Free Printable Algebra 2 Advanced First Semester Final Exam Review

1.

Factor the following x⁴-13x²+36 completly.

a)

(x²-4)(x²-9)

b)

(x-2)(x+2)(x-3)(x+3)

c)

(x-2)²(x-3)²

d)

(x+2)²(x+3)²

2.

Find the product: $\left(2x+5\right)^3$

a)

$8x^3+60x^2+150x+125$

b)

$8x^3+125$

c)

$8x^3+150x^2+60x+125$

d)

$8x^3+20x^2+50x+125$

3.

Find the product: $\left(m-2\right)^3$

a)

$m^3-6m^2+12m-8$

b)

$m^3-8$

c)

$m^2-4m+4$

d)

$m^3-2m^2+6m-8$

4.

How do you write 23% as a decimal?

a)

23.0

b)

2.3

c)

0.23

d)

0.023

5.

How do you write 5% as a decimal?

a)

5.0

b)

0.5

c)

0.05

d)

0.005

6.

What is 5.6% written as a decimal?

a)

5.6

b)

0.56

c)

0.056

d)

0.0056

7.

Aiydan puts $5000 into a savings account with a 3% interest rate. The interest compounds yearly. How much money will he have in his account after 8 years?

a)

$150

b)

$5300

c)

$6333.85

d)

$40786.54

8.

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

9.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

10.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

11.

Simplify.

$\frac{r^2+3r+2}{r+2}\cdot\frac{r-9}{r+1}$

a)

$\frac{r+7}{3}$

b)

$r-9$

c)

$\frac{r+10}{r+1}$

d)

$-9$

12.

Multiply and Simplify

a)

$\frac{\left(5a-25\right)}{\left(a-5\right)\left(a+9\right)}$

b)

$\frac{5}{\left(a+9\right)}$

c)

$\frac{\left(5a-25\right)}{\left(a+9\right)}$

d)

$\frac{1}{\left(a+9\right)}$

13.

Multiply and Simplify

a)

$\frac{4\left(x+3\right)}{\left(x+2\right)}$

b)

$\frac{\left(x+2\right)}{4\left(x+1\right)}$

c)

$\frac{\left(x+2\right)}{4\left(x+3\right)}$

d)

$\frac{4\left(x+1\right)}{\left(x+2\right)}$

14.

$\sqrt{4x^2y^4z^3}$ Simplify

a)

$2xy^2z\sqrt{z}$

b)

$2z^3\sqrt{x^7y^5}$

c)

$2xyz\sqrt{x^6y^5z^8}$

d)

$2x^3y^2z^4\sqrt{xyz}$

15.

$2\sqrt{27}+8\sqrt{3}+5\sqrt{8}$

a)

$24\sqrt{3}$

b)

$24\sqrt{3}+5\sqrt{8}$

c)

$14\sqrt{3}+10\sqrt{2}$

16.

a)

∛-234

b)

-3∛2

c)

7∛2

d)

3∛2

17.

$\sqrt[4]{x^6}-2\sqrt[4]{x^6}=$

a)

$-x\sqrt[4]{x^2}$

b)

$3\sqrt[4]{x^6}$

c)

$-2x$

d)

$3.2$

18.

Simplify

$3^{\ \ 3}\sqrt{54}-2^{\ \ 3}\sqrt{2}+7^{\ \ 3}\sqrt{-16}$

a)

$-7^{\ \ 3}\sqrt{2}$

b)

$3^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14$

c)

$9^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14^{\ \ 3}\sqrt{2}$

19.

What is the conjugate of -2i + 7

a)

-2i - 7

b)

2i - 7

c)

-7 + 2i

d)

7 + 2i

20.

What is the conjugate of i + 4?

a)

i + 4

b)

i - 4

c)

-i-4

d)

-i+4

21.

Which conjugate would you use to simplify this quotient?

a)

$1-3i$

b)

$5+2i$

c)

$-1-3i$

d)

$-5+2i$

22.

a)

x = 5

b)

x = -6

c)

x = 14

d)

x = -1

23.

Solve the cube root equation

a)

27

b)

20

c)

3

d)

30

24.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

25.

a)

b)

c)

d)

26.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

27.

Simplify the expression:

a)

a⁵ b⁴

5c

b)

5a⁵b⁴c

c)

5 c

a⁵b⁴

d)

2a⁵b⁴

10c

28.

a)

b)

c)

d)

29.

a)

b)

c)

d)

30.

$\left(\frac{xy^4}{2x^2y^2}\right)^4$

Simplify

a)

$\frac{y^8}{8x^4}$

b)

$\frac{y^8}{16x^4}$

c)

$\frac{y^2}{16x^4}$

d)

$\frac{y^2}{8x^4}$

31.

a)

$\frac{27x^{15}z^3}{y^6}$

b)

$\frac{9x^{15}z^3}{y^6}$

c)

$27x^8yz^4$

d)

$\frac{27x^8z^4}{y}$

32.

Simplify (-8v⁴ + 4v³ + 3v) + (- 8v⁴+ 4v - 7)

a)

-17v⁴ + 4v³ + 2v - 7

b)

-16v⁴ + 4v³ + 10v - 7

c)

-16v⁴ + 4v³ + 7v - 7

d)

-16v⁴ + 4v³ + 2v - 7

33.

Add to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

34.

Simplify $\left(3x^4y\ +2x^3y^2-8x^2y^3+xy^4\right)-\left(-8x^4y+5x^2y^3\right)$

a)

$11x^4y-2x^3y^2-8x^2y^3+xy^4$

b)

$11x^4y+2x^3y^2-13x^2y^3+xy^4$

c)

$11x^4y-2x^3y^2+8x^2y^3-xy^4$

d)

$-11x^4y+2x^3y^2-8x^2y^3+xy^4$

35.

Factor by grouping:

x³ + 7x² - 2x - 14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

36.

Factor by grouping:

4p³ + 8p² + 3p + 6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

37.

Factor completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

38.

Factor Completely:
x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

39.

Factor Completely x⁸ - 16

a)

(x⁴ - 4)(x⁴ + 4)

b)

(x⁴ - 8)(x⁴ + 2)

c)

(x² - 2)(x² - 2)(x⁴ + 4)

d)

(x² + 2)(x² - 2)(x⁴ +4)

40.

Factor x³ + 2x² - 49x - 98

a)

(x² - 49) (x + 2)

b)

(x² - 49) (x + 2) (x + 2)

c)

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

41.

n² - 15n + 56 = 0

a)

{3, 0}

b)

{-8, 8}

c)

{-3, 6}

d)

{7, 8}

42.

$5x^2-12=17x$

a)

$\left\{-3,20\right\}$

b)

$\left\{-\frac{3}{5},\ 4\right\}$

c)

$\left\{-4,\ \frac{3}{5}\right\}$

d)

$\left\{-20,3\right\}$

43.

Find the domain of

y=\frac{2}{x+1}

.

a)

$x\ne-1$

b)

$x\ne0$

c)

$x\ne1$

d)

$x\ne2$

44.

What is the domain of

y=\frac{\left(x-1\right)\left(x+4\right)}{\left(x+2\right)\left(x-3\right)}

? (Check all that applies.)

a)

$x\ne-2$

b)

$x\ne-1$

c)

$x\ne3$

d)

$x\ne4$

45.

What expression is equivalent to

$\left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$ ?

a)

$x=5$

b)

$-5<x<5$

c)

$x\ne5$

d)

$x=-5$

e)

$x=\infty$

46.

Find the domain of

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

.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,-1\right)\cup\left(-1,\infty\right)$

c)

$\left(-\infty,1\right)\cup\left(1,\infty\right)$

d)

$\left(-\infty,-1\right)\cup\left(-1,1\right)\cup\left(1,\infty\right)$

47.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{x+4}

.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

48.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

49.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

50.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

51.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

52.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

53.

Simplify: $\frac{6x}{x^2-1}+\frac{3}{2\left(x+1\right)}$

a)

$\frac{6x+3}{2\left(x+1\right)\left(x-1\right)}$

b)

$\frac{15x-3}{2\left(x+1\right)\left(x-1\right)}$

c)

$\frac{12x+3}{2\left(x+1\right)\left(x-1\right)}$

d)

$\frac{9x-3}{2\left(x+1\right)\left(x-1\right)}$

54.

a)

b)

c)

d)

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

Simplify the expression:

a)

A

b)

B

c)

C

d)

D

58.

Simplify the expression:

a)

A

b)

B

c)

C

d)

D

59.

Solve for x

a)

x = 10

b)

x = $-\frac{30}{13}$

c)

x = 6

d)

no solution

60.

Solve

a)

A

b)

B

c)

C

d)

D

61.

Solve

a)

No Solution

b)

x = 6

c)

x = 7

d)

x = 5

62.

a)

A

b)

B

c)

C

d)

D

63.

a)

A

b)

B

c)

C

d)

D

64.

Write using a rational exponent: $\sqrt[5]{x^3}$

a)

$x^{\frac{5}{3}}$

b)

$x^{\frac{3}{5}}$

c)

$x^2$

d)

$x^8$

65.

Write using a rational exponent: $\sqrt[]{x^{11}}$

a)

$x^{\frac{11}{2}}$

b)

$x^{11}$

c)

$x^9$

d)

$x^{10}$

66.

Write using a radical: $x^{\frac{8}{5}}$

a)

$\sqrt[5]{x^8}$

b)

$\sqrt[8]{x^5}$

c)

$\sqrt[]{x^{\frac{5}{8}}}$

d)

$x^{-3}$

67.

a)

$\frac{a^6}{b^{12}}$

b)

$\frac{b^{12}}{a^4}$

c)

$\frac{a^{12}}{b^6}$

d)

$\frac{1}{a^6b^{10}}$

68.

Simplify each expression. Give final answer in simplest radical form.

$\left(28^{\frac{3}{5}}\right)^{\frac{5}{6}}$

69.

Simplify each expression. Give final answer in simplest radical form.

$\frac{x^{\frac{7}{3}}}{x^{\frac{2}{3}}}$

70.

Simplify the radical

a)

$2w^3x\ ∜2wx$

b)

$2w\left|x\right|\ ∜2w^3$

c)

$8wx\ ∜2w^3$

d)

$4wx\ ∜2w^3$

71.

Simplify the radical

a)

$\left|g^3\right|h^2\ \ ∜h^{ }$

b)

$\left|g^3h^2\right|\ ∜h$

c)

$h\ ∜g^3h^2$

d)

$h^2\ ∜g^3h^{ }$

72.

$\left(4\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}-\sqrt{3}\right)$

a)

$20\sqrt{2}-14\sqrt{6}+2\sqrt{3}$

b)

$46-14\sqrt{6}$

c)

$32\sqrt{6}$

d)

$40-14\sqrt{6}+6\sqrt{3}$

73.

$3\sqrt{6}\left(\sqrt{6}-2\sqrt{10}\right)$

a)

$18-12\sqrt{15}$

b)

$6\sqrt{15}$

c)

$-3\sqrt{24}$

d)

$3\sqrt{36}-6\sqrt{60}$

74.

$\sqrt[]{15}\ \left(3\sqrt[]{5}-2\sqrt[]{3}\right)$

a)

$2\sqrt[]{3}+3$

b)

$4\sqrt[]{5}+2$

c)

$4\sqrt[]{3}+3$

d)

$15\sqrt[]{3}-6\sqrt[]{5}$

75.

$\sqrt[]{6}\ \left(\sqrt[]{2}+3\right)$

a)

$2\sqrt[]{3}\ +\ 3\sqrt[]{6}$

b)

20

c)

$-30-2\sqrt[]{30}$

d)

$\sqrt[]{30}+3\sqrt[]{2}$

76.

Solve for n.

a)

n=25

b)

n=-25

c)

n=5

d)

n=-5

77.

Solve for x

a)

x=27

b)

x=-3

c)

x=81

d)

x=3

78.

Solve for x

a)

x=243 and x=-243

b)

x=9 and x=-9

c)

x=3 and x=-3

d)

x=-117.5 and x=125.5

79.

a)

a

b)

b

c)

c

d)

d

80.

a)

a

b)

b

c)

c

d)

d

81.

a)

a

b)

b

c)

c

d)

d

82.

Solve the following equation:

x^2\ -\ 5x\ +\ 10\ =\ 0

a)

$\frac{\left(5\ -\ \sqrt{15}\ i\right)}{2}\ \ ,\ \frac{\left(5\ +\ \sqrt{15}\ i\right)}{2}$

b)

$\frac{\left(5\ -\ \sqrt{15}\right)}{2}\ ,\ \frac{\left(5\ +\ \sqrt{15}\right)}{2}$

c)

$\frac{\left(5\ -\ \sqrt{65}\ i\right)}{2}\ ,\ \frac{\left(5\ +\ \sqrt{65}\ i\right)}{2}$

d)

$\frac{\left(5\ -\ \sqrt{65}\right)}{2}\ ,\frac{\left(5\ +\ \sqrt{65}\right)}{2}$

83.

Use the quadratic formula to find the solutions for
$y=-x^2-5x+12$

a)

No Real Solution

b)

$\frac{5\pm\sqrt{73}}{-2}$

c)

$\frac{-5\pm\sqrt{73}}{-2}$

d)

$\frac{5\pm\sqrt{73}}{2}$

84.

Determine the value of the discriminant and describe the number and type roots for the following:

x² + 7x + 13

a)

101, 2 real roots

b)

3, 2 real roots

c)

-101, 2 imaginary roots

d)

-3, 2 imaginary roots

85.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

86.

When the discriminant is zero , there is ________ solution

a)

2 Real

b)

1 Real

c)

2 Imaginary

d)

None

87.

The discriminant equals 49, describe the number and nature of the roots.

a)

2 real irrational roots

b)

2 imaginary rational roots

c)

1 real rational root

d)

2 real rational roots

Algebra 2 Advanced First Semester Final Exam Review

Total questions: 87

Worksheet time: 8hrs 4mins

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