-4)
88.
x-4y = 16
5x + 4y = 8
5x + 4y = 8
a)
(4,-3)
b)
(-3,4)
c)
(4,3)
d)
(3,-4)
89.
x + y = 3
3x - y = 1
3x - y = 1
a)
(2,1)
b)
(-1,2)
c)
(1,2)
d)
(-2,-1)
90.
Solve for x
l 2x−1 l = 9
l 2x−1 l = 9
a)
x = 5 and x =-4
b)
x = 5 and x = -5
c)
Only x = 5
d)
No Solution
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