Free Printable Final Exam Review Algebra 2

1.

What Is the end behavior of this graph?

a)

lim f(x)→∞ as x→∞
lim f(x)→−∞ as x→-∞

b)

lim f(x)→-∞ as x→∞
lim f(x)→-∞ as x→-∞

c)

lim f(x)→∞ as x→∞
lim f(x)→∞ as x→-∞

d)

lim f(x)→-∞ as x→∞
lim f(x)→∞ as x→-∞

2.

Is the Graph an even or odd degree polynomials?

a)

Odd

b)

Even

3.

What is the degree of this function?

a)

4

b)

3

c)

2

d)

1

4.

What is the leading coefficient of this function?

a)

1

b)

4

c)

-3

d)

18265603

5.

Identify the degree of the polynomial and the sign of the leading coefficient, using the graph.

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

6.

Simplify :

(x⁵y¹⁰z¹¹ )⁰=

a)

1

b)

0

c)

(xyz)¹

d)

(x⁵y¹⁰z¹¹)¹

7.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

8.

The answer to a division problem is known as the...?

a)

product

b)

sum

c)

difference

d)

quotient

9.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

10.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

11.

Classify by number of terms:
3x² – 8x + 1

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

12.

1 Term

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

13.

Choose all the binomials ( 3 Correct answers)

a)

x + 5

b)

2x - 6y

c)

8x

d)

5x - 9y + 7

e)

76a - 90b²

14.

Choose all the monomials ( 3 correct answers )

a)

5

b)

7xy

c)

8u + 5s

d)

18a

e)

6x + 5y

15.

Put in Standard Form.
12 - 3x³ - 10x - x²

a)

- 3x³ - x² - 10x + 12

b)

3x³ - x² + 10x + 12

c)

12 - 3x³ - 10x - x²It is in Standard Form.

d)

12 - 10x - 3x³ - x²

16.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

17.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

18.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

19.

DOMAIN?

a)

(-∞,∞)

b)

[0,∞)

c)

(-∞,0]

d)

(0,∞)

20.

RANGE?

a)

(-∞,∞)

b)

[0,∞)

c)

(-∞,0]

d)

(0,∞)

21.

Name the parent function.

a)

cube root

b)

square root

c)

quadratic

d)

linear

22.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

23.

What is the first step in finding the equation of the inverse of a function?

a)

get x by itself

b)

switch x and y

c)

solve for y

d)

write the function in inverse function notation

24.

Are these inverse functions?

a)

yes

b)

no

c)

no way to tell

25.

Evaluate

a)

0

b)

1

c)

Cannot be done

d)

None of the above

26.

Evaluate

a)

0

b)

1

c)

10

d)

None of the above

27.

Evaluate

a)

0

b)

1

c)

e

d)

None of the above

28.

a)

8

b)

8x

c)

8x²

d)

8x³

29.

Factor with GCF:

a)

3v²( v²−9v−10)

b)

3( v²−9v−10)

c)

3v( v²−9v−10)

d)

9v( v²−3v−10)

30.

How many x-intercepts does this function have?

a)

1

b)

2

c)

3

d)

4

31.

True or false:

The solution, root, x-intercept, and zero of a problem are the same.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

32.

Given y = 2x⁷+ 3x⁵+... What is the degree and how many solutions?

a)

Degree 7 , 7 solutions

b)

Degree 2 , 3 solutions

c)

Degree 7 , 5 solutions

d)

Degree 5 , 7 solutions

33.

Given y= (x−1)(x−2)(x+3)(x+4) ; What is the degree of this polynomial?

a)

1

b)

2

c)

3

d)

4

34.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

35.

What is the Fundamental Theorem of Algebra?

a)

The degree of the polynomial determines what the x value will be

b)

The degree of the polynomial tells us how many solutions the polynomial will have.

c)

The number of possible rational zeros

d)

States that a complex number and its conjugate are solutions

36.

How many extrema (maxes and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

37.

The domain of a polynomial function is always (-∞, +∞).

a)

True

b)

False

38.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

39.

Given x²+ 9x - 36

The correct factor for -36 is

a)

+12 and - 3

b)

+9 and - 4

c)

-12 and +3

d)

-9 and - 4

40.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

41.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

42.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

43.

What is the term classification of the following polynomial?
x³-7x²+3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

44.

Which is an example of a linear polynomial?

a)

x²-5

b)

6x+4

c)

5x⁵

d)

2x³-9x²

45.

What is the leading coefficient of the following polynomial?
5x²-3x+6

a)

2

b)

-3

c)

5

d)

6

46.

What is the classification of the following polynomial?
x²-8x+10

a)

quadratic binomial

b)

cubic trinomial

c)

linear binomial

d)

quadratic trinomial

47.

Add the following polynomials:
(x³-2x²+3)+(2x³+3x²-1)

a)

3x³-2x²+3x+2

b)

3x³+x²+2

c)

3x³-5x²-2

d)

3x³-x²+1

48.

Subtract the following polynomials:
(3x²-3x+2)-(x²-2x+1)

a)

2x²+x+1

b)

2x²-5x+3

c)

2x²-x+1

d)

4x²-5x+3

49.

What is the GCF in this polynomial?
3x²+6x-18

a)

2

b)

3

c)

6

d)

18

50.

What is the GCF of the following polynomial?
2x³+4x²-12x?

a)

2

b)

4x

c)

x

d)

2x

51.

For which x value is the minimum for the function?

a)

A

b)

B

c)

C

d)

D

52.

What word phrase can you use to represent "5x + 2"?

a)

five times the sum of a number x and two

b)

two times the sum of a number x and five

c)

a number x times the sum of five and two

d)

the sum of five times a number x and two

53.

$\left(\left(2x^5-3x^4\right)^3\right)^0=?$

a)

Not enough information

b)

0

c)

1

d)

6

54.

Question #2

a)

A

b)

B

c)

C

d)

D

55.

What is the slope of the line shown in the graph?

a)

-2

b)

-7/6

c)

-6/7

d)

2

56.

5x − y = 11

2x − 2y = 7

Based on the system of equations above, what is the value of 3x + y?

a)

−2

b)

0

c)

2

d)

4

57.

a)

A

b)

B

c)

C

d)

D

58.

$3x\left(2x\ -5\right)=$

a)

$5x^2-8$

b)

6x - 10

c)

$6x^2-15x$

d)

$6x^2-15$

59.

a)

A

b)

B

c)

C

d)

D

60.

On SAT exam are you penalized for incorrect answers?

a)

Yes

b)

No

61.

Look at the following systems of equation and determine if they have solutions

y = 2x - 5

y = 2x -10

a)

1 solution

b)

2 solution

c)

No solution

d)

Infinitely many solutions

62.

Given the matrix in your calculator RREF screen for x, y and z in order. What is the value of x?

a)

5

b)

6

c)

8

d)

1

63.

If 4x + 6 = 19, what is the value of 4x + 5?

a)

-18

b)

8

c)

13

d)

18

64.

The graph of a polynomial function p(x) is shown above. How many zeros does the graph have

a)

1

b)

2

c)

3

d)

4

65.

Solve 3x + 5 = 8

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

66.

pV = nRT
solve for R

a)

R= pV/nT

b)

R= p/n + V/T

c)

R= pV - nT

d)

R= (pV-n)/T

67.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (3, 1)

d)

One Solution: (1, 3)

68.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (0, 4)

d)

One Solution: (0, 6)

69.

What is the solution to the system of equations graphed below?

a)

No Solution

b)

Infinite Solutions

c)

One Solution: (0, 2)

d)

One Solution: (2, 6)

70.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

71.

How many solutions does the system of equations below have?

a)

No Solution

b)

Infinite Solutions

c)

One Solution

72.

How many solutions does the system of equations below have?

a)

No Solution

b)

Infinite Solutions

c)

One Solution

73.

How many solutions does the system of equations below have?

a)

No Solution

b)

Infinite Solutions

c)

One Solution

74.

A system of equations with one solution will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

75.

A system of equations with infinitely many solutions will have lines that...

a)

are the same

b)

cross in one place

c)

are parallel and never touch

76.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

77.

Solve for x and y
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

78.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, write down the system of equations for this situation.

a)

S + A = 530

3S + 4A = 1740

b)

S + A = 530

4S + 3A = 1740

c)

S + A = 1740

3S + 4A = 530

d)

S + A = 1740

4S + 3A = 530

79.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

a)

1.5x+0.5y=78.5
x+y=87

b)

1.5x+0.5y=78.5
1.5x+0.5y=87

c)

x+y=78.5
1.5x+0.5y=87

d)

x+y=78.5
x+y=87

80.

What are systems of linear equations?

a)

a set of two or more linear equations in the same variables

b)

a polynomial with three terms

c)

set of two or more linear inequalities in the same variables

81.

Solve the system of equations:
x + y + z = 4
x = -2y
z = -3y

a)

(2, -1, 3)

b)

(2, 3, 1)

c)

None of these

d)

(4, 1, -1)

82.

What is your solution if your variables go away and you are left with 0 = 0?

a)

No Solution

b)

All Real Numbers

c)

Infinitely Many Solutions

d)

(x, y, z)

83.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

a)

x + y = 33
y = 2x - 3

b)

x + y = 33
x = 2y - 3

c)

x + y = 33
x = 3 - 2y

d)

x + y = 3
x = 33 - 2y

84.

All of the x values or inputs are called what?

a)

Domain

b)

Range

85.

All of the y values or outputs are called what?

a)

Domain

b)

Range

86.

What is the range?
Remember range is the "y" values (up and down)
And an open circle means it DOES NOT equal that number - use < and >
Only use ≤ and ≥ with a closed circle.

a)

-4 < x ≤ 5

b)

-4 ≤ x < 5

c)

-3 < y < 3

d)

-3 ≤ y ≤ 3

87.

What is the domain?
Remember domain is the "x" values.
And an open circle means it DOES NOT equal that number - use < and >
Only use ≤ and ≥ with a closed circle.

a)

-4 < x ≤ 5

b)

-4 ≤ x < 5

c)

-3 < y < 3

d)

-3 ≤ y ≤ 3

88.

What is the DOMAIN of this graph?
Remember: DOMAIN is the x from left to right.

a)

x < -3

b)

x ≤ -3

c)

x > -3

d)

x ≥ -3

89.

IS THIS GRAPH DISCRETE or CONTINUOUS?

a)

DISCRETE

b)

CONTINUOUS

c)

NEITHER

90.

IS THIS GRAPH DISCRETE or CONTINUOUS?

a)

CONTINUOUS

b)

DISCRETE

c)

NEITHER

91.

What is the range of the function?

a)

-7≤x≤6

b)

-7<x<6

c)

-8<y<2

d)

-8≤y≤2

92.

What is the Range?

a)

y ≥ 6

b)

$-\infty<y\le6$

c)

-10 ≤ y ≤ 6

d)

-10 ≤ x ≤ 6

93.

Which graph is not a function?

a)

b)

c)

d)

94.

What is the test to determine if a graph represents a function?

a)

Horizontal line test

b)

Vertical line test

c)

Heidelberg Uncertainty Test

d)

Obi Wan Kenobi Test

95.

When factoring

3v² - 4v - 7

You will break up the middle term using a pair of factors of

a)

$-21$

b)

$-4$

c)

$-12$

d)

$28$

96.

When factoring

3a² + 4a + 1

You will break up the middle term in this fashion

a)

2a + 2a

b)

Not factorable

c)

3a + 1a

d)

5a - 1a

97.

When factoring: 2x² + x - 6

You will break up the middle term in this fashion

a)

4x - 3x

b)

7x - 6x

c)

6x - 5x

d)

11x - 10x

98.

First thing you do when factoring

5x² - 13x + 6

is

a)

Multiply 5 and -13

b)

Multiply 6 and -13

c)

Multiply 5 and 6

d)

Multiply 5, 6 and -13

99.

Factor: ( Hint: GCF )

17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

x(17y)

100.

Factor:

5x³- 7x²

^{Hint: Try GCF}

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Cannot be factored

101.

What is the greatest number of solutions that a Quadratic Equation can have?

Remember a quadratic equation is of degree 2.

a)

0

b)

1

c)

2

d)

3

102.

A system of equations with one solution will have lines that have ...

a)

same slope and same y intercept

b)

same slope and different y intercept

c)

different slopes

d)

same slopes

103.

Which one is the correct way to write the answer to this long division?

a)

$x^2+x+9+\frac{21}{\left(x-3\right)}$

b)

$\frac{x^2+x+9}{\left(x-3\right)}+\frac{21}{\left(x-3\right)}$

c)

$x^2+x+9+21$

d)

$x^2+x+9+\frac{21}{\left(x^2+x+9\right)}$

104.

What would be the first thing you will write on the quotient position?

a)

$4t^2$

b)

$t^3$

c)

$4t$

d)

$4$

105.

The place holder term in the dividend is

a)

$8t^3$

b)

$0t^2$

c)

$14t$

d)

$8$

106.

What is the equation of the graph below?

a)

f(x) = I x I + 1

b)

f(x) = I x I - 1

c)

f(x) = -I x I + 1

d)

f(x) = -I x I - 1

107.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x + 2 I +2

c)

f(x) = I x - 2 I +2

d)

f(x) = I x - 2 I

108.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

109.

Solve | 2x - 1 | = -4

a)

x = ¹/₂ and x = -4

b)

No Solution

c)

x = ^-3/₂ and x = ⁵/₂

d)

x = ³/₂ and x = ^-5/₂

110.

Solve | 3x - 6 | - 9 = -3

a)

No Solution

b)

x = 0 or x = 4

c)

x = 2 or x = -2

d)

x = -4 or x = 4

111.

What's a way to define absolute value?

a)

The value of a number

b)

The opposite of a number

c)

The distance of a number from zero

d)

The multiplicative inverse of a number

112.

What is the absolute value of -4?

a)

-4

b)

4

c)

0

113.

What is the absolute value of 3?

a)

-3

b)

3

c)

0

114.

What is the absolute value of $\left|-6\right|$ ?

a)

6

b)

-6

c)

0

115.

Compare. >, <, =

$\left|196\right|$ ______ $\left|-196\right|$

a)

>

b)

<

c)

=

116.

Absolute value tells the distance of a positive or negative number from 0.

a)

True

b)

False

c)

do not answer

d)

do not answer

117.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

118.

| x + 3 | ≤ 2

a)

No Solution

b)

x ≤ -1

c)

-5 ≤ x and x ≤ -1

d)

1 ≤ x and x ≤ 5

119.

The average temperature in Las Vegas in July is 110 degrees. If the temperature can vary up to 10 degrees, which equation represents this situation?

a)

| x - 10 | < 110

b)

| 110 - x | < 10

c)

| x - 110 | < 10

d)

| 10 - x | < 110

Final Exam Review Algebra 2

Total questions: 119

Worksheet time: 10hrs 6mins

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