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Algebra 2 Course Review Part I

Total questions: 73

Worksheet time: 6hrs 5mins

Name
Class
Date
1.

Factor

10x2 + 15x - 5

a)

25(10x3 + 45x - 15)

b)

5(2x3 + 3x2 - x)

c)

x(10x3 + 15x - 5)

d)

5(2x2 + 3x - 1)

2.
Factor:
x2 + 7x - 30
a)
(x + 10)(x - 7)
b)
(x - 10)(x + 3)
c)
(x + 10)(x + 3)
d)
(x + 10)(x - 3)
3.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
4.
Find the 32nd term of this sequence.
34, 37, 40, 43, ...
a)
32
b)
64
c)
127
d)
356
5.
Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)
a)
an = 4n + 29
b)
an = -4n + 25
c)
an = -4n + 29
d)
an = 4n + 25
6.
Find the common ratio: 4, -16, 64, -256, ...
a)
r = -4
b)
r = 2
c)
r = -2
d)
r = 4
7.
Find the common ratio: 4, -16, 64, -256, ...
a)
r = -4
b)
r = 2
c)
r = -2
d)
r = 4
8.
What is the vertex of the graph?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
9.
What is the arrow pointing at? How can you use this value?
a)
The arrow is pointing at the y-intercept. The x-value is the axis of symmetry and the y-value of this point is equivalent to the maximum/minimum 
b)
The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum and the y-value is the axis of symmetry
c)
The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum
d)
The arrow is pointing at the vertex. The x-value is the axis of symmetry and the y-value is equivalent to the minimum/maximum
10.

Solve by factoring and setting equal to zero.

a)

{-3, 4}

b)

{3, 4}

c)

{-4, -3}

d)

{-3}

11.
What is f(1)?
a)
1
b)
5
c)
0
d)
4
12.

Where is the AoS (Axis of Symmetry) for

y = 4x2 + 4

a)

x = 0

b)

x = 1

c)

x = -1

d)

x = 4

13.

-6i + 3i

a)

3i

b)

-3i

c)

-2i

d)

-3i2

14.

Which of the following is equivalent to

(3 - 5i) - (6 + 2i)

a)

-3 - 7i

b)

-3 - 3i

c)

3 - 3i

d)

9 - 7i

15.

Which of the following is equivalent to

(5 - 3i) + (-6 + 2i)?

a)

-1 - 5i

b)

-1 - i

c)

11 - i

d)

-30 - 6i

16.
A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t2 + 256.  How many seconds did it take the raft to hit the water? 
a)
-4
b)
2
c)
4
d)
8
17.
What is the end behavior of the polynomial function?
a)
Up / Up
b)
Up / Down
c)
Down / Down
d)
Down / Up
18.
Classify the polynomial by number of terms:
-10x5
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
19.

Classify by number of terms:

4r6 - 3r2 - 8r4

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

20.
Classify by number of terms:
3x3 – 6x
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
21.

Classify by degree of polynomial:

-2x2 – x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

22.
Given the polynomial:
9x7 + 3x6 - 5 + x2
What is the constant?
a)
9
b)
3
c)
5
d)
-5
23.
Which of the following is a binomial?
a)
x3
b)
x + 3
c)
x2 + 3x + 1
d)
3x
24.
If the leading coefficient of a polynomial is negative and the degree is even, then end behavior will be ____ and ____.
a)
Up and Up
b)
Down and Down
c)
Up and Down
d)
Down and Up
25.
If the leading coefficient of a polynomial is negative and the degree is odd, then end behavior will be ____ and ____.
a)
Up and Up
b)
Down and Down
c)
Up and Down
d)
Down and Up
26.
If the leading coefficient of a polynomial is positive and the degree is odd, then end behavior will be ____ and ____.
a)
Up and Up
b)
Down and Down
c)
Up and Down
d)
Down and Up
27.
What is the degree of the polynomial:
7x3 – 8x2 + 9
a)
5
b)
2
c)
6
d)
3
28.
What is the standard form of the polynomial,
 9x2 + 5x + 27 + 2x3
a)
27 + 5x + 9x2 + 2x3
b)
9x2 + 5x + 2x3 + 27
c)
9x2 + 5x + 27 + 2x3
d)
2x3 + 9x2 + 5x + 27
29.
Write a polynomial in factor 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)
30.
What are the solutions for the polynomial x3 + 4x2 = 12x
a)
x = 1, x = 4, and          x = 12
b)
x = 0, x = 1, and         x = 4
c)
x = 0 and x = 2
d)
x = 0, x = 2 and          x = -6
31.
Write a polynomial with the given zeros
x = 1, -1, 2
a)
x3 - 2x2 - x + 2
b)
x3 + 2x2 + x - 2
c)
x3 - 2x2 + x + 2
d)
x3 - 2x2 - x - 2
32.
What is the degree of the polynomial?
y = 3x2 - 7x4 + 9 - x4
a)
constant
b)
linear
c)
cubic
d)
quartic
33.
Using your calculator what is the relative maximum of the polynomial
y = x4 - 4x -1
a)
(1, -4)
b)
too many to find!
c)
none
d)
(-4, 1)
34.
Solve
x2 + 49 = 0
a)
-7
b)
-7
c)
7i
d)
±7i
35.
Simplify
3i - (4 + 7i)
a)
-4 + 10i
b)
21 - 12i
c)
4 - 10i
d)
-4 - 4i
36.
What is the possible degree of the polynomial?
a)
2
b)
3
c)
4
d)
5
37.

Given the sequence:

125, 25, 5, ....

Write the explicit rule:

a)

t(n) = 125(5)(n)

b)

t(n) = 625(1/5)(n)

c)

t(n) = 625(5)(n)

d)

t(n) = 125 + 5n

38.
Given
an = 3(2)(n-1),      
what is the 14th term?
a)
14
b)
24, 576
c)
49,152
d)
3,188,646
39.
Which quadratic function is represented by the graph?
a)
y = 2(x - 4)2 + 5
b)
y = 2(x + 4)2 + 5
c)
y = -2(x - 4)2 + 5
d)
y = -2(x + 4)2 + 5
40.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
41.

Solve by factoring:

3x2 + 5x + 2 = 0

a)

x = -2/3 and x = -1

b)

x = -3/2 and x = -1

c)

x = 2/3 and x = 1

d)

x = 2/3 and x = -1

42.
Identify the common difference.
97, 86, 75, 64, ...
a)
8
b)
11
c)
-11
d)
-8
43.
Solve Using the Quadratic Formula
 x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
44.
Answer.
a)
A
b)
B
c)
C
d)
D
45.
What is this formula?
a)
This is the speed of light formula.
b)
This is the quadratic formula.
c)
This is the zero product property.
d)
This is scary.
46.
If the blue graph is
f(x) = x2 
the red must be...
a)
g(x) = (x + 3)2
b)
g(x) = (x - 3)2
c)
g(x) = x2 + 3
d)
g(x) = x2 - 2
47.

Given the equation for this parabola:

y= - (x-4)2 - 3,

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

c)

Not enough information

48.
Which set of values is a function?
a)
(9,5) (10,5) (9,-5) (10,-5)
b)
(3,4) (4,-3) (7,4) (3, 8)
c)
(6,-5) (7, -3) (8, -1) (9, 1)
d)
(2, -2) (5, 9) (5, -7) (1, 4)
49.

How did we transform from y = x2 to

y = - 3x2

a)

reflection in x-axis and vertical shift down

b)

reflection x-axis and vertical stretch

c)

horizontal stretch

d)

reflection x-axis and vertical compression

50.
Divide the polynomial by the monomial.
a)
2x8-8x2-28x
b)
2x8-2x2-7x
c)
8x7-8x-28x
d)
2x7 -2x -7
51.
Find the difference.
(7p + 4p3 - 8) - (-3p2 + 2 - 9p)
a)
-3p2 + 4p3 -15 + 9
b)
3p3 + 4p2 - p + 3
c)
4p3 + 3p2 +16p -10
d)
4p3 +3p2 + 16p + 10
52.
What is the quotient when (10n2 - 37n - 12) is divided by (n - 4)?
a)
(10n - 3)
b)
(3n - 10)
c)
(10n + 3)
d)
(3n + 10)
53.

if f(x) = 3x2 -9x -20, find the value of f(5) using synthetic division or remainder theorem.

a)

0

b)

10

c)

15

d)

-7

54.
if f(x) = x3+8x+24, then find f(-2) using synthetic division.
a)
12
b)
8
c)
0
d)
-6
55.

How does the parabola open? y = 4x - x2 - 1

a)

up

b)

down

c)

left

d)

right

56.

In the equation f(x)=1/2(x + 9)2 - 1, what happens to the parabola?

a)

Reflect, horizontal compress by 1/2, left 9, down 1

b)

Vertical compress by 1/2, left 9, down 1

c)

Horizontal Compress by 1/2, right 9, down 1

d)

Vertical Stretch by 1/2, left 9, down 1

57.
Evaluate (9 + 3i) (9 - 3i). 
a)
81 -9i
b)
90
c)
81 + 27i -9i2
d)
81i - 9
58.
The product of (3 -2i) and (7+6i) is
a)
21-12i
b)
9 + 4i
c)
33 + 4i
d)
21 + 16i
59.
 The function below represents the flight of a ball being thrown by a girl who is standing on a box.  What is the maximum height of the ball?
y = -1/2x2 + 2x + 2?
a)
2 feet
b)
About 5 feet
c)
0 feet
d)
4 feet
60.
The vertex is... 
a)
The highest point or the lowest point of the parabola 
b)
The imaginary line that divides the parabola in half 
c)
The point where the graph crosses the x-axis
d)
The point where the graph crosses the y-axis
61.

Simplify.

(5 - i)(5 + i)

a)

26

b)

24

c)

25+i2

d)

25-i2

62.
Simplify
(3 + i)(1 - 4i)
a)
7 - 11i
b)
3 - 4i
c)
3 - 11i - 4i2
d)
2 - 3i
63.
Which of the following is not the same as "solution"?
a)
x-intercept
b)
roots
c)
zeros
d)
y-intercept
64.

What is the y-intercept of the equation

y = 2x2 + 8x + 3

a)

(0,3)

b)

(3,0)

c)

(0,2)

d)

y=8

65.

f(n)=2n+1

g(n)=3n

Find f(n) + g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

66.

f(n)=x2+1

g(n)=2x-5

Find f(n) - g(n)

a)

x2-2x+6

b)

-x2+2x+4

c)

-x2-2x-6

d)

x2-2x-4

67.
Given
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
68.
Given a quadratic model.  Find the height of the ball when it traveled a distance of 10 feet.
a)
12.8 ft
b)
13.3 ft
c)
11.1 ft
d)
17 ft
69.

f(x) = 4x+8
g(x) = x+3

 Find f(x)⋅g(x)Find\ f\left(x\right)\cdot g\left(x\right)  

a)

4x2+24

b)

4x2+20x+24

c)

4x2+12x+24

d)

4x2+4x+24

70.

Find the remainder:

 (2x3−5x−7)x+2\frac{(2x^3-5x-7)}{x+2}  

a)

-9

b)

11

c)

-13

d)

-1

71.

True or False.
x = 5 is a solution for

 f(x) = x3−5x2f\left(x\right)\ =\ x^3-5x^2  ?

a)

TRUE

b)

FALSE

72.

Is x = 1 a solution of

f(x)= x3 + 7x2 - x - 5?

a)

No, x=1 is not a solution. There is a remainder.

b)

No, x=1 is a solution. The remainder is zero.

c)

Yes, x=1 is not a solution. There is a remainder.

d)

Yes, x=1 is a solution. The remainder is zero.

73.
Let f(x) = 4x2 - 33x - 27.  
Is x = 9 a zero of the function?
a)
yes
b)
no

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