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ExamReviewM2 PreCalc Polynomials Functions Transformations

Total questions: 100

Worksheet time: 25hrs 0mins

Name
Class
Date
1.
Find the difference. 
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
2.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
3.
Find the product
(3x – 1)(x + 5) 
a)
3x2 + 4x + 5
b)
3x2 + 4x - 5
c)
3x2 + 14x + 5
d)
3x2 + 14x - 5
4.
Find the product
(3x + 2)(2x + 4)
a)
6x2 + 16x + 8
b)
5x2 +11x + 6
c)
5x2 + 16x + 6
d)
6x2 + 11x + 8
5.
Which is an example of a linear polynomial?
a)
x²-5
b)
6x+4
c)
5x⁵
d)
2x³-9x²
6.
Which is an example of a cubic binomial?
a)
x³+5
b)
x²+3
c)
x²+5x-6
d)
5x³
7.
What is the GCF in this polynomial?
3x²+6x-18
a)
2
b)
3
c)
6
d)
18
8.
What is the GCF of the following polynomial?
4x²+6x-20
a)
1
b)
2
c)
4
d)
6
9.
(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
10.
Which polynomial is written in standard form?
a)
8x - 11x2
b)
4x3 + 7x - 9
c)
12 + 4x
d)
13x + 7x2 - 9x3 + 12
11.
What is the degree of the polynomial 3x4 + 2x2 + 5x ?
a)
1
b)
2
c)
3
d)
4
12.
Name and Classify the Polynomial:
x² − 4
a)
quadratic binomial
b)
quadratic monomial
c)
linear binomial
d)
linear monomial
13.
Factor completely:
16x2 - 20xy
a)
4 (4x2 - 5xy)
b)
4x (4x - 5y)
c)
4x2 (4 - 5y)
d)
2(duck)
14.
Factor completely:
4x2y - 12xy + 5y
a)
(2xy - 1) (2x - 5)
b)
prime
c)
y (2x - 1) (2x - 5)
d)
4 (xy - 5) (x - 1)
15.
Factor completely:
y2 - 7y + 12
a)
(y - 3) (y - 4)
b)
(y + 3) (y - 4)
c)
(y + 3) (y + 4)
d)
(y - 2) (y - 6)
16.
Factor completely:
2x2 + 7x + 6
a)
(2x - 3) (x - 2)
b)
(2x + 3) (x + 2)
c)
(x + 3) (2x + 2)
d)
prime
17.
Factor completely:
49p2 + 84p + 36
a)
(7p - 6)(7p - 6)
b)
(7p - 6)2
c)
(7p + 6)(7p - 6)
d)
(7p + 6)(7p + 6)
18.

Name the expression.

a)

monomial

b)

binomial

c)

trinomial

19.
Divide: 
(6x + 9) / (3x)
a)
2 + 9/3x
b)
2 + 9
c)
2 + 9/3
d)
2
20.
Divide:
(24x + 4) / (6x+1)
a)
4
b)
4 + 4/6x+1
c)
4x + 0
d)
4x
21.
Simplify
(p − 8)2

 Hint: (p − 8)2 = (p − 8)(p − 8)
a)
p 2 − 16p − 64 
b)
p 2 + 16p + 64 
c)
p 2 − 16p − 8
d)
p 2 − 16p + 64 
22.
f(x)=(x+4)(x-3)(x-2)
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
23.
How many zeros does the polynomial function
 P(x) = 3x4+4x-8 have?
a)
1
b)
2
c)
3
d)
4
24.
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
25.
The polynomial
f(x) = 5x4 + 2x3 + 2x − 7 can have, at most, how many solutions?
a)
5
b)
4
c)
3
d)
2
26.
a)
The function has an Even degree
b)
The function has a Negative coefficient
c)
The function has an Odd degree
d)
The function has 3 real zeros
27.
Determine the y-intercept 
f(x) = x3 - 5x2 - 25x + 125
a)
(0,0)
b)
(0,25)
c)
(0,125)
d)
(0,5)
28.
Over the interval (−1, 2), the graph of the polynomial shown could be described as
a)
decreasing
b)
increasing
c)
quadratic
d)
complex
29.
w3 + 3w
a)
3w(1)
b)
w(w2 + 3)
c)
w3(w + 3)
30.
What is the GCF? 12x+8
a)
12
b)
8
c)
4
d)
x
31.

Find a zero of the polynomial p(x) = 2x + 1.

a)

1/2

b)

0

c)

-1/2

d)

none of these

32.

Consider the polynomial p(x) = 5x3 – 2x2 + 3 x – 2.

p(1)=

a)

-4

b)

4

c)

3

d)

none of these

33.

Find the remainder obtained on dividing p(x) = x3 + 1 by x + 1.

a)

0

b)

1

c)

2

d)

3

34.

Check whether the polynomial

q(t) = 4t3 + 4t 2 – t – 1 is a multiple of

2t + 1.

a)

no

b)

cannot be determined

c)

yes

d)

none of these

35.

1.

Find the remainder when

x3 – ax2 + 6 x – a is divided by x – a.

a)

a

b)

2a

c)

-5a

d)

5a

36.
Which equation below is a quadratic function translated up 5 units?
a)
y = x2 + 5
b)
y = (x + 5)2
c)
y = 5x2
d)
y = -x2 - 5
37.
Which equation below is a quadratic function translated left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
38.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Horizontal right 5, vertical down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch of 2, and horizontal right 5

c)

Reflected over the x-axis, vertical stretch of -2, and horizontal left 5

d)

Horizontal right 5, Vertical down 2

39.
What is the equation of this graph?
a)
f(x) = (x + 2)2 - 3
b)
f(x) = (x - 2)2 - 3
c)
f(x) = |x + 2| - 3
d)
f(x) = |x - 2| - 3
40.
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
41.
What is the RANGE?
a)
(-∞,∞)
b)
[0,∞)
c)
(-∞,0]
d)
[-∞,∞]
42.
DOMAIN?
a)
(-∞,∞)
b)
[0,∞)
c)
(-∞,0]
d)
-2, 2
43.
Identify the transformation from the graph of f(x)=x2 to the graph g(x)= -(x+5)2 
a)
shifted up five units
reflection in x-axis
b)
shifted down five units
reflection in x-axis
c)
shifted left 5 units
reflection x-axis
d)
shifted right 5 units
reflection x-axis
44.
Name the parent function.
a)
linear
b)
quadratic
c)
cube root
d)
cubic
45.
What type of function is shown?
a)
absolute value
b)
quadratic
c)
linear
d)
exponential
46.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
47.
Which parent function matches the graph?
a)
y = |x|
b)
y = x
c)
y = x2
d)
y = 2x
48.
What type of function is shown?
a)
cube root
b)
square root
c)
logarithm
d)
exponential
49.
Describe the transformation
a)
left 2 up 5
b)
right 2 up 5
c)
left 2 down 5
d)
right 2 down 5
50.

If f(x) = 3x-1 and g(x) = x2+2,

what is (f ° g)(x) ?

a)

3x2 +5

b)

x2 +1

c)

3x2 +1

d)

3x2 +6

51.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x2-1

d)

5x2-5

52.

If  f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find  g(f(−1))g\left(f\left(-1\right)\right)  

a)

2

b)

15

c)

7

d)

-9

53.

If  f(x)=2xf\left(x\right)=2x   and  g(x)=2x2−1g\left(x\right)=2x^2-1   find  f(g(3))f\left(g\left(3\right)\right)  

a)

34

b)

71

c)

35

d)

142

54.

Factor completely.

x2 - 144

a)

( x - 12 ) 2

b)

( x - 12 ) ( x - 12 )

c)

( x + 12 ) ( x + 12 )

d)

( x + 12 ) ( x - 12 )

55.

Factor completely.

121x2 - 49

a)

( 11x - 7 ) 2

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

56.

Factor completely.

64x2 - 49y2

a)

( 8x + 7 ) ( 8x - 7 )

b)

( 8x - 7y ) ( 8x - 7y )

c)

( 8x + 7y ) ( 8x - 7y )

d)

( 8x - 7y )2

57.
Factor:   x3 + 1
a)
(x + 1)3
b)
(x+1)(x2 - x + 1)
c)
(x - 1) (x2 + x - 1)
d)
(x + 1)(x2 - 2x + 1)
58.
Fully Factor the Following
8x3-27
a)
(2x+3)(4x2-6x+9)
b)
(2x-3)(4x2+6x+9)
c)
(2x-3)(4x2+6x-9)
d)
(2x-3)(2x2+6x+9)
59.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

60.

We can't factor using difference of two square this

49x2 + 4y2. Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

61.

What is the equation of the axis of symmetry?

a)

y = 4

b)

y = -4

c)

x = 4

d)

x = -4

62.
How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
63.
What is the arrow pointing at? How can you use this value to determine the minimum/maximum values?
a)
The arrow is pointing at the y-intercept. 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
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 y value is equivalent to the minimum/maximum
64.
Determine the values of
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
65.
What's the axis of symmetry of y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
66.

In the equation y= ax2 + bx + c , if a > 0, then...

a)

the graph of the parabola will have a maximum.

b)

the graph of the parabola will open down

c)

the graph of the parabola will open up

d)

the vertex will be (0, 0).

67.

What are the roots of the following quadratic?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

68.

Determine the vertex for the following quadratic: y = x2 - 9x + 20

a)

(2,3)

b)

(4,5)

c)

(4.5, -.25)

d)

(-4.5, .25)

69.

Comparing the functions, which is the most narrow?

a)

f(x)=3x2

b)

g(x)= -2x2

c)

h(x)=0.5x2

d)

a(x)=12x2

70.

Changing the c value of a standard form quadratic (y=ax2+bx+c) transforms the graph how?

a)

Up and down

b)

Left or right

c)

Reflects over x axis

d)

Up only

71.
The highest or lowest point on a quadratic is called the...
a)
Max
b)
Vertex
c)
Axis of Symmetry
d)
Intercept
72.
The line that goes through the vertex of a parabola is called the...
a)
Vertex
b)
Axis of Symmetry
c)
x-intercept
d)
y-intercept
73.
A point on a graph that has the coordinates (0,___) is called a...
a)
x-intercept
b)
vertex
c)
maximum
d)
y-intercept
74.
The point (4, -3) is a...
a)
Maximum
b)
Minimum
75.
How many x-intercepts does this quadratic have?
a)
0
b)
1
c)
2
d)
infinitely many
76.
What is the equation of the axis of symmetry of this parabola?
a)
2
b)
0
c)
x=2
d)
x=0
77.

All possible x-values

a)

Domain

b)

Range

c)

Parabola

d)

Vertex

78.
The discriminant is
a)
aX2  + bX  +  c
b)
b - 4ac
c)
b2 - 4ac
d)
b2 + 4ac
79.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

80.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

81.
A function has a discriminant of 25.
______________
How many solutions does it have?
a)
0
b)
1
c)
2
d)
5
82.
In the equation
y = x2 +5x +7, match each leading coefficient with its correct letter 
a)
a=0, b=5, c=7
b)
a=1, b=5, c=7
c)
a=7, b=5, c=1
83.
Determine the value of the discriminant and name the nature of the roots for the following:
x2 + 7x + 13
Remember:  b2 - 4ac
a)
400, 2 real root 
b)
0, 1 real root with a multiplicity of 2
c)
-400, 2 imaginary roots
d)
-3, 2 imaginary roots
84.
A function has a discriminant of -3.
______________
How many x-intercepts does it have?
a)
0
b)
1
c)
2
d)
3
85.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
86.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
87.
What  are the solutions of this graph?
a)
-2 and 3
b)
-1/2 and -6
c)
-2 and -6
d)
3 and -6
88.
a)
y =  _(x + 2)(x - 1)2
b)
y = -(x - 2)(x + 1)2
c)
y = (x - 2)(x + 1)2
d)
y = -x3
89.

a)

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

b)

y = x(x - 3)2 (x+2)

c)

y = x(x + 3)2 (x - 2)

d)

y = -x(x + 3)2 (x - 2)

90.

Which function is graphed?

a)

(x - 4)(x + 2)(x - 8)=y

b)

(x - 4)(x - 2)(x + 8)=y

c)

(x - 4)(x + 2)(x + 8)=y

d)

(x + 4)(x + 2)(x + 8)=y

91.
Match the graph to the function
a)
f(x) = -x⁴-x³+5x²-6
b)
f(x) = x⁴+3x²-3x+1
c)
f(x) = -x³+2x²-x-6
d)
f(x) = x⁴+x³+5x²-6
92.

Which of the following graphs represents the quadratic function above?

a)
b)
c)
d)
93.
Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root. 
a)
-3+5i
b)
-3-5i
c)
-5i
d)
3-5i
94.
Use the Complex Conjugate Root Theorem to state another complex solution. Given that -2-5i is a root. 
a)
-2-5i
b)
-2+5i
c)
2+5i
d)
5i
95.
Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root. 
a)
7i
b)
-7i+1
c)
1-7i
d)
1+7i
96.
What is the degree of the following polynomial that has 4 real roots and 2 complex roots?
a)
4
b)
2
c)
8
d)
6
97.
All imaginary roots comes in pairs.
a)
True
b)
False
98.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

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

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

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

99.
Factor: 8x3 - 1
a)
(2x - 1)(4x2 + 2x + 1)
b)
(2x + 1)(4x2 - 2x + 1)
c)
(2x - 1)(4x2 - 2x - 1)
d)
(2x + 1)(4x2 +2x + 1)
100.

Write in factored form using the following roots.


7, -2i

a)

(x-7)(x-2i)

b)

(x-7)(x+2i)(x-2i)

c)

(x-7)(x+2i)

d)

(x-7)(x+7)(x-2i)

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