Free Printable Practice 2nd Semester Exam Algebra 2

1.

Graph y = (x+4)^2 + 3

2.

Graph

y = -x^2

3.

Graph

y = (x+5)(x-1)

4.

Graph

f(x) = x^2 + 10x + 21

5.

graph

y = (x-2)^2+5

6.

graph

f(x) = (-2x+6)(x+1)

7.

Graph

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

8.

Plot the solutions (2 points) to the system

y = -x - 2

y = x^2 - 5x - 2

9.

Factor Completely: 5n² - 6n - 27

a)

(5n + 3)(n-9)

b)

(5n - 3)(n + 9)

c)

(5n + 9)(n - 3)

d)

(5n - 9)(n + 3)

10.

Factor
2c² + 4c - 84

a)

(c-6)(2c+14)

b)

(c+7)(2x-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

11.

Factor Completely: 3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

12.

Factor
r² - 12r + 27

a)

(r - 3)(r + 9)

b)

(r + 3) (r + 9)

c)

(r - 3) (r - 9)

d)

(r + 3) (r - 9)

13.

Factor Completely: 9x² - 49

a)

(3x + 7)(3x + 7)

b)

(3x + 7)(3x - 7)

c)

(3x - 7)(3x - 7)

d)

Not factorable

14.

Find the expression equivalent
to (x-1)(x-9)

a)

x²+9

b)

x²-10x+9

c)

x²-10x-9

d)

x²+10x+9

15.

Factor out the GCF:
45ab²-20ab

a)

5ab(7b-4)

b)

20ab(3b-1)

c)

5ab²(7a-4)

d)

ab(45b-20)

16.

Find the factors of:
x²-12x-45

a)

(x-10)(x-2)

b)

(x-9)(x+5)

c)

(x-15)(x+3)

d)

(x-6)(x-6)

17.

Find the factors of:
x²-25

a)

(x-25)(x+25)

b)

(x+5)(x-5)

c)

(x-12)(x+2)

d)

(x²-5)(x²+5)

18.

(x + 5)²

a)

x² + 25

b)

x² + 10x + 25

c)

x² + 10 x + 10

d)

x² + 10

19.

Which of the following is the correct set up for the Box Method when multiply (x + 3) (2x - 4) _{(click on the question to see the image in the background)}

a)

A

b)

B

c)

C

d)

D

20.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

21.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

22.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

23.

Explain the transformation of this graph when compared with y = x²:

y= - (x - 1)²+ 11

a)

right 1 , up 11

b)

vertically reflected, right 1, down 11

c)

reflected, right 1, up 11

d)

left 1, up 11

24.

$f\left(x\right)=-\left(x-4\right)^2+1$ Choose the correct graph for the given equation.

a)

b)

c)

d)

25.

Which is the graph of

$y=\left(x-3\right)\left(x+5\right)$

a)

b)

c)

d)

26.

What is the axis of symmetry?

$y=5\left(x+10\right)\left(x-6\right)$

(a)

27.

What is the domain of the function y = x² + 3?

a)

All Real Numbers

b)

x>3

c)

x<3

d)

It is impossible to determine.

28.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

29.

Which way does the graph move if the equation looks like y = (x - 3)²?

a)

Graph moves UP 3 units

b)

Graph moves to the RIGHT 3 units

c)

Graph moves DOWN 3 units

d)

Graph moves to the LEFT 3 units

30.

Which way does the graph move if the equation looks like y = (x + 4)² ?

a)

Graph moves UP 4 units

b)

Graph moves to the RIGHT 4 units

c)

Graph moves DOWN 4 units

d)

Graph moves to the LEFT 4 units

31.

When you subtract a constant from y=x²what happens to the graph? Eg y = x² - 2

a)

Graph moves UP

b)

Graph moves to the RIGHT

c)

Graph moves DOWN

d)

Graph moves to the LEFT

32.

State the turning point (vertex) for the equation:
y = -(x + 1)²+ 4

a)

(1, -4)

b)

(-1, 4)

c)

(-4, 1)

d)

(4, -1)

33.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

34.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

35.

If y = x² - 6x + 8, will it open up or down?

a)

Up

b)

Down

c)

To the right

d)

To the left

36.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

37.

Which letter in a quadratic formula represents the y-intercept?

a)

a

b)

b

c)

c

38.

Name the vertex.

a)

(-2, 6)

b)

(2, 6)

c)

(-2, -6)

d)

7

39.

Determine the interval in which this function is INCREASING.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(∞, -3)

d)

(-∞, -4)

40.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

41.

Determine the interval in which this function is DECREASING.

a)

(-∞, 2)

b)

(2, ∞)

c)

(2, -∞)

d)

(-∞, 1)

42.

Determine the interval of this function's RANGE.

a)

(-4, ∞)

b)

(-3, ∞)

c)

No solution

d)

(-∞, -4)

43.

Find the zeros.

a)

0 and 4

b)

0 and -4

c)

0

d)

-4

44.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing.

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

45.

What are the solutions to this equation? (x-3)(x+2)=0

a)

x=3,-2

b)

x=-3,2

c)

x=2,3

d)

x=3,2

46.

Solve using any method.

x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

47.

Solve the equation using any method:

4x²+2x - 6 = 0

a)

x = 1 & -1.5

b)

x = -1 & 1.5

c)

x = (-2 ±√92)/8

d)

x = (-2 ± √100)/8

48.

Solve for x:

(x + 6)²= 49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

49.

Determine how many roots:

a)

One Solution

b)

Two Solutions

c)

No Solutions

d)

Infinitely Many Solutions

50.

Solve:
x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = -7, x = 1

51.

$The\ solutions\ of\ 2x^2-8x\ =\ 0\ are$

a)

$-2\ and\ \ 2$

b)

$0,\ -2,\ and\ \ 2$

c)

$0\ and\ -4$

d)

$0\ and\ 4$

52.

What is this formula?

a)

Pythagorean Formula

b)

Quadratic Formula

c)

Distance Formula

d)

Correlation Formula

53.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

54.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

55.

What is/are the solution(s) to

$3x^2-1=74$ ?

Show your work on paper!

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

56.

Solve by the Extraction of Roots method: (x - 2) ² = 49

Show your work on paper!

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

57.

Find the roots of the quadratic equation $4x^2-36=0$

Show your work on paper!

a)

x=-9+√6 & x=-9-√6

b)

x=3 & x=-3

c)

x=-6 & x=-12

d)

so solution

58.

Simplify $\sqrt{54}$

a)

$3\sqrt{6}$ or $-3\sqrt{6}$

b)

$3\sqrt{6}$ only

c)

$6\sqrt{3}$ only

d)

$6\sqrt{3}$ or $-6\sqrt{3}$

59.

$\frac{1}{3}x^2=48$

a)

16 or -16

b)

4 or -4

c)

12 or -12

d)

$4\sqrt{3}\$ or $-4\sqrt{3}$

60.

Use the square root technique to find the TWO solutions to the equation

(2x - 1)² = 49

a)

25 or -24

b)

-7 or 7

c)

-4 or 3

d)

-3 or 4

61.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

62.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

63.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

64.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

65.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

66.

√-36

a)

6

b)

-6

c)

-6i

d)

6i

67.

Simplify.

a)

b)

c)

d)

68.

Simplify using the imaginary number $i$
$\sqrt{-20}$

a)

$10i$

b)

$-10i$

c)

$2i\sqrt{5}$

d)

$-i\sqrt{20}$

69.

Find the solutions to the equation:

2x² +23 = 5

a)

$x=3i$

b)

$x=\pm3i$

c)

$x=3$

d)

$x=\pm3$

70.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

71.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

72.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

73.

Classify the polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial.

$f\left(x\right)=9x^2-8+0.18x-9x^3$

a)

Cubic
Leading Term: $-9x^3$
Leading Coefficient: $-9$
Degree: $3$

b)

Constant
Leading Term: $-8$
Leading Coefficient: $-8$
Degree: $1$

c)

Cubic
Leading Term: $x^3$
Leading Coefficient: $-9$
Degree: $3$

d)

Quadratic
Leading Term: $9x^2$
Leading Coefficient: $9$
Degree: $2$

74.

Find the correct end behavior diagram for the given polynomial function.

$f\left(x\right)=-x^5-3x^3-2x+8$

a)

b)

c)

d)

75.

Find the correct end behavior diagram for the given polynomial function.

$f\left(x\right)=-x^6+9x^5-x^2-2x+3$

a)

b)

c)

d)

76.

Use the leading-term test to match the function with the correct graph.

$f\left(x\right)=x^5-x^4+x^3+6$

a)

b)

c)

d)

77.

What is the leading coefficient of the polynomial function $f\left(x\right)=2x\ +x^3+4$ ?

a)

1

b)

2

c)

3

d)

4

78.

What is the degree of the polynomial function $f\left(x\right)=6x^4+2x^3+x^2-x+4$ ?

a)

6th

b)

4th

c)

3rd

d)

2nd

79.

What is the constant term of the polynomial function $f\left(x\right)=3x^7+2x^5+x^3-x$ ?

a)

7

b)

5

c)

3

d)

0

80.

How many x-intercepts does the polynomial function $f\left(x\right)=x^3-x^2-4x+4$ have?

a)

1

b)

2

c)

3

d)

4

81.

What are the end behaviors of the graph of $f\left(x\right)=-2x+x^3+3x^5-4$ ?

a)

Rises to the left and falls to the right

b)

Falls to the left and rises to the right

c)

Rises to both direction

d)

Falls to both direction

82.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

83.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

84.

The polynomial is...

a)

Odd degree, positive leading coefficient.

b)

Odd degree, negative leading coefficient.

c)

Even degree, positive leading coefficient.

d)

Even degree, negative leading coefficient.

85.

Identify the type of polynomial shown

2x² + 3x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with more than 3 terms

86.

Identify the type of polynomial shown

5x² + 7x - 2

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with more than 3 terms

87.

Simplify the expression

(4x² - 6x - 8) + (3x² - 2x - 9)

a)

x² - 4x + 1

b)

7x² - 8x - 17

c)

12x² + 12x + 72

d)

7x⁴ - 8x² - 17

88.

Simplify the expression

(3x² + 6x - 3) - (5x² + 3x - 3)

a)

-2x² + 9x - 6

b)

-2x² + 3x - 6

c)

-2x² + 9x

d)

-2x² + 3x

89.

Simplify the expression

(11x⁵ - 3x³) - (8x⁴ - 2x³ + 6x + 9)

a)

11x⁵ - 8x⁴ + x³ - 6x - 9

b)

11x⁵ - 8x⁴ - x³ - 6x - 9

c)

11x⁵ - 8x⁴ - 5x³ + 6x + 9

d)

11x⁵ - 8x⁴ - 5x³ - 6x - 9

90.

What is the value of the coefficient?
−3x+6

a)

3

b)

6

c)

−3

d)

x

91.

What is the degree of the monomial?

a)

5

b)

3

c)

8

d)

9

92.

1. Which of the following is NOT a Polynomial Function?

a)

$f\left(x\right)=\pi$

b)

$f\left(x\right)=-\frac{2}{3}x^2+1$

c)

$f\left(x\right)=-x+\sqrt[]{5x^3}$

d)

$f\left(x\right)=x^{\frac{1}{5}}-2x^2$

93.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

94.

Expand
(b - 2)³

a)

b³ - 2b² + 4b - 8

b)

5b³ - 20b² + 40b - 40

c)

b³ - 6b² + 12b - 8

d)

4b³ - 12b² + 16b - 8

95.

Find the 2nd term in the expansion of
(2b + 1)³

a)

12b²

b)

6b

c)

8b³

d)

4b²

96.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

97.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

98.

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

99.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

100.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

101.

Is the binomial (x - 9) a factor of 4x² - 33x - 27?

a)

yes

b)

no

102.

Divide
(4b² + b - 2) ÷ (4b + 5)

a)

b + 1 - 3/4b +5

b)

b - 1 + 3/4b - 5

c)

b + 1 + 3/4b + 5

d)

b - 1 + 3/4b + 5

103.

a)

2x² + 3x + 8 + -57/x-4

b)

2x² - 13x - 56

c)

2x² + 3x + 8 +7/x-4

d)

2x² - 3x - 16 + -89/x-4

104.

Factor each completely. If the expression does not factor, write does not factor. x³ −18x² + 81x

a)

$x\left(x^2-18x+81\right)$

b)

$x\left(x-9\right)\left(x+9\right)$

c)

$x^2\left(x-18\right)$

d)

$x\left(x-9\right)^2$

105.

Factor each completely. If the expression does not factor, write does not factor. $x^3-7x^2+12x$

a)

$x(x+3)(x+4)$

b)

$x^3\left(x-7\right)$

c)

$x\left(x-3\right)\left(x+4\right)$

d)

$x(x-4)(x-3)$

106.

Factor the following expression:
$x^2-9x$

a)

$x\left(x-9\right)$

b)

$x\left(x-1\right)$

c)

$x\left(x-4\right)$

d)

$\left(x+8\right)\left(x-4\right)$

107.

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)

108.

Factor: $12x^3y^2-24x^2y+18x$

109.

What are the factors of
25x² - 81?

110.

x²+ 81

a)

Not factorable

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

111.

Factor by finding a GCF:
4b⁵+ 4b³+ 16b²

a)

4b³(b⁴+ b²+ 4b)

b)

4b³(b⁴+ 4b + 5)

c)

4(b⁵+ b³+ 4b²)

d)

4b²(b³+ b + 4)

112.

Factor by finding a GCF:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

6c³(4c² - 2)

113.

Factor:

a)

$\left(x-5\right)\left(x^2+5x+25\right)$

b)

$\left(x+5\right)\left(x^2-5x+25\right)$

c)

$x-5$

d)

$\left(x^2-5x\right)\left(x-5x+25\right)$

114.

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)

115.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

116.

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)

117.

What is the factored form of 35x² + 5x + 56x + 8

a)

(5x + 8)(7x + 1)

b)

(5x + 7)(x + 1)

c)

(5x² + 8)(7x + 1)

d)

5x (7x² + x + 7x + 1)

118.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

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

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

119.

All imaginary roots comes in pairs.

a)

True

b)

False

120.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

121.

Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)

a)

x=-2, x=3, x=5/3

b)

x=2, x=-3, x=-3/5

c)

x=2, x=-3, x=5/3

d)

x=-2, x=3, x=5

122.

Write the cubic polynomial in factored form with
zeros -1, 1, and 4

a)

(x + 1) (x - 1) (x - 4)

b)

x³ - 4x² - x + 4

c)

(x + 1) (x - 1) (x + 4)

d)

x³ - 4x² - x - 4

123.

a)

A

b)

B

c)

C

d)

D

124.

Simplify $8^{\frac{5}{3}}$

a)

2

b)

16

c)

64

d)

32

125.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

126.

Solve for x:

x^3/2 + 7 = 71

a)

2

b)

4

c)

16

d)

8

127.

Solve

a)

243

b)

1

c)

3

d)

729

128.

Solve. (3x - 5)^1/4+ 3 = 4

a)

4/3

b)

2

c)

-2

d)

-4/3

129.

When f(x) = 9 - 3x and g(x) = 5x - 7

find f(x) + g(x).

a)

14x - 10

b)

-8x + 2

c)

2x + 2

d)

2x - 2

130.

$f\left(g\left(5\right)\right)$ (just give the final value)

(a)

131.

Perform the operation. Express you final answer in standard form!

a)

$-2x^2+11x-14$

b)

$12x^2+11x-4$

c)

$2x^2+11x+14$

d)

$2x^2+11x-4$

132.

Perform the operation. Express your answer in standard form.

a)

$6t^4-11t^2+7$

b)

$8t^4-t^2+15$

c)

$6t^4-t^2+15$

d)

$8t^4-11t^2+7$

133.

Perform the operation. State all answers in standard form.

a)

$-21x^2-14x-6$

b)

$-21x^2-26x-8$

c)

$-21x^2-2x-12$

d)

$-21x^2+2x-8$

134.

Perform the operations.

a)

-51

b)

-11

c)

-48

d)

-17

135.

$f\left(x\right)\ =\ x^{2\ }+\ 3x\ -\ 4$ and $g\left(x\right)\ =\ x-1,$ and $x\ne1,$ find $\left(\frac{f}{g}\right)\left(x\right).$

a)

x+4

b)

x+7

c)

x+2

d)

x+3

136.

a)

x^1/2

b)

x³

c)

x²

d)

x^-2

137.

Simplify:

9x^6y^2\cdot5x^2y^3

a)

$14x^8y^5$

b)

$14x^{12}y^6$

c)

$45x^8y^5$

d)

$45x^{12}y^6$

138.

Simplify:

\left(x^8\right)^3

a)

$x^{24}$

b)

$x^{512}$

c)

$x^{11}$

d)

$x^5$

139.

Simplify:

\frac{x^{-7}}{x^{12}}

a)

$\frac{1}{x^5}$

b)

$x^5$

c)

$x^{19}$

d)

$\frac{1}{x^{19}}$

140.

Simplify:
(a⁴b¹⁹c²¹d^-14)⁰

a)

1

b)

0

c)

a⁴b¹⁹c²¹d^-14

d)

a^-4b^-19c^-21d¹⁴

141.

a)

b)

c)

d)

142.

$\frac{16m^2}{24m^7}$ ---> Simplify the rational expression.

a)

$\frac{1}{8}$

b)

$\frac{2}{3m^5}$

c)

$2-3m$

d)

$\frac{2}{3}$

Practice 2nd Semester Exam Algebra 2

Total questions: 142

Worksheet time: 11hrs 37mins

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