Free Printable Algebra 2 MP1 Review

1.

What is the first step to solve the following equation?

-2|x + 3| = -10

a)

Set up 2 equations

-2(x + 3) = 10

-2(x + 3) = -10

b)

Add 2 to both sides

c)

Subtract 3 from both sides

d)

Divide by -2 on both sides

e)

No Solution

2.

When do you set up 2 equations?

|x + 2| + 3 = 4

a)

That is the first step.

b)

After you subtract 3 from both sides.

c)

After you add 2 and 3.

3.

What is the first step to solve the following equation?

|2x - 1| = -5

a)

Add 1 to both sides

b)

Set up 2 equations:

2x - 1 = 5

2x - 1 = -5

c)

No Solution

d)

Divide by 2 on both sides.

4.

Solve. Select BOTH solutions.
$\left|10x-8\right|=38$

a)

$3$

b)

$-3$

c)

$\frac{23}{5}$

d)

$\frac{19}{5}$

5.

| x - 6 | < 4
Is this an "and" or an "or" problem?

a)

and

b)

or

6.

| x - 2 | > 3
Is this an "and" or an "or" problem?

a)

and

b)

or

7.

| 2x + 12 | < 8
Which is the correct first step?

a)

2x + 12 < 8 and 2x+12 >-8

b)

2x + 12 < 8 or 2x+12 >-8

c)

2x + 12 < 8 and 2x+12 <-8

d)

2x + 12 < 8 or 2x+12 >-8

8.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

9.

x + 8 < 3 or - 8x < -40

a)

x > -5 or x < 5

b)

x < -5 and x > 5

c)

x < -5 or x > 5

d)

x > -5 and x < 5

10.

What inequality is graphed?

a)

x > 2 and x < 4

b)

2 ≤ x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

11.

Look at the graph. Write the inequality in interval notation.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

12.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

13.

a)

n > 1 or n < -7

b)

n > -1 or n < -7

c)

-7 < n < -1

d)

no solution

14.

a)

no solution

b)

-6 ≤ r ≥ 8

c)

6 > r > -8

d)

-6 < r < 8

15.

Look at the picture. Which number line corresponds to [-2, 5]?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

16.

-8<2(x+4) or -3x+4>x-4

a)

No solutions

b)

x<-8 or x<2

c)

x>-8 or x<2

d)

x<-8 and x<2

17.

0 < x + 7 < 9

a)

-7<x and x<2

b)

-7<x or x<2

c)

-7>x and x>2

d)

-7>x or x>2

18.

What is the missing step for solving the equation?

a)

$-14x-2=5x+34$

b)

$-14x+2=5x+34$

c)

$14x-2=5x+34$

d)

$14x-2=-5x-34$

19.

Solve for w:

$\frac{2w}{5}-9=11$

a)

$w=50$

b)

$w=10$

c)

$w=32$

d)

$w=23$

20.

$t\ -\frac{2}{3}=\frac{4}{9}$

a)

$t=1\ \frac{1}{9}$

b)

$t=\frac{2}{9}$

c)

$t=\frac{1}{2}$

d)

$t=1\ \frac{6}{12}$

21.

Solve for x:

$50=\frac{5}{4}\left(3x-8\right)$

a)

$x=\frac{16}{3}$

b)

$x=16$

c)

$x=4$

d)

$x\ =\ \frac{15}{4}$

22.

$-\frac{3}{4}=\frac{2}{7}+\frac{5}{14}x$

(a)

23.

$\frac{2}{5}x-\frac{7}{10}=\frac{23}{30}$

(a)

24.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

25.

Determine the number of solutions to the equation:

2(x - 1) = x + x - 3

a)

one solution

b)

no solution

c)

infinitely many solutions

26.

Determine the number of solutions to the equation:

5x + 8 - 7x = -4x + 1

a)

one solution

b)

no solution

c)

infinitely many solutions

27.

Determine the number of solutions to the equation:

-4x - 7 + 10x = -7 + 6x

a)

one solution

b)

no solution

c)

infinitely many solutions

28.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

29.

What is the factored form of x²+16x+15

a)

(x+1)(x+15)

b)

(x+3)(x+5)

c)

(x-3)(x-5)

d)

(x-1)(x+15)

30.

Factor:

4h² - 12h + 9

a)

(2h - 3)(2h - 3)

b)

4(h + 9)(h + 1)

c)

(2h - 3)(2h + 3)

d)

(h - 9)(4h - 1)

31.

Factor: 25x²- 9

a)

(5x + 3)(5x - 3)

b)

(x + 5)(x - 3)

c)

(x - 3)(x + 5)

d)

(5x + 3)(3x + 5)

32.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

33.

Solve
4m² - 100 = 0

a)

m=25, -25

b)

m=96

c)

m=5, -5

d)

m=-96

34.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

35.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

36.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation 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

37.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

38.

x² + 44 = -15x

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

39.

Solve using Zero-Product Property
(x-11)(5x+1) = 0

a)

x = 11 or x = -1/5

b)

x = -11 or x = -1/5

c)

x = 11 or x = 1/5

d)

x = -11 or x = 1/5

40.

a)

2i√6

b)

8i√3

c)

-2√6

d)

-2i√6

41.

a)

6i√5

b)

-8√5

c)

8i√5

d)

-8i√5

42.

a)

i

b)

-1

c)

1

d)

-i

43.

a)

6

b)

-6

c)

6i

d)

6i²

44.

a)

√2

b)

i√2

c)

i²√2

d)

-√2

45.

a)

30

b)

30i

c)

-30

d)

-30i

46.

x² + 36 = 0

a)

x = ±6

b)

x = 6i

c)

x = -6

d)

x = ±6i

47.

33 = 18 - 3x²

a)

x = ±5i

b)

x = ±i√5

c)

x = ±√5

d)

x = i√5

48.

2(x - 8)² + 40 = 16

a)

x = 8 ± 2i√3

b)

x = 8 ± √-12

c)

x = -8 ± 2i√3

d)

x = 8 ± 3i√2

49.

Simplify:
2i(4 - 3i)

a)

6 + 8i

b)

6 - 8i

c)

8i - 6i²

d)

8i + 6i²

50.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

51.

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

a)

22 - 7i

b)

22 + 7i

c)

22 - 7i²

d)

22 + 7i²

52.

Simplify

a)

± 10i

b)

± 10

c)

± √10i

d)

± √10

53.

Match the following imaginary variables to their equivalent form.

a)

$\sqrt[]{-1}$

1.

$i$

b)

-1

2.

$i^2$

c)

$-i$

3.

$i^3$

d)

$1$

4.

$i^4$

54.

Match the decimal remainder (after dividing the exponent by 4) to the corresponding value

a)

0.25

1.

i

b)

0.5

2.

-1

c)

0.75

3.

-i

d)

Whole number

4.

1

55.

$i^{10}$

a)

-1

b)

1

c)

i

d)

-i

56.

$i^{21}$

a)

-1

b)

1

c)

i

d)

-i

57.

$i^{36}$

a)

-1

b)

1

c)

i

d)

-i

58.

$i^{45}$

a)

-1

b)

1

c)

i

d)

-i

59.

Solve for $x:\ x^2-\ 4x+5$

a)

x = {-4, -1}

b)

x = {-1, -4}

c)

x = {2+i, 2-i}

d)

x = {-2+i, -2-i}

60.

Solve for $x:\ x^2-5x+8$

a)

$x=\frac{7\pm\sqrt{5}i}{2}$

b)

$x=\frac{5\pm\sqrt{7}i}{2}$

c)

$x=\frac{8\pm\sqrt{7}i}{2}$

d)

$x=\frac{-5\pm\sqrt{-7}i}{2}$

61.

Solve for $x:\ 3x^2-6x+6$

a)

$x\ =\ 1\pm i$

b)

$x=3,\ -6$

c)

$x=2\pm2i$

d)

$x\ =\ -i\ \pm1$

62.

How many REAL solutions does this quadratic have?

a)

Infinitely Many

b)

One

c)

Two

d)

None

63.

How many REAL solutions does this quadratic have?

a)

Infinitely many

b)

One

c)

Two

d)

None

64.

What is the solution set for the equation $x^2+49=0$ ?

a)

$x=\pm7$

b)

$x=\pm7i$

c)

$x=\pm14i$

d)

$x=\pm49i$

65.

Solve for $x:\ x^2+6x+13$

a)

$x=-3\pm2i$

b)

$x=7,6$

c)

$x=2\pm\sqrt{3}i$

d)

$x=2\pm3i$

66.

Find the roots: $x^2+3x+17=-x+4$

a)

$x=-2\pm3i$

b)

$x=3+4i,\ 4+3i$

c)

$x=1\pm5i$

d)

$x=5\pm3i$

67.

Which of the following have complex roots?

$f\left(x\right)\ =\ 4x^2+7x+8$

$g\left(x\right)\ =\ 2x^2-17x-29$

$h\left(x\right)\ =\ x^2\ +2x\ +9$

a)

$f\left(x\right)$

b)

$f\left(x\right)$ and $h\left(x\right)$

c)

$h\left(x\right)$

d)

$g\left(x\right)$ and $h\left(x\right)$

68.

Which phrase correctly describes the roots of the following function?

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

a)

2 Real Roots

b)

2 Imaginary Roots

c)

1 Real Root

d)

1 Imaginary Root

69.

Multiply: (4 + 8i)(1 + i)

a)

4 + 12i

b)

-4 + 12i

c)

12 + 4i

d)

12 - 4i

70.

Find the conjugate of:
5 + 7i

a)

5 − 7i

b)

-5 − 7i

c)

-5 + 7i

71.

Find the conjugate of:
-4 − 8i

a)

-4 + 8i

b)

4 − 8i

c)

4 + 8i

72.

Solve the quadratic inequality: $x^2+11x+10\ge0$

a)

$x\le-10\ ,\ \ x\ge-1$

b)

$x\ge1\ ,\ \ x\le10$

c)

$1\le x\le10$

d)

$-1\le x\le11$

73.

Which of the following is the solution of the given Quadratic Inequality?

a)

y ≥ -2 or y ≤ -5/2

b)

y ≤ -2 or y ≥ -5/2

c)

y ≥ 2 or y ≤ 5/2

d)

y ≤ 2 or y ≥ 5/2

74.

Which of the following is the solution of the given Quadratic Inequality?

a)

1/2 ≤ x ≤ 2

b)

-1/2 ≤ x ≤ 2

c)

-2 ≤ x ≤ -1/2

d)

-2 ≤ x ≤ 1/2

75.

Which of the following is the solution of the given Quadratic Inequality?

a)

5 < y < 12

b)

7 < y < 10

c)

8 < y < 9

d)

6 < y < 11

76.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

77.

Simplify the expression:
(5b - 3b³ - 8b²) - (2b³ - 4b² + 6b - 3b⁴)

a)

3b⁴ - 5b³ - 11b² - b

b)

3b⁴ - 5b³ - 11b² - 9b

c)

3b⁴ - 5b³ - 11b² - 15b

d)

3b⁴ - 5b³ - 4b² - b

78.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

79.

Multiply.
-3x²(7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

80.

Simplify:
(3x - 5) ( 4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

81.

Find the product:

(2x + 7)²

a)

4x²+ 49

b)

4x²+ 28x + 49

c)

4x² + 14x + 49

82.

Simplify:
(3x - 5) ( 4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

83.

Determine whether $x-4$ is a factor of $f\left(x\right)=x^5-2x^3+4x+1$

a)

Yes, because the remainder is 0

b)

Yes, because the remainder is not equals to 0

c)

No, because the remainder is 0

d)

No, because the remainder is not equals 0

84.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

85.

Is $(x-2)$ a factor of $f(x)=x^3-8x^2+14x-4$ ?

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.

86.

Divide using synthetic division $(2x^3+4x^2-5)\div(x+3)$

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

87.

Multiply:

(x + 1) (x - 6) (x + 4)

a)

x³ - x² - 26x - 24

b)

x³ - 9x² - 14x - 24

c)

x³ - 11x² - 24x - 24

d)

x² - 5x - 6

88.

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

89.

Multiply:

(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

90.

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)

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

91.

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)

92.

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)

93.

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)

94.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

95.

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)

96.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

97.

64x³ + 1

a)

(4x - 3)(16x² + 12x + 9)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x - 1)(4x² + 2x + 1)

d)

(4x + 1)(16x² - 4x + 1)

98.

64x³ + 125

a)

(4x - 5)(16x² + 20x + 25)

b)

(4x + 5)(16x² - 20x + 25)

c)

(4x - 5)(16x² + 20x - 25)

d)

(4x + 5)(16x² - 20x - 25)

99.

125x³ - 64

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(3x - 1)(9x² + 3x + 1)

d)

(4x - 3)(16x² + 12x + 9)

100.

Which expression is an example of a Difference of Cubes?

a)

$x^2-16$

b)

$8x^3-27$

c)

$x^3-x^2-x-1$

d)

$x^3+1000$

101.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

102.

factor 10x²y – 30xy²

a)

xy(10 - 30)

b)

10xy(x - 3y)

c)

10x²y(3y)

d)

10xy²(x)

103.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁶)

d)

3x²(80x³-40-60x⁵)

104.

What is the GCF? 2x²-4x+8

a)

2x

b)

2

c)

x

d)

1

105.

Factor the GCF

10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

106.

Factor: 3x+9

a)

3(x+3)

b)

3(x+9)

c)

3x(x+3)

d)

3(3x+9)

107.

Factor: 5n+10n²

a)

5n(1-2n)

b)

5(n+2n²)

c)

5n(1+2n)

d)

n(5+10n)

108.

Factor: 4x⁵y³+10x²y

a)

2x²y(2x³y²+5)

b)

2x²y(2x³y+5)

c)

2x²y(2x³y²+5x)

d)

2x²y(2x³y²-5)

109.

Factor: 5x²+10x+35x³

a)

5x(x+2+7x²)

b)

5(x+2+7x²)

c)

5x(x+2-7x²)

d)

5x(x+2+7x²)

110.

Factor:
2n²+16n+12

a)

2n(n²+24n+6)

b)

2(n²+8n+6)

c)

2n(n²+8n+6)

d)

3(n²+8n+6)

111.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁵)

d)

3x²(80x³-40-60x⁵)

112.

Factor:
80x⁵-70x²-60x⁷

a)

2x²(80x³-70-60x⁶)

b)

10x²(80x⁴-70x-60x⁶)

c)

10x²(8x³-7-6x⁶)

d)

3x²(80x³-40-60x⁵)

113.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

114.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

115.

Factor by grouping

x³ - 4x² - 4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

116.

Factor this difference of cubes:
x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

117.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

118.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

119.

How many x-intercepts does x⁴+6x²+9= 0 have?

a)

2

b)

1

c)

4

d)

None

120.

To determine how many x-intercepts the polynomial has, look at the …

a)

Degree of the function

b)

End behavior

c)

Coeffients

d)

Y-intercept

121.

What are the solutions to the equation

2x³+x²=8x+4

a)

x=2, x=-2, x=-1/2

b)

x=4, x=-4, x=-1/2

c)

x=2, x=-1, x=-1/2

d)

x=1, x=-2, x=-1/2

122.

What are the x-intercepts of the polynomial
y = 3 (x + 4) (x + 1) (x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

123.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

124.

Solve by finding the Zeros

2x³ - 11x² + 12x + 9 = 0

a)

-1, 1, 3

b)

-1, 3/2, 3

c)

-1/2, 3, 3

d)

-1/2, 1, 3

125.

What is the least degree of the graph of the above polynomial?

a)

3

b)

4

c)

5

d)

Not enough information

126.

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

127.

What are the zeros of the polynomial function?

y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

128.

Find all complex roots of the polynomial. $x^3+2x^2+4x+8=0$

a)

$\left\{2,\ 2i,\ -2i\right\}$

b)

$\left\{-2,\ 2i,\ -2i\right\}$

c)

$\left\{-2,\ 2,\ -2i,\ 2i\right\}$

d)

$\left\{2,\ 2i\right\}$

129.

Find all complex roots.
$f\left(x\right)=x^3-2x^2+x-2$

a)

$\left\{2,\ 1\right\}$

b)

$\left\{-2,\ 2,\ -1,\ 1\right\}$

c)

$\left\{2,\ 1\ ,\ 1\right\}$

d)

$\left\{2,\ 1,\ -1\right\}$

Algebra 2 MP1 Review

Total questions: 129

Worksheet time: 22hrs 30mins

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