WorksheetsAlgebra 2 Sem 1 Final Prep
Total questions: 120
Worksheet time: 5hrs 31mins
Name
Class
Date
1.
Find f(2) if f(x) = 2x2- 5x
a)
6
b)
-6
c)
-2
d)
2
2.
find f(0) if f(x) = -3x2 + 5x + 1
a)
1
b)
-2
c)
3
d)
5
3.
Find f(0) if f(x) = 5x3 + 2x2 +3x
a)
3
b)
10
c)
-2
d)
0
4.
find f(-2) if f(x) = (x-3)2
a)
-25
b)
25
c)
1
d)
-1
5.
Find f(2) if f(x) = (x-4)(x-4)
a)
4
b)
-4
c)
0
d)
-3
6.
(2x + 5y - z) + (-6x - 4y + 7z)
a)
-4x +6y + 6z
b)
4x + y + 6z
c)
-4x - y + 6z
d)
-4x + y + 6z
7.
(3x + 4y - 3z) - (2x - 6y + 7z)
a)
x + 10y - 10z
b)
-x +10y - 10z
c)
x -10y - 10z
d)
-x -10y - 10z
8.
(4x3-5x2+3x)+(-2x3-x2+6x)
a)
2x3-6x2-9x
b)
2x3+6x2+9x
c)
-2x3-6x2+9x
d)
2x3-6x2+9x
9.
(5x4 - 4x3 - 2x2 + x - 19) - (x4 + 5x3 + 8x2 + x + 5)
a)
4x4 - 9x3 - 10x2 - 24
b)
4x4 - 9x3 - 10x2 - 2x - 24
c)
4x4 - 9x3 - 10x2 + 2x - 24
d)
-4x4 - 9x3 - 10x2 - 24
10.
5(2x+5)
a)
10x + 5
b)
10x + 25
c)
7x + 10
d)
7x + 25
11.
-3(x - 4)
a)
-3x - 12
b)
3x - 12
c)
3x + 12
d)
-3x + 12
12.
(x+3)(x+1)
a)
x2+3x+3
b)
2x+4x+3
c)
x2+4x+3
d)
5x + 3
13.
5x(2x + 3)
a)
10x2 + 15x
b)
7x + 15x
c)
7x2 + 8x
d)
25x2
14.
(x-2)(x+1)
a)
x2-2x-2
b)
x2-2
c)
x2+x+2
d)
x2-x-2
15.
(x+5)2
a)
x2+25
b)
2x+10
c)
x2+10x+25
d)
12x
16.
(x-3)2
a)
x2-6x+9
b)
x2 - 9
c)
x2 + 9
d)
x2
17.
(2x + 1)(x - 3)
a)
-3x - 3
b)
2x2 + 5x - 3
c)
2x2 - 5x - 3
d)
2x2 - 5x +3
18.
(3x - 2)(6x + 1)
a)
21x2
b)
18x2 + 9x + 2
c)
9x2 - 9x - 2
d)
18x2 - 9x - 2
19.
(2x + 3)(x2 + 4x + 1)
a)
2x3 + 10x2 + 14x + 4
b)
2x3 + 11x2 + 14x + 3
c)
-2x3 - 11x2 + 14x + 5
d)
x3 - 11x2 + 14x + 3
20.
Add or Subtract to Simplify:
(x5 + x3) - (6x - x3 + 6x5)
(x5 + x3) - (6x - x3 + 6x5)
a)
-5x5 + 2x3 - 6x
b)
7x5 - 6x
c)
-5x3 + 2x2 - 6x
d)
-5x5 - 6x
21.
(x +2)(x + 3)
a)
x2 + 5x + 6
b)
x2 + x + 6
c)
x2 + 5x + 5
d)
x2 + 6x + 6
22.
Multiply.
(x + 7)2
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
23.
Multiply.
(5x + 2)(x2 - 3x + 6)
(5x + 2)(x2 - 3x + 6)
a)
5x3 - 17x2 +24x +12
b)
5x3 + 17x2 - 24x +12
c)
5x3 - 13x2 + 24x +12
d)
5x3 +13x2 - 24x - 12
24.
Multiply.
(x + 7)2
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
25.
5x2 is an example of a....
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
26.
7xy + 8 is an example of a...
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
27.
13x - 16y + 5y2 is an example of a....
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
28.
7x + 8y - 2x3 + 19xy is an example of a....
a)
Monomial
b)
Binomials
c)
Trinomial
d)
Polynomial
29.
What is the perimeter of the triangle shown?
a)
9r2+r-5
b)
9r4+r2-4
c)
9r2-r+4
d)
9r2+r-4
30.
What is the perimeter of the rectangle?
a)
x²+8x-5
b)
2x²+16x-10
c)
2x²+10x-8
d)
6x-2
31.
Which expression represents the perimeter?
a)
3x + 3
b)
4x + 3
c)
4x + 6
d)
6x + 6
32.
Pick the 2 names that correspond to
3x + 12
3x + 12
a)
Linear Binomial
b)
Linear Monomial
c)
Quadratic Binomial
d)
Quadratic Monomial
33.
What is the degree of the polynomial 3x4 + 2x2 + 5x ?
a)
1
b)
2
c)
3
d)
4
34.
What is the degree of the polynomial x2-2x+5?
a)
1
b)
2
c)
3
d)
0
35.
What is the type of polynomial?
4x5 - 3x3
4x5 - 3x3
a)
monomial
b)
binomial
c)
trinomial
d)
polynomial
36.
What is the standard form of the polynomial,
9x2 + 5x + 27 + 2x3
9x2 + 5x + 27 + 2x3
a)
27 + 5x + 9x2 + 2x3
b)
9x2 + 5x + 2x3 + 27
c)
9x2 + 5x + 27 + 2x3
d)
2x3 + 9x2 + 5x + 27
37.
What is the standard form of the polynomial,
7x - 125 - 6x4 + 14x2
7x - 125 - 6x4 + 14x2
a)
125 + 7x - 14x2 +6x4
b)
6x4 -14x2 - 7x +125
c)
125 + 14x2 + 7x - 6x4
d)
-6x4+ 14x2 + 7x - 125
38.
The length of a rectangle is (3x – 8) and the width is (4x + 5). What is the area of the rectangle?
a)
7x -3
b)
12x2 + 17x + 40
c)
12x2 - 17x - 40
d)
12x2 - 47x - 40
39.
(3y⁴)²
a)
9y⁸
b)
9y⁶
c)
6y⁸
d)
6y⁶
40.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
41.
3x⁻³
a)
1⁄3x³
b)
3⁄x³
c)
3x³
d)
-3x³
42.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
43.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
44.
Use synthetic division
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
45.
a)
2
b)
1
c)
4
d)
None
46.
Classify the function:
a)
quadratic
b)
cubic
c)
quartic
d)
linear
47.
Find all zeros of the polynomial function P(x) = x3+6x2+9x+54
a)
6, 3, -3
b)
-6, 3, -3
c)
-6, 3i, -3i
d)
6, 3i, -3i
48.
What is the relative max?
a)
(0, 36)
b)
(-2.55, -6.55), (2.55, -6.55)
c)
(-∞, ∞)
d)
None
49.
What is the degree of the polynomial:
2x – 9
2x – 9
a)
0
b)
1
c)
2
d)
3
50.
Classify by number of terms:
3x2 – 8x + 1
3x2 – 8x + 1
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
51.
Factor x2-20x+51
a)
(x-17)(x+3)
b)
(x+17)(x+3)
c)
(x+17)(x-3)
d)
(x-17)(x-3)
52.
Factor x2-x-72
a)
(x-9)(x+8)
b)
(x+9)(x-8)
c)
(x+9)(x-8)
d)
(x-9)(x-8)
53.
Factor x2-11x-60
a)
(x-12)(x-5)
b)
(x-15)(x+4)
c)
(x-15)(x-4)
d)
(x+12)(x-5)
54.
Factor x2-14x+24
a)
(x-8)(x+3)
b)
(x+12)(x-2)
c)
(x+8)(x+3)
d)
(x-12)(x-2)
55.
Factor x2+12x+20
a)
(x-4)(x+5)
b)
(x+10)(x+2)
c)
(x-10)(x-2)
d)
(x+4)(x+5)
56.
Factor x2-6x+8
a)
(x-4)(x-2)
b)
(x+4)(x+2)
c)
(x-4)(x+2)
d)
(x+4)(x-2)
57.
Factor x2-2x-15
a)
(x+5)(x-3)
b)
(x-5)(x-3)
c)
(x-5)(x+3)
d)
(x+5)(x+3)
58.
Factor x2+4x-32
a)
(x+8)(x-4)
b)
(x-8)(x-4)
c)
(x-8)(x+4)
d)
(x+8)(x+4)
59.
x2-x-12
a)
(x+6)(x+2)
b)
(x-4)(x+3)
c)
(x+4)(x+3)
d)
(x-4)(x-3)
60.
Factor x2-8x+7
a)
(x+1)(x+8)
b)
(x+1)(x+7)
c)
(x-7)(x-1)
d)
(x+1)(x-7)
61.
Factor the polynomial.
x2-12x+27
x2-12x+27
a)
(x-9)(x-3)
b)
(x+2)(x-3)
c)
(x-12)(x+27)
d)
(x+10)(x-2)
62.
Factor completely
10x2 + 15x-5
10x2 + 15x-5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
63.
Factor completely:
3x2 + 18x +15
Hint: Factor GCF first.
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
64.
Find the greatest common factor. 6x4y3-12x4y2+6x3y2
a)
6
b)
6xy
c)
6x3y2
d)
6x9y6
65.
Factor by grouping:
3x3-x2+6x-2
3x3-x2+6x-2
a)
(x2+2)(3x+1)
b)
(x2+2)(3x-1)
c)
(3x3+6x)(x2-2)
d)
none of the aboe
66.
Solve a3-9a2+14a=0.
a)
-7, -2
b)
7, 2
c)
0, -7, -2
d)
0, 7, 2
67.
Solve n4-49n2=0
a)
0, 7
b)
0, -7, 7
c)
0, -7
d)
7, -7
68.
Solve 𝑦4 – 7𝑦3 – 18𝑦2 = 0
a)
-2, 0, -9
b)
2, 0, -9
c)
-2, 0 ,9
d)
2, 0, 9
69.
What is the GCF of the trinomial?
3x2 - 9x -120
3x2 - 9x -120
a)
3
b)
2
c)
6
d)
9
70.
Multiply.
(b+3)(b2+2b+1)
(b+3)(b2+2b+1)
a)
b3+6b2+6b+3
b)
b3+5b2+7b+3
c)
4b3+8b2+3b
d)
3b3+6b2+3b
71.
Find the product.
(x + 7)2
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
72.
x2 - 25
a)
( x + 5 ) ( x - 5 )
b)
( x - 5 ) ( x - 5 )
c)
( x + 5 ) ( x + 5 )
d)
Prime
73.
x2 - 400
a)
( x - 200) ( x + 200)
b)
( x + 20) ( x + 20)
c)
Prime
d)
( x - 20) ( x + 20)
74.
What is the GCF of 18k and 15k3
a)
3k2
b)
3k3
c)
3k
d)
5k
75.
Factor the polynomial.
x2-4x-32
x2-4x-32
a)
(x-8)(x+4)
b)
(x-4)(x-32)
c)
(x+3)(x-4)
d)
x+2)(x+5)
76.
x2 + 81
a)
Prime
b)
( x - 9 ) ( x + 9 )
c)
( x + 9 ) ( x + 9 )
d)
( x - 9 ) ( x - 9 )
77.
Simplify the expression:
(8 - 3x2 - 7x) + (x4 - 4x - 7x2)
(8 - 3x2 - 7x) + (x4 - 4x - 7x2)
a)
x4 - 6x2 - 11x + 8
b)
x4 - 10x2 - 11x + 8
c)
x4 - 6x2 - 11x + 15
d)
-3x4 - 6x2 - 11x + 15
78.
x4-y4
a)
(x2+y2)(x2-y2)
b)
(x2+y2)(x-y)(x+y)
c)
(x+y)(x-y)(x+y)(x-y)
d)
(x2-y2)(x+y)(x-y)
79.
16q3-48q2+32q
a)
16q(q2-3q+2)
b)
16q(q-2)(q-1)
c)
2q(8q2-24q+16)
d)
2q(q2-24q+128)
80.
13x5-13x
a)
13x(x4-1)
b)
13x(x2-1)(x2+1)
c)
13x(x2+1)(x-1)(x+1)
d)
13x(x-1)(x+1)(x-1)(x+1)
81.
81y4-1
a)
(9y2+1)(9y2-1)
b)
(9y2+1)(3y-1)(3y+1)
c)
(3y-1)(3y+1)(3y-1)(3y+1)
d)
(9y2-1)(3y+1)(3y-1)
83.
2x3-128x
a)
2x(x2-64)
b)
2x(x-8)(x+8)
c)
2(x3-64x)
d)
2x(x-8)(x-8)
83.
2x3-128x
a)
2x(x2-64)
b)
2x(x-8)(x+8)
c)
2(x3-64x)
d)
2x(x-8)(x-8)
84.
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
85.
Use the quadratic formula to solve 2x2 + 2x - 12?
a)
-2, 3
b)
2, 3
c)
2, -3
d)
-2, -3
86.
What is the name of the imaginary line that cuts a parabola in half and goes through the vertex?
a)
the middle
b)
axis of symmetry
c)
minimum
d)
standard form
87.
If the graph of a quadratic does not intercept the x-axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
88.
Does the equation open or or down?
Y = -3x2 +7x - 2
Y = -3x2 +7x - 2
a)
up
b)
down
89.
What form is this equation in?
2x2+4x-3=0
2x2+4x-3=0
a)
general form
b)
vertex form
c)
factored form
d)
none of these
90.
Identify the 'b' value: y = 16x2 -8x -24
a)
16
b)
-8
c)
8
d)
-24
91.
Identify the 'a' value: y = 16x2 -8x -24
a)
16
b)
8
c)
-8
d)
-24
92.
.How many zeros does this parabola have?
a)
3
b)
2
c)
0
d)
1
93.
Solve 2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
94.
Solve 8x2 - 6x + 1 = 0
a)
No Solution
b)
0 or 1
c)
-0.5 or -0.25
d)
0.25 or 0.5
95.
Solve 3x2 - 11x + 10
a)
1.7 or 2
b)
1 or 2
c)
1.5 or 2
d)
-1.7 or 2
96.
Identify the 'c' value: y = 16x2 -8x -24
a)
16
b)
-8
c)
24
d)
-24
97.
find x for
2x2-8x-24=0
2x2-8x-24=0
a)
x= 6, -2
b)
x= 2, -6
c)
x= 4, 2
d)
x= 2, 6
98.
Name the x-intercept(s)?
a)
0
b)
4
c)
2
d)
0 and 4
99.
Use the graph to determine the solutions.
a)
-1 and -3
b)
1 and -3
c)
1 and 3
d)
-1 and 3
100.
Solve.
a)
-3, 4
b)
3, 4
c)
-4, -3
d)
-3
101.
Determine the values of
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
*remember right side should =0
a, b, and c for
the quadratic equation:
4x2 – 8x = 3
*remember right side should =0
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
102.
Solve
b2 + b - 56 = 0
b2 + b - 56 = 0
a)
7 & -8
b)
-7 & 8
c)
1.8 & -1.4
d)
2.5 & -0.5
103.
Solve
2x2 + 7x - 15 = 0
2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
104.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
105.
The quadratic equation can be used to solve quadratic equations that cannot be factored.
a)
True
b)
False
106.
Solve using the quadratic formula:
4x2 + 4x + 1 = 0
4x2 + 4x + 1 = 0
a)
x = -½
b)
x = -2
c)
x = 0
107.
Solve Using the Quadratic Formula
x2 + 4x - 40 = -8
x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
108.
2x2-x -3=0
a)
x=-3/2 x=1
b)
x= 3/2 x= -1
c)
x= -3/2 x= -1
d)
x= 3/2 x= 1
109.
What are the zeros (x-intercepts)?
a)
x = 2,-2
b)
x = 2,-2,0
c)
x = 2,0
d)
x = -4,-2,2,0
110.
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)
111.
Determine the y-intercept
f(x) = x3 - 5x2 - 25x + 125
f(x) = x3 - 5x2 - 25x + 125
a)
(0,0)
b)
(0,25)
c)
(0,125)
d)
(0,5)
112.
The polynomial
f(x) = 5x4 + 2x3 + 2x − 7 can have, at most, how many solutions?
f(x) = 5x4 + 2x3 + 2x − 7 can have, at most, how many solutions?
a)
5
b)
4
c)
3
d)
2
113.
How many zeros does the polynomial function
P(x) = 3x4+4x-8 have?
P(x) = 3x4+4x-8 have?
a)
1
b)
2
c)
3
d)
4
114.
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
115.
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
116.
Over the interval (−1, 2), the graph of the polynomial shown could be described as
a)
decreasing
b)
increasing
c)
quadratic
d)
complex
117.
Over the interval (−3, -1), the graph of the polynomial shown could be described as
a)
decreasing
b)
increasing
c)
quadratic
d)
complex
118.
On the polynomial graph shown, 1 is a(an)
a)
absolute maximum
b)
absolute minimum
c)
relative maximum
d)
relative minimum
119.
In the polynomial graph shown,
−4 is a(an)_______.
−4 is a(an)_______.
a)
Absolute maximum
b)
Absolute minimum
c)
Zero
d)
Vertex
120.
Write a cubic polynomial in factored form that has zeros at x = 1, x = -1, and 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)
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