Free Printable Algebra 2 Second Semester Final Review 2020-21

1.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

2.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

3.

Simplify: $\frac{\left(4x^2y^3\right)^0}{8x^3}$

a)

$\frac{1}{8x^3}$

b)

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

c)

$\frac{4y^3}{8x}$

d)

$1$

4.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

5.

$64^{\frac{2}{3}}\ \$ is the same as

a)

$\ ^3\sqrt{64^2}\$ so the answer is 8

b)

$\ ^3\sqrt{64^2}\ \$ so the answer is 16

c)

$\ ^3\sqrt{64^2}\ \$ so the answer is 4

d)

$64\ \times\frac{2}{3}\ \ \$ so the answer is $\frac{32}{3}$

6.

$9^{\frac{1}{2}}$ is the same as

a)

$\sqrt{9}\$ so the value is 3

b)

$9\ \times\ \frac{1}{2\ }\$ so the value is 4.5

7.

$27^{\frac{1}{3}\ \ }$ is the same as

a)

$27\ \times\ \frac{1}{3}\$ so the value is 9

b)

$\ ^3\sqrt{27}\$ so the value is 3

8.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

9.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

10.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

11.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

12.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

13.

An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?

a)

101

b)

102

c)

103

d)

104

14.

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. Suppose f(20) = 49. Which of the following is true?

a)

After 20 days, there are 49 ants in the colony.

b)

After 49 days there are 20 ants in the colony.

c)

The amount of ants times 20 is 49.

d)

After 20 days the amount of ants remaining decreases by 49.

15.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

a)

The predicted increase in number of elephants in the refuge each year.

b)

The predicted decrease in number of elephants in the refuge each year.

c)

The number of years it will take for the elephant population to stop increasing.

d)

The initial amount of elephants in the park.

16.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.

What does the value 1.015 represent?

a)

The number of elephants was 1,015 in 1975.

b)

The number of elephants increases by 1.5% each year.

c)

The number of elephants increases by 101.5% each year.

d)

The number of elephants is multiplied by 1.015 each year.

17.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

18.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

19.

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

20.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

21.

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

22.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

Vertical compression with a factor of 2

c)

Vertical stretch with a factor of 2

d)

Right 2 Units

23.

Describe the transformation that occurred

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

a)

Up 5 Units

b)

Vertical compression with a factor of 1/5

c)

Vertical stretch with a factor of 1/5

d)

Down 5 Units

24.

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

25.

Describe the transformation from dotted to solid.

a)

f(x + 4)

b)

f(x - 4)

c)

f(x) + 4

d)

f(x) - 4

26.

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

27.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

28.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

29.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

30.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

31.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

32.

Find the domain for the given graph.

a)

b)

c)

d)

33.

What is the range of this function?

a)

b)

c)

d)

34.

Solve

a)

104/5

b)

124/5

c)

25

d)

14/5

35.

Solve.

[Hint: You can always check answer choices]

a)

x=2

b)

x=9

c)

x=4

d)

x=1

36.

Solve for x:
(2x - 1)^3/4 + 9 = 36

a)

27

b)

13

c)

41

d)

82

37.

Solve for x:
7 + x^3/2 = 71

a)

2

b)

4

c)

16

d)

8

38.

Given that $f\left(x\right)$ is an even function and that $f\left(-3\right)=19$ , which statement must also be true?

a)

$f\left(3\right)=19$

b)

$f\left(-3\right)=-19$

c)

$f\left(3\right)=-19$

d)

$f\left(19\right)=-3$

39.

Given that $g\left(x\right)$ is an odd function and that $g\left(2.5\right)=4$ , which statement must also be true?

a)

$g\left(-2.5\right)=-4$

b)

$g\left(2.5\right)=-4$

c)

$g\left(-2.5\right)=4$

d)

$g\left(4\right)=2.5$

40.

$y=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

41.

$y=8x^{12}-8x^4+6x+22$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

42.

$y=12x^7+6x^5-8x^3+4x$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

43.

The function in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

44.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

45.

Given the following table of values, construct the function that represents the sequence.

a)

y = 3(4)^x

b)

y = 3x + 4

c)

y = 4(3)^x

d)

y = 4x + 3

46.

Write the equation of the exponential function for the given table.

a)

y = 2(1/3)^x

b)

y = -2(1/3)^x

c)

y = 1/3(2)^x

d)

y = 2(-1/3)^x

47.

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

48.

Describe the end behavior of the graph.

a)

x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty;\ x\ \rightarrow\ \infty,\ y\ \rightarrow-\infty

b)

$x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty;\ x\ \rightarrow-\infty,\ y\ \rightarrow\ \infty$

c)

$x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty;\ x\ \rightarrow-\infty,\ y\ \rightarrow\ 0$

d)

$x\ \rightarrow\ \infty,\ y\ \rightarrow\ 0;\ x\ \rightarrow-\infty,\ y\ \rightarrow\ \infty$

49.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

50.

Which of the following is a perfect square trinomial?

a)

x² – 18x + 81

b)

x² – 12x + 6

c)

x² + 20x + 40

d)

x² – 12x – 36

51.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

52.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

53.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

54.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

55.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

Algebra 2 Second Semester Final Review 2020-21

Total questions: 55

Worksheet time: 3hrs 13mins

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