Free Printable Algebra 2 Spring Final Review 2023

1.

What are the first 5 terms of the given sequence?

$a_n=5n+3$

(a)

2.

Which of the following is an example of an arithmetic sequence?

a)

4, 8, 16, 32, 64

b)

1, 2, 4, 7, 11

c)

15, 13, 11, 9, 7

d)

3, 6, 12, 24, 48

3.

Which sequence is NOT an arithmetic sequence?

a)

12, 18, 24, 30,...

b)

10, 3, -4, -11,...

c)

2, 4, 8, 16,...

d)

16, 20, 24, 28,...

4.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

5.

Define arithmetic sequences.

a)

A sequence whose terms change by adding the same number each time.

b)

A sequence whose terms change by multiplying the same number each time.

c)

A sequence whose terms change by dividing the same number each time.

d)

A list of numbers that often (but not always) form a pattern.

6.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

7.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

8.

Select the explicit rule that represents the sequence.

a)

a_n = 14(-3)(n - 1)

b)

a_n = 3 + 14(n - 1)

c)

a_n = 14 - 3(n - 1)

d)

a_n = -3 + 14(n - 1)

9.

Select the explicit rule that represents the sequence.

a)

a_n = 6 + 5(n - 1)

b)

a_n = 4 + 6(n - 1)

c)

a_n = 6 - 4(n - 1)

10.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

11.

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

a)

a_n = a_n-1 x 3

b)

a_n = 5(3)^n-1

c)

a_n = 3(5)^n-1

d)

a_n = 5 + (n-1)3

12.

Write the explicit rule for the following geometric sequence:

2, -12, 72, ...

a)

a_n = 72(-6)^n-1

b)

a_n = 2(-6)^n-1

c)

a_n = 2(6)^n-1

d)

a_n = 72(-6)^n-1

13.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

14.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

15.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

16.

(a)

17.

Evaluate - use the i key on your calculator.

(a)

18.

This symbol is:

a)

a funky looking "E"

b)

theta

c)

pi

d)

sigma

19.

Calculate the final sum/total of the series.

a)

6

b)

21

c)

9

d)

2

20.

Is this sum finite or infinite?

a)

Finite, because there are only 11 terms to add up.

b)

Infinite, because there are an infinite number of terms to add up.

21.

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

a)

Permutation

b)

Combination

c)

Neither

22.

If all items chosen are treated the same it is a ....

a)

Comparision

b)

Permutation

c)

Combination

d)

Position

23.

If all items chosen are treated differently it is a ...

a)

Comparision

b)

Permutation

c)

Combination

d)

Position

24.

Permutation, combination, or neither? Rob and Mary are planning trips to 9 countries this year. There are 13 countries they would like to visit. They are deciding which countries to skip. (order of going doesn't matter)

a)

combination

b)

permutation

c)

neither

25.

What does ₁₀P₅mean?

a)

Permutations with 5 choices and 10 positions

b)

Permutations with 10 choices and 5 positions

c)

Permutations with 5 numbers and 10 operations

d)

Permutations with 5 hot dogs and 10 drinks

26.

Is the order of arrangement important? Find the number of ways to form a team of three players for a game out of a group of 10 individuals. Each player has a specific position to play.

a)

Yes

b)

No

27.

Determine whether the following scenario is a permutation or a combination: Selecting a lead and an understudy for a school play.

a)

Combination

b)

Permutation

28.

In the orchestra, there are eight violinists in the front row. How many different ways can they be seated? Violinists are seated by rank; 1st chair, 2nd chair, etc.

a)

40320

b)

1

c)

64

d)

8

29.

The ski club with ten members is to choose three officers for captain, co-captain and secretary. How many ways can those offices be filled?

a)

720

b)

120

c)

10!

30.

Eva has eight glasses of water. In how many different orders can the glasses of water be arranged?

a)

8

b)

64

c)

8!

d)

56

31.

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?

a)

90

b)

100

c)

12

d)

24

32.

A disc jockey has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs? Once a song is played it can't be played again.

a)

84

b)

504

c)

9!

d)

3!

33.

Permutation, combination, or neither? Rob and Mary are planning trips to 9 countries this year. There are 13 countries they would like to visit. They are deciding which countries to skip. They don't have a preference for where they go first.

a)

combination

b)

permutation

c)

neither

34.

What does ₁₀P₅mean?

a)

Permutations with 5 choices and 10 positions

b)

Permutations with 10 choices and 5 positions

c)

Permutations with 5 numbers and 10 operations

d)

Permutations with 5 hot dogs and 10 drinks

35.

Permutation, combination, or neither?
The batting order for seven players on a 12 person team.

a)

combination

b)

permutation

c)

neither

36.

At a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

a)

180

b)

23

c)

12

d)

60

37.

A coin is tossed 5 times. How many total outcomes are possible?

a)

32

b)

10

c)

5

d)

2

38.

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?

a)

32

b)

192

c)

40,320

d)

51,200

39.

Simplify this

a)

6

b)

30

c)

1/5

d)

1/6

40.

What is 4! called?

a)

Fabulous Four

b)

Final Four

c)

Four Factorial

d)

Four Factored

41.

To find the .................. you put all numbers in order from least to greatest and find the number that is in the middle.

a)

Mean

b)

Median

c)

Mode

d)

Range

42.

Determine the median and mode for the set of data.

25, 15, 30, 25, 20, 15, 24

a)

median: 22, mode: none

b)

median: 22, mode: 15 and 25

c)

median: 24, mode: none

d)

median: 24, mode: 15 and 25

43.

Determine the mean for the set of data.

23, 30, 26, 25, 21

a)

21

b)

25

c)

26

d)

30

44.

Find the median of this set of numbers:
7, 6, 19, 12, 16, 19, 19, 6

a)

16

b)

14

c)

15

d)

6

45.

Find the mode of this set of numbers:
19, 19, 9, 11, 13, 20, 19, 10

a)

9

b)

19

c)

13

d)

20

46.

What does this symbol represent?

a)

Standard Deviation

b)

Variance

c)

Mean Absolute Deviation

d)

Sigma

47.

1. Which of the following illustrations represents normal distribution?

a)

b)

c)

d)

48.

If the standard deviation of a data set is 4, what is the variance?

a)

2

b)

16

c)

4

49.

Solve: $\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}$

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

50.

Which value of x makes the expression undefined?

a)

-2

b)

2

c)

-6

d)

-3

51.

$\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$

State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

52.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

53.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

54.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

55.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

56.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

57.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

58.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

59.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

60.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

61.

Expand the logarithm
log₁₀ 7x

a)

(log₁₀ 7)(log₁₀ x)

b)

log₁₀ 7 + log₁₀ x

c)

7log₁₀ x

d)

xlog₁₀ 7

62.

In Change of Base Formula, $\log_ba$ becomes: (select all that applies)

a)

$\frac{\log\left(a\right)}{\log\left(b\right)}$

b)

$\frac{\log\left(b\right)}{\log\left(a\right)}$

c)

$\frac{\ln\left(b\right)}{\ln\left(a\right)}$

d)

$\frac{\ln\left(a\right)}{\ln\left(b\right)}$

63.

What is $\log_22.9$ ? (use change of base!)

a)

1.536

b)

2.685

c)

12

d)

0.987

64.

In the expression log 25, the base of the log is equal to

a)

10

b)

1

c)

e

d)

2

65.

4^{3x + 5} = 16

a)

-5/3

b)

-1

c)

-3/2

d)

2/3

66.

a)

A

b)

B

c)

C

d)

D

67.

a)

A

b)

B

c)

C

d)

D

Algebra 2 Spring Final Review 2023

Total questions: 67

Worksheet time: 11hrs 10mins

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