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WorksheetsAlgebra 2 midterm review
Total questions: 90
Worksheet time: 20hrs 9mins
Name
Class
Date
1.
f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.
List the zeros for this function.
a)
x = -4, x = 3, x = -2
b)
x = -4, x = 3, x = 2
c)
x = -4, x = -3, x = 2
d)
x = 4, x = 3, x = 2
2.
Which of the following is a solution to the function? (x - 8)(x - 9) = 0
a)
8
b)
-9
c)
-17
d)
0
3.
Give the x-intercept
3x + 8y = 24
3x + 8y = 24
a)
(8, 0)
b)
(0, 8)
c)
(3, 0)
d)
(0, 3)
4.
Give the y-interecept
3x + y = 5
3x + y = 5
a)
-3
b)
(0,5)
c)
-5
d)
(0, -3)
5.
Subtract the two complex numbers and put your answer in a + bi form.
(10+3i) - (2-9i)
a)
20-27i
b)
12-7i
c)
8+12i
d)
20-27i2
6.
Add the two complex numbers and put your answer in a + bi form.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
7.
(-4i)(3i)(4i)
a)
24
b)
-48i
c)
48i
d)
60
8.
(5-i)(5-i)
** Remember i * i = i 2 and i 2 = -1 **
a)
15-8i
b)
36
c)
24+10i
d)
24-10i
9.
What does i2 = ?
a)
-1
b)
√-1
c)
1
d)
-√1
10.
a)
2i√6
b)
8i√3
c)
-2√6
d)
-2i√6
11.
Factor completely:
3x2 + 18x +15
Hint: Assign x a value and check answers
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
12.
Five times Mike's age, increased by nine
a)
5(x+9)
b)
9(5+x)
c)
9x+5
d)
5x+9
13.
4 times the sum of y and 5
a)
4 + y + 5
b)
4y + 5
c)
4(y + 5)
d)
4 − y + 5
14.
What is the correct term for the answer you get when you multiply?
a)
Product
b)
Quotient
c)
Sum
d)
Difference
15.
Find the zeros: y = x(x - 1)(x + 3)
a)
0, 1, -3
b)
-3, 1
c)
-1, 3, 0
d)
-1, 3
16.
Which polynomial is in standard form?
a)
2x3 + 3x2 + x + 4
b)
x4 + x7
c)
2 + x2 + 3x
d)
2 + x + 4
17.
What are the zeros in (x-5)(x+4)
a)
x = 5, -4
b)
x = -5, -4
c)
x = -5, 4
d)
0
18.
How many terms are there is 2x3 +x2 + 4x + 6
a)
4
b)
2
c)
1
d)
6
19.
Find the solutions to the equation:
2x2 + 11x = -12.
2x2 + 11x = -12.
a)
-4, -1.5
b)
4, 1.5
c)
-4, 1.5
d)
4, -1.5
20.
Factor: x2 - 6x + 9
a)
(x - 3)(x - 3)
b)
(x + 3)(x + 3)
c)
(x - 6)(x +3)
d)
(x - 9)(x - 1)
21.
Simplify:
-6x2 - 4x + 10 - 9 + 2x + 10x2
-6x2 - 4x + 10 - 9 + 2x + 10x2
a)
-4x2 + 2x + 1
b)
4x2 + 2x - 1
c)
-4x2 - 2x + 1
d)
4x2 - 2x + 1
22.
Simplify:
7[(x2 - 5x + 6)-(x +2)]
7[(x2 - 5x + 6)-(x +2)]
a)
7x2 - 42x - 28
b)
7x2 - 42x + 28
c)
7(x - 2)2
d)
7(x - 2)(x - 4)
23.
Find the zeroes for:
f(x) = x2 - 6x - 27
f(x) = x2 - 6x - 27
a)
x = 9, x = -3
b)
x = 9, x = 3
c)
x = -9, x = 3
d)
x = -9, x = -3
24.
The cost of renting a bike is $8 for the first hour and $3 for each additional hour. Which of the following represents this situation, where C is the cost of renting the bike for h hours?
a)
C = 11h
b)
C = 8h + 3
c)
C = 8 + 3h
d)
C = 3(h - 1) + 8
25.
If f(x)=x^2-4x-5, find f(-1)
a)
f(-1)=0
b)
f(-1)= -6
c)
f(-1)=3
d)
f(-1)=6
26.
Decide whether the following expressions are equivalent (x+3)^2 and x^2+6x+9
a)
maybe equivalent
b)
equivalent only when upside down
c)
equivalent
d)
not equivalent
27.
Multiply the following expression. x^2(2x-1)
a)
2x^3+x^2
b)
2x^3+x
c)
4x^2-2x
d)
2x^3-x^2
28.
Identify the zeros:
a)
x=-2, x=-1, x=0
b)
x=-2, x=0
c)
x=-1, x=0, x=2
d)
x=-2, x=0, x=1
29.
How many zeros should the polynomial function
P(x) = 3x4+4x-8 have?
P(x) = 3x4+4x-8 have?
a)
1
b)
2
c)
3
d)
4
30.
What is the equation in factored form of this graph?
a)
f(x) = (x-4)(x-1)2(x+2)(x+4)
b)
f(x) = (x-4)(x+1)2(x+2)(x+4)
c)
f(x) = (x-4)(x-1)2(x-2)(x+4)
d)
f(x) = (x+4)(x+1)2(x-2)(x-4)
31.
What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)
y = x(x - 6)(x + 5)
a)
0, 6, -5
b)
6, -5
c)
0, -6, 5
d)
1, -6, 5
32.
Which equation MOST LIKELY matches the graph?
a)
y = x4 - x3 + 3x2 + 2
b)
y = -x4 + x3 + 5x + 2
c)
y = x3 - 2x2 + 1x + 3
d)
y = -x3 - 2x2 + 1x + 3
33.
Is the leading coefficient positive or negative
a)
positive
b)
negative
34.
What is the factored form of a function if it has zeros of 2, 3 and -1?
a)
(x-2)(x-3)(x+1)
b)
(x-1)(x-2)(x-3)
c)
(x-1)(x+2)(x+3)
d)
(x+1)(x+2)(x+3)
35.
What is the leading coefficient?
a)
Positive
b)
Negative
36.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
37.
Simplify the expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3
b)
-7n2 - 8n + 3
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
38.
Which is leading coefficient and Is it even or odd
a)
Positive/Odd
b)
Negative/Even
c)
Positive/Even
d)
Negative/Odd
39.
What is the leading coefficient and is it even or odd?
a)
Negative/Odd
b)
Negative/Even
c)
Positive/Odd
d)
Positive/Positive/Odd
40.
What is the End behavior on the left side
a)
x →-∞, y→∞
b)
x →∞, y→-∞
c)
x →-∞, y→-∞
d)
x →∞, y→∞
41.
3+√-4
a)
1
b)
3-2i
c)
5
d)
3+2i
42.
Simplify:
(10+ 15i) - (48 - 30i)
(10+ 15i) - (48 - 30i)
a)
58 - 45i
b)
58 - 15i
c)
-38 - 15i
d)
-38 + 45i
43.
Find the sum.
(5-2i) + (-7+8i)
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
44.
Determine the values of
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
45.
Use the quadratic formula to solve 2x2 + 2x - 12?
a)
-2, 3
b)
2, 3
c)
2, -3
d)
-2, -3
46.
Factor the quadratic into binomials
x2+5x+6
x2+5x+6
a)
(x+1)(x-6)
b)
(x-3)(x+2)
c)
(x+3)(x+2)
d)
(x+4)(x+2)
47.
Simplify:
-6x2 - 4x + 10 - 9 + 2x + 10x2
-6x2 - 4x + 10 - 9 + 2x + 10x2
a)
-4x2 + 2x + 1
b)
4x2 + 2x - 1
c)
-4x2 - 2x + 1
d)
4x2 - 2x + 1
48.
Name the x-intercept(s)?
a)
(0, 0)
b)
(2, 4)
c)
(0, 0) and (0, 4)
d)
(0, 0) and (4, 0)
49.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
50.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
51.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
52.
x-3
a)
1/x3
b)
1/x-3
c)
3x
d)
1/3x
53.
a)
y=3x
b)
y=6x-4
c)
y=3x2-2
d)
4x3
54.
Select the correct description of the function.
a)
Facing:up
vertex:(-1,-8)
y-intercept:-6
vertex:(-1,-8)
y-intercept:-6
b)
Facing:down
vertex:(-1,-8)
y-intercept:4
vertex:(-1,-8)
y-intercept:4
c)
Facing:up
vertex:(-2,-4)
y-intercept:-8
vertex:(-2,-4)
y-intercept:-8
55.
Is the leading coefficient positive or negative
a)
positive
b)
negative
56.
2x3 + 5x2 + 9 ÷ x + 3
a)
2x2 - x + 3
b)
2x3 - x2 + 3x
c)
2x2 + 11x + 33 + 108/x+3
d)
2x2 - 5x + 12
57.
2x3 - 5x2 + 3x + 7 ÷ x - 2
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
58.
Factor Completely: x2-7x-8
a)
(x+1)(x-8)
b)
(x+1)(x+8)
c)
5(x+4)(x+5)
d)
(x-1)(x+8)
59.
Factor completely:
3x² + 5x - 12
3x² + 5x - 12
a)
(3x + 4)(x-3)
b)
(3x - 4)(x + 3)
c)
(3x + 3)(x -4)
d)
(3x - 3)(x + 4)
60.
20x3-25x2+4x-5
a)
(5x2-5)(4x+1)
b)
5(x2-1)(4x+5)
c)
(5x2+1)(4x-5)
d)
(5x2+1)(4x-1)
61.
7r3-8r2+42r-48
a)
(r2+6)(7r+8)
b)
(r2+6)(7r-8)
c)
(r2+6)(r2+8)
d)
(r2+6)(7r+6)
62.
√-54
a)
3i√6
b)
-3√6
c)
14i√13
d)
-13√5
63.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
64.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
65.
Simplify
a)
9i/5
b)
2i
c)
8i/5
d)
13i/5
66.
Factor Completely:
x2 - 36
x2 - 36
a)
(x + 9)(x - 4)
b)
(x - 6)(x - 6)
c)
(x - 9)(x + 2)(x - 2)
d)
(x + 6)(x - 6)
67.
What is the solution to this system?
x - y = 6
y= 2x - 5
x - y = 6
y= 2x - 5
a)
(1,3)
b)
(-1,3)
c)
(-1,-7)
d)
(1,-7)
68.
Simplify: (2i10)(-4i12)(-5i7)
a)
-40
b)
40i
c)
-40i
d)
40
69.
Does the equation open up, down, left, or right?
Y = -3x2 +7x - 2
Y = -3x2 +7x - 2
a)
up
b)
down
c)
right
d)
left
70.
Factor.
a)
(3x²-3)
b)
3(x²-3)
c)
(3x-3)²
d)
3(2x²-3)
71.
What is it?
a)
hippopotamus
b)
rhino
c)
hipopotamus
d)
bull
72.
Divide (x2 + 5x - 8) by (x + 3). What is the remainder?
a)
16
b)
12
c)
-14
d)
-16
73.
What are all the x-intercepts?
a)
(-2.55, 0), (2.55, 0)
b)
(-3,0), (-2,0), (2,0), (3,0)
c)
(0, 36)
d)
(-∞,∞)
74.
Classify the degree?
a)
Positive
b)
Negative
c)
Odd
d)
Even
75.
What is the degree?
y = 8x2 - 5x8 + 3x7-10x5
y = 8x2 - 5x8 + 3x7-10x5
a)
8
b)
7
c)
2
d)
22
76.
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
77.
What is the transformation described?
a)
horizontal shift to the right 4 and vertical shift down 2
b)
horizontal shift to the left 4 and vertical shift up 2
c)
horizontal shift to the right 4 and vertical shift up 2
d)
horizontal shift to the left 4 and vertical shift down 2
78.
Simplify the following radical: √243
a)
81√3
b)
3√3
c)
13√3
d)
9√3
79.
How do you determine the amount and type of solutions that an equation has
a)
b^2 - 4ac
b)
quadratic formula
c)
guess
d)
trick question: use your calculate
80.
What is another way to say "to solve" an equation?
a)
zeros
b)
x-intercepts
c)
solutions
d)
roots
e)
Quadratic formula
81.
Select true or false for each statement.
A
B
C
D
E
F
G
H
82.
Consider the function f(x) = -x3. What is the Domain of this function?
a)
[0,∞)
b)
(-∞,0]
c)
[-0,0]
d)
(-∞,∞)
83.
Consider the function f(x) = x3. What is the Range of this function?
a)
[0,∞)
b)
(-∞,0]
c)
[-0,0]
d)
(-∞,∞)
84.
What is the range of the graph?
a)
All real numbers
b)
To infinity and beyond
c)
y ≥ -1
d)
x ≥ 0
85.
What is the domain of the graph?
a)
All real numbers
b)
To infinity and beyond
c)
y ≥ -1
d)
x ≥ 0
86.
What is the domain and the range for the graph?
a)
Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4
Range : 0 ≤ y ≤ 4
b)
Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2
Range : -2 ≤ y ≤ 2
c)
Domain : All real #s
Range : y ≤ 4
Range : y ≤ 4
d)
Domain : -2 ≤ x ≤ 2
Range : y ≤ 4
Range : y ≤ 4
87.
The domain of a polynomial function is always (-∞, +∞).
a)
True
b)
False
88.
The range of a polynomial function is always (-∞, +∞).
a)
True
b)
False
89.
Match the graph to the function
a)
f(x) = -2x⁶+9x²
b)
f(x) = x⁶-7x⁴+12x²-x-2
c)
f(x) = x⁶-3x³+x+2
d)
f(x) = -x⁶+5x⁴+3x-2
90.
Select the two descriptions that best describe the polynomial FUNction's graph.
a)
Even degree
b)
Odd degree
c)
Positive leading coefficient
d)
Negative leading coefficient
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