Free Printable Algebra II Final Exam Review

1.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

2.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

3.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

4.

Find the product:
(x + 7)²

a)

x²+ 7x + 7x + 49

b)

x²+ 7x + 7

c)

7x²+ x + 7

d)

x² + 14x + 49

5.

Find the perimeter of the rectangle

a)

P= 10x + 2

b)

P= 12x

c)

P = 12

d)

P = 6x² + 3x

6.

^{The perimeter of the
triangle is 10x+20. Find the length of the missing side}

a)

6x+10

b)

15x+30

c)

5x+10

d)

5x-10

7.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

8.

What is the degree of the polynomial?

a)

2

b)

3

c)

4

d)

5

9.

Find the choice that is correct

a)

The leading coefficient is 2, the degree is 4

b)

The leading coefficient is 3, the degree is 2

c)

The leading coefficient is 3, the degree is 4

d)

The leading coefficient is 2, the degree is 2.

10.

What is the degree of the polynomial?

g\left(x\right)=\left(x-4\right)^2\left(x+7\right)^3

a)

6

b)

5

c)

1

d)

9

11.

What are the roots 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

12.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

13.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

14.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

15.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

16.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

17.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

18.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

19.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

20.

a)

b)

c)

d)

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

23.

Simplify

a)

x⁴/3

b)

3x¹⁰

c)

36x¹⁰

d)

3x⁴

24.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

25.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

26.

a)

(6v)³

b)

6v^3/2

c)

(6v)^3/2

d)

(6v)^2/3

27.

Write the expression in exponential form:
∛x²

a)

x^3/2

b)

x^2/3

c)

x^1/2

d)

x^1/3

28.

Write the expression in exponential form:
∜x⁵

a)

x^4/5

b)

x^5/4

c)

x⁵

d)

x^1/4

29.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

30.

a)

36

b)

18

c)

-18

d)

27

31.

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

32.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

33.

$3+3i+8-2i-7$

(a)

34.

√-4

a)

-2

b)

-2i

c)

2

d)

2i

35.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

36.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

37.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

38.

(-3-i)(6-i)

a)

-21-7i

b)

-19-3i

c)

-15-5i

d)

-17-9i

39.

Simplify:
i⁷

a)

i

b)

-i

c)

1

d)

-1

40.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

41.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

42.

What is a, the initial amount, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

43.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

44.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

45.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

46.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

47.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

Down 9 units

c)

Left 9 units

d)

Right 9 Units

48.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

49.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

50.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

51.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

52.

Describe the transformation from dotted to solid.

a)

f(x + 4)

b)

f(x - 4)

c)

f(x) + 4

d)

f(x) - 4

53.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

54.

what are the dimensions of matrix A?

a)

3x2

b)

2x4

c)

3x3

55.

In matrix A, find the element $a_{2,3}$

a)

2

b)

4

c)

0

56.

What are the dimensions of matrix P?

a)

4x3

b)

3x4

c)

3x3

57.

When given $a_{3,2}$ to find the element in the matrix you would go....

a)

down 2 right 3

b)

left 2 right 2

c)

down 3 right 2

58.

Find B-A

a)

-3 1
7 -1

b)

1 0
1 -4

c)

4 0
-6 1

d)

not possible because rows do not match columns

59.

What is the condition of adding and subtracting 2 matrices?

a)

Two matrices can be added and substracted even they have different size.

b)

Two matrices can be added and subtracted if they have the same size.

60.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

Algebra II Final Exam Review

Total questions: 60

Worksheet time: 3hrs 3mins

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