Free Printable Algebra 2 Final Exam Review

1.

1) Distribute (2x - 3)²

a)

4x² - 9

b)

4x² + 9

c)

4x² - 12x + 9

d)

4x² - 12x - 9

2.

Rewrite f(x) = x² - 10x + 14 in graphing/vertex form by completing the square.

a)

y = (x - 5)² + 14

b)

y = (x - 5)² - 11

c)

y = (x + 5)² + 14

d)

y = (x + 5)² - 11

3.

What is the vertex of y = (x + 3)² - 5

a)

(3, -5)

b)

(-3, 5)

c)

(-3, -5)

d)

(3, 5)

4.

Simplify Completey: x⁵ ⋅ x^-3⋅ x¹²

a)

x^-180

b)

x¹⁴

c)

x¹⁸⁰

d)

x^-14

5.

Solve the following absolute value equation:
∣ x + 3 ∣ +7 = - 14

a)

x = -24 or 18

b)

x = 24 or -18

c)

no solution

d)

infinite solutions

6.

Solve the following absolute value inequality:
∣ 2x - 3 ∣ ≤ 5

a)

- 1 < x < 4

b)

-1 ≤ x ≤ 4

c)

x ≤ -1 or x ≥ 4

d)

x < -1 or x ≥ 4

7.

Find f(-3) in the function
f(x) = x³ - 3x² +5x -18

a)

-87

b)

-33

c)

150

d)

-121

8.

What is the equation of the inequality:

a)

y > - ½x - 4

b)

y > -2x - 4

c)

y ≥ - ½x - 4

d)

y > ½x - 4

9.

How is the equation shifted from its parent graph: y = x²?
y = - (x + 8)² + 12

a)

Right 8, up 12, reflected in the x axis

b)

Left 8, up 12, reflected in the x axis

c)

Right 8, down 12, reflected in the x axis

d)

Left 8, up 12

10.

Simplify the exponents:
(x⁴ y³ z)⁵(4zx⁸)²

a)

16x³⁶y¹⁵z⁷

b)

8x³⁶y¹⁵z⁷

c)

16x³⁶y⁸z⁶

d)

16x¹⁹y⁸z⁷

11.

Solve for x:
8x² + 24 = 0

a)

x = ± i √ (3)

b)

x = ± 3i

c)

x = ± √(3)

d)

x = ± 2

12.

Multiply
(4 - 9i)(7 + i)

a)

37 - 59i

b)

19 - 59i

c)

19 - 67i

d)

28 - 72i

13.

Simplify: i¹²¹

a)

i

b)

-i

c)

1

d)

-1

14.

What is factored form of the parabola?

a)

(x - 4)(x + 1) = y

b)

( x + 4)(x - 1) = y

c)

(x - 1.5)(x + 6.3) = y

d)

x² - 3x - 4 = y

15.

What is the vertex of the parabola:
x² - 8x + 5 = y

a)

(4 , -11)

b)

( -8, 5)

c)

(4, 3)

d)

No Solution

16.

Which function is graphed?

a)

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

b)

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

c)

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

d)

f(x) = -2|x - 4|

17.

Which function is graphed?

a)

f(x) = -|2x - 3| + 5

b)

f(x) = -|x + 5| - 3

c)

f(x) = -|2x + 6| + 5

d)

f(x) = -2|x + 5| - 3

18.

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

19.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

20.

Which of the following trinomials is a perfect square trinomial?

a)

r² - 6r + 36

b)

4y² + 10y + 25

c)

x² + 16x + 16

d)

9a² - 12a + 4

21.

Factor, if possible: 4x²+36x+81

a)

(4x+81)²

b)

(2x+9)²

c)

Prime /
Not factorable.

d)

(2x-9)²

22.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

23.

a)

9

b)

-9

c)

7

d)

-7

24.

x³ - 27

a)

(x - 4)(x² + 4x + 16)

b)

(x + 3)(x² - 4x + 16)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 3)(x² + 3x + 9)

25.

Solve

8x³+125=0

a)

x=-5/2, x=(-5±5i√3)/4

b)

x=-5/2, x=(5±5i√3)/4

c)

x=-2/5, x=(-5±5i√3)/4

d)

x=-2/5, x=(5±5i√3)/4

26.

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

27.

Multiply:
(4 – 3i)(7 + 2i)

a)

A. 22 - 13i

b)

B. 28 - 19i

c)

C. 34 - 13i

d)

D. -34 - 29i

28.

Solve 2x² - 5x = 1

a)

b)

c)

d)

29.

Simplify

a)

b)

c)

d)

30.

Which is the graph of the function?

a)

b)

c)

d)

31.

a)

b)

c)

d)

32.

2x²(-3x²+3x³) in standard form

a)

6x⁵-6x⁴

b)

-x⁵-6x⁴

c)

-x+5x⁴

d)

6x⁵-9x⁴

33.

a)

$t=\frac{s}{5r^4}$

b)

$t=\frac{s}{5-r}$

c)

$t=r4-5s$

d)

$t=\frac{625r}{s}$

34.

Find the slope of the line: -5x-4y=11

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$-\frac{5}{4}$

d)

$\frac{5}{4}$

35.

Write the equation that is the translation of y = |x| left 10 units and down 5 units.

a)

y = |x + 10| - 5

b)

y = |x - 5| - 10

c)

y = |x + 5| - 10

d)

y = |x - 10| - 5

36.

a)

$Domain:\ R;\ Range:\ \left[1,\ \infty\right)$

b)

$Domain:R\ ;\ Range:\ \left(1,\ \infty\right)$

c)

$Domain:\ R\ ;\ Range:\ \left(\infty,\ 1\right]$

d)

$Domain:\ R\ ;\ Range:\ \left(\infty,1\right)$

37.

Divide 4x³+ 2x² + 3x + 4 by x + 4.

a)

4x² - 14x + 59

b)

4x²+ 18x - 53

c)

4x² + 18x - 53, R 240

d)

4x² - 14x + 59, R - 232

38.

Simplify the difference.

a)

b)

c)

d)

39.

Find each product.

a)

b)

c)

d)

40.

Factor.

a)

b)

c)

d)

41.

Simplify.

a)

b)

c)

d)

42.

A polynomial is in Standard Form if the terms of the polynomial are arranged in descending order of degree.

Which polynomials are in standard form? Select all correct answers.

a)

$3z\ -\ 1$

b)

$2\ +\ 4x\ -\ 5x^2$

c)

$-5p^5\ +\ 2p^2\ -\ 3p\ +\ 1$

d)

None of the above

43.

$4m^2\ -\ 3m^6\ +\ 5m^4$

What is the degree of the polynomial?

(a)

44.

x =

Separate your answer using a comma (example 1,2)

(a)

45.

x =

(a)

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

x is inceasing when

a)

x > -2

b)

x < -1

c)

x > 1

d)

X < -2

51.

a)

4x^3(x-5)(x+5)

b)

4x^3(x^2-25)

c)

4x^2(x-5)(x+5)

d)

4x^2(x^2-25)

52.

Where is the graph DECREASING?

a)

$\left(-0.593,\ 0.843\right)$

b)

$\left(-\infty,-0.593\right)\cup\left(0.843,2\right)$

c)

$\left(-0.593,0.843\right)\cup\left(2,\infty\right)$

d)

$\left(-0.593,0.843\right)\cup\left(2,-\infty\right)$

53.

What is the range of the following?

a)

$\left[2,\infty\right)$

b)

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

c)

$\left[-3.2,\infty\right)$

d)

$\left[-2,\infty\right)$

54.

Find the factored equation if the zeros are:

0, -2, 6

a)

$y=\left(x-2\right)\left(x+6\right)$

b)

$y=x\left(x-2\right)\left(x-6\right)$

c)

$y=x^2\left(x-2\right)\left(x+6\right)$

d)

$y=x\left(x+2\right)\left(x-6\right)$

55.

Rewrite the following in SIMPLIFIED radical notation:

$a^{\frac{5}{6}}b^{\frac{13}{6}}c^{\frac{21}{6}}$

a)

$ab^2c^3\ \ \sqrt[6]{abc}$

b)

$bc^2\ \ \sqrt[6]{a^5bc}$

c)

$b^2c^3\ \ \sqrt[6]{a^5bc^3}$

d)

$\sqrt[6]{a^5b^{13}c^{21}}$

56.

Simplify: $\frac{\sqrt[]{32a^{10}b^3}}{\sqrt[]{2a^2b^{15}}}$

a)

$\frac{4a^4}{b^6}$

b)

$\sqrt[]{\frac{16a^8}{b^6}}$

c)

$\frac{16a^8}{b^{12}}$

d)

$\frac{4a^4}{b^3}$

57.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

58.

a)

10 / 14a⁴

b)

21 / 49a⁴

c)

3 / a⁴

d)

3 / 7a⁴

59.

Simplify
3√5 + √20 - √45

a)

3√-20

b)

2√-20

c)

3√5

d)

2√5

60.

Find the Error
What error did the student make when solving the equation:
1/5x + 6 = 3/5x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

a)

The student found an incorrect common denominator

b)

The student did not multiply all terms by the common denominator

c)

The student did not use opposite operations appropriately

d)

The student did not correctly eliminate the variable from one side of the equation

61.

Factor Completely: 2x² + x - 6

a)

(x + 2) (2x -3)

b)

(x - 6) (2x + 1)

c)

(x + 1) (2x - 6)

d)

(x - 2) (2x + 3)

62.

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

63.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

64.

Find the slope of the line that passes through
(-2, 8) and (0, 8)

a)

0

b)

-2

c)

2

d)

1/2

65.

Determine the slope.

a)

m=3/2

b)

m=6

c)

m=-3/2

d)

m=1/6

Algebra 2 Final Exam Review

Total questions: 65

Worksheet time: 16hrs 15mins

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