Free Printable Algebra 2 Spring 25 Review

1.

4^{3x + 5} = 16

a)

-5/3

b)

-1

c)

-3/2

d)

2/3

2.

Solve log₂ (2 - 2x) + log₂ (1 - x) = 5

a)

4

b)

5

c)

-2

d)

-3

3.

Solve log₅ (x + 3) = log₅ x + log₅ 3

a)

3/2

b)

9/2

c)

2/3

d)

No Solution

4.

Solve 2.8^x = 41

a)

0.277

b)

3.607

c)

-0.282

d)

3.684

5.

Solve log₂ (x² - 1) = 3 + log₂ (x - 1)

a)

4

b)

2

c)

1

d)

7

6.

Solve log₉ (x - 4) + log₉ (x + 1) = log₉ (x + 5) + log₉ (x - 6)

a)

17/2

b)

-9/16

c)

13

d)

-8

7.

Solve 4^{2x - 1} = 5^{x + 2}

a)

2.167

b)

3.959

c)

2.008

d)

0.253

8.

Solve ln (x - 2) - ln (3x) = 0

a)

-1

b)

2

c)

e

d)

e⁵

9.

Solve 8 ^. 3^x = 5

a)

0.506

b)

2.337

c)

-0.516

d)

-0.428

10.

Solve e^2x = -x + 2 using a graphing utility

a)

0.273

b)

1.727

c)

0.448

d)

2.448

11.

Solve for x.

$11^x=74$

a)

4.8816

b)

1.7949

c)

1.8692

d)

4.3041

12.

Solve for x.

$3^{\left(x-7\right)}-3=24$

a)

3

b)

8

c)

10

d)

No solution

13.

Solve the following exponential equation:
$5^{-3x}=125$

a)

$x=-1$

b)

$x=-4$

c)

$x=-3$

d)

$x=1$

14.

7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

15.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

16.

Solve for x:

5 e^x= 1.5

a)

1.3

b)

0.23

c)

-3.07

d)

-1.6

17.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

18.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

19.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

20.

Solve.
e^4x=12

a)

2.48

b)

9.94

c)

0.62

d)

3

21.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What is your total return?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

22.

You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?

a)

$13,693.90

b)

$1,363.90

c)

$72,693.90

d)

$73,793.90

23.

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

24.

Principal: $999
Interest Rate: 5.45%
Time: 19 years
Compounded Quarterly
State the future account balance.

a)

$2794.10

b)

$2738.11

c)

$2774.98

d)

$2807.11

25.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much total will they have paid after 30 years?

a)

$412,749.79

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

26.

Karla invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Karla earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

27.

Courtney saved up $2,200 working as a waitress over the summer. She put this money into a bank account that earned 5.2% interest and is compounded daily. How much will she have in her account at the end of 4 years?

a)

$2201.25

b)

$2694.55

c)

$2707.45

d)

$2708.63

28.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

29.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

30.

Heather

invested $8,000 in a 4-year Certificate of Deposit (CD) that pays 4.1% interest

compounded annually. What is the value of the CD at the end

of the 4 years?

a)

$9,394.92

b)

$9,312.00

c)

$1394.00

d)

$1312.00

31.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

32.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

33.

Which is the correct ratio?

a)

sin 28 = x/14

b)

cos 28 = x/14

c)

tan 28 = x/14

d)

tan 28 = 14/x

34.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

35.

Which trig equation would you use to find the measure of the indicated angle (?)

a)

$\cos\left(?\right)=\frac{23}{28}$

b)

$\sin\left(?\right)=\frac{23}{28}$

c)

$\tan\left(?\right)=\frac{23}{28}$

d)

$\tan\left(?\right)=\frac{28}{23}$

36.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

32°

b)

44°

c)

61°

d)

50°

37.

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle

a)

33°

b)

49°

c)

39°

d)

41°

38.

a)

$81\degree$

b)

$93\degree$

c)

$82\degree$

d)

$79\degree$

39.

a)

$m\angle C\ =62\degree,\ m\angle A=42\degree,\ b=19.1$

b)

$m\angle C\ =60\degree,\ m\angle A=44\degree,\ b=19.1$

c)

$m\angle C\ =54\degree,\ m\angle A=50\degree,\ b=19.1$

d)

$m\angle C\ =54\degree,\ m\angle A=50\degree,\ b=20.5$

40.

a)

$m\angle A\ =30\degree,\ b=28.9,\ c=46.1$

b)

$m\angle A\ =30\degree,\ b=28.9,\ c=42.9$

c)

$m\angle A\ =30\degree,\ b=28.9,\ c=42$

d)

$m\angle A\ =30\degree,\ b=27.6,\ c=46.1$

41.

What kind of sequence is illustrated below?
400, 200, 100, 50, 25, ...

a)

Arithmetic

b)

Geometric

c)

Neither

42.

Which kind of sequence has a common difference?

a)

Arithmetic

b)

Geometric

43.

What is the 8th term in the sequence below?
3, 9, 27, 81, ...

a)

19,683

b)

6,561

c)

2,187

d)

729

44.

The next term of the series 11,8,5,2 is...

a)

-1

b)

-2

c)

1

d)

2

45.

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

a)

Arithmetic

b)

Geometric

c)

Neither

46.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

47.

Is the sequence 2, 4, 12, 48,... geometric?

a)

yes

b)

no

48.

Evaluate the Arithmetic Series

a)

105

b)

210

c)

100

d)

420

49.

Find the sum of the infinite geometric series, if it exists:

5 + 4 + 3.2 + 2.56 + ...

a)

25

b)

5

c)

-1

d)

0.8

50.

Determine whether the sequence could be geometric or arithmetic:

6, 10, 15, 21, ...

a)

Geometric with r = 5/3

b)

Arithmetic with d = 4

c)

Geometric with r = 4

d)

Neither

51.

What is the sum of the first 10 terms for the following geometric series:
2-6+18-54+...

a)

59048

b)

-29524

c)

524288

d)

3069

52.

What is the value of r for the following sequence.
1/2+1/4+1/8+1/16+...

a)

2

b)

-2

c)

1/2

d)

-1/2

53.

Find the sum for the following series.

a)

1.49

b)

3.14

c)

1.33

d)

1.66

54.

Evaluate the series.

a)

36

b)

85

c)

35

d)

86

55.

Which sequence is represented by the equation 2(7)^n-1 ?

a)

7, 14, 28, 56...

b)

2, 14, 98, 686...

c)

2, 9, 16, 23...

d)

7,9,11,13...

56.

Find the indicated sum of the series if $a_1=-3,\ r=-2,\ n=6.$

a)

96

b)

63

c)

-33

d)

$\frac{-189}{2}$

57.

Find the indicated sum of the series if $a_1=58,\ n=18,\ a_n=14$

a)

648

b)

666

c)

630

d)

612

58.

Find the sum of the first 25 terms of the series: 6+14+22+30+...

a)

450

b)

2650

c)

2550

d)

550

59.

Which series are Arithmetic? (select ALL that apply)

a)

2 + 4 + 8 + 16...

b)

7 + 15 + 23 + 31...

c)

80 + 68 + 56 + 44...

d)

1 + 3 + 7 + 11...

e)

-10 + (-8) + (-6) + (-4)...

60.

Find the sum of the first 718 terms for the series

2 + 4 + 6 + ... + 1436

a)

1,797

b)

116,236

c)

321,704

d)

516,242

61.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

62.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

63.

Multiply

a)

25
25
5

b)

-25
25
-5

c)

-10
-10
-6

d)

10
10
6

64.

Calculate the determinant

a)

0

b)

none

c)

-32

d)

-8

65.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The column of the 1st must equal the row of the 2nd.

66.

Find the determinant of the matrix

a)

-28

b)

-20

c)

20

d)

0

67.

Multiply

a)

1 2
6 -8

b)

-3 -5
-5 -11

c)

-2 8
-6 -12

d)

2 -3
5 -2

68.

Dimensions?

a)

a

b)

b

c)

c

d)

d

69.

Find A−B

a)

-3 1
7 -1

b)

1 0
1 -4

c)

-4 0
6 -1

d)

not possible because rows do not match columns

70.

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

71.

Perform the indicated operation. If it’s not possible, select Not Possible.

a)

1 3
9 16

b)

1 3
9 -16

c)

-1 3
9 -16

d)

Not Possible

72.

Multiply the matrices

a)

A

b)

B

c)

C

d)

D

73.

Calculate the determinant

a)

0

b)

none

c)

-32

d)

-8

74.

Find the determinant's value

a)

-18

b)

-23

c)

-2

d)

2

75.

Calculate the determinant

a)

0

b)

-15

c)

-70

d)

10

76.

a)

a

b)

b

c)

c

d)

d

77.

Can the operation be performed?

a)

Yes

b)

No

c)

Sometimes

d)

only your teacher knows

78.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

79.

Calculate the determinant

a)

13

b)

-3

c)

-5

d)

13

80.

Solve the system using Cramer's Rule. Answers are written in the following form (x,y).

a)

(5,1)

b)

(1,5)

c)

(5,-1)

d)

(-1,5)

81.

Solve systems using Cramer's Rule. Answers are written in following form (x,y).

a)

(-1,1)

b)

(-1,-1)

c)

(1,-1)

d)

(1,1)

82.

Solve systems using Cramer's rule. Answers are written in the following form (x,y).

a)

(10,-8)

b)

(-10,8)

c)

(-8,10)

d)

(8,-10)

83.

Solve using Cramer's Rule...

$2x+y-3z=-5$

$5x+2y-2z=8$

$3x-3y+5z=17$

What is the y-coordinate of the SOLUTION?

(a)

84.

How do you graph a circle given its equation in standard form?

a)

Connect the points on the graph to form a circle

b)

Plot the center and use the radius to plot points around it to form the circle.

c)

Use the equation to find the slope and intercept

d)

Graph the equation as a straight line

85.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

86.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

87.

What is the center of the given equation?

a)

(h, k) = (4, 3)

b)

(h, k) = (-4, -3)

c)

(h, k) = (-4, 3)

d)

(h, k) = (4, -3)

88.

Identify the center and the length of a and b.

a)

C: (0,4) a= 25, b=4

b)

C: (0,0) a= 4, b=25

c)

C: (0,5) a= 2, b=5

d)

C: (0,0) a= 5, b=2

89.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

90.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

(3, -5) and (3, 7)

d)

(3, 1)

91.

What is the center of this hyperbola?

a)

(4,-2)

b)

(4,2)

c)

(-2,4)

d)

(2, 4)

e)

(7.5,3)

92.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Line

d)

None of these

93.

What type of conic section is $3x^2-y^2-11x+4=0$ ?

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

94.

What type of conic section is

2x^2+2y^2-4x-16y-9=0

?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

95.

What is the sample standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

6.89

b)

10.1

c)

7.26

d)

9

96.

All of the below sets have the same mean.

Set 1-Standard Deviation=3.1

Set 2-Standard Deviation=4.9

Set 3-Standard Deviation=1.7

Set 4-Standard Deviation=3.2

Which set of data probably has the points closest to the mean?

a)

1

b)

2

c)

3

d)

4

97.

Four data sets are shown below.
Set 1: {10, 19, 38, 50, 51}
Set 2: {5, 21, 26, 39, 51}
Set 3: {9, 38, 50, 50, 51}
Set 4: {5, 28, 28, 28, 51}
Which data set has the largest standard deviation?

a)

Set 1

b)

Set 2

c)

Set 3

d)

Set 4

98.

What does this symbol represent?

a)

Population Standard Deviation

b)

Sample Standard Deviation

c)

Mean Absolute Deviation

d)

Mean

99.

What is the sample standard deviation for the data given:

{12, 13, 29, 18, 61, 35, 21}

a)

293.67

b)

15.87

c)

17.14

d)

41.98

100.

Find the mean of these numbers:
5,11,2,12,4,2

a)

4.1

b)

6

c)

4.5

d)

4

101.

What is the mean?

a)

# happening the most

b)

the number in the middle

c)

biggest-smallest

d)

the average

102.

To find the _________ you add up all the numbers and then divide by how many numbers you have.

a)

Mean

b)

Median

c)

Mode

d)

Range

103.

Roger bowled 7 games last weekend. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the range of Roger's scores?

a)

193

b)

127

c)

60

d)

66

104.

The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for

snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1,

14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6

What are the mean and SAMPLE standard deviation for these data, to the nearest hundredth?

a)

mean = 9.46; standard deviation = 3.74

b)

mean = 9.46; standard deviation = 3.85

c)

mean = 9.45; standard deviation = 3.74

d)

mean = 9.45; standard deviation = 3.85

105.

What is the sample variance for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

47.47

b)

102.01

c)

52.77

d)

81

106.

For a population of five university students with GPAs of 2.5, 2.3, 1.7, 1.4, and 1.1, find the population standard deviation.

a)

0.53

b)

0.41

c)

0.35

d)

0.22

107.

Given a variance of 64, what is the standard deviation?

a)

8

b)

4096

c)

0

d)

6.8

108.

the square of this value will give the variance

a)

standard deviation

b)

variance

c)

mean

d)

median

109.

Which measure of central tendency would best represent this data?

a)

Mean

b)

Median

c)

Mode

d)

Range

110.

The height of three basketball players is 210 cm, 220 cm and 191 cm.
What is their average height?

a)

210

b)

207

c)

220

d)

200

111.

Find the mean giraffe heights.

a)

15

b)

15.5

c)

15.7

d)

28.2

112.

Find the mean of these numbers:
2, 57, 38, 42, 6

a)

29

b)

38

c)

50

d)

145

113.

Which of the following is a measure of variability?

a)

mean

b)

median

c)

mode

d)

standard deviation

114.

If test scores for a class are: 100, 100, 90, 90, 80, 80, 70, 70, 60, and 60, what are the mean and sample standard deviation?

a)

mean = 80, stdev = 14.9

b)

mean = 70, stdev = 14.9

c)

mean = 80, stdev = 13.9

d)

mean = 80, stdev = 12.9

e)

mean = 85, stdev = 14.9

115.

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the z-score for a player who runs a time of 5.6 seconds?

a)

-1.33

b)

1.33

c)

0.88

d)

1.02

116.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What is the probability that in a week there would be fewer (less) than 5 accidents?

a)

0.6915

b)

0.1762

c)

0.8238

d)

-0.93

117.

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What is the probability that in a week there would be more than 7 accidents?

a)

0.3446

b)

0.2856

c)

0.4

d)

0.6554

118.

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.

If waist sizes are normally distributed, estimate the probability that a teenager will have a waist size greater than 31 inches.

a)

.924

b)

.105

c)

.16

d)

.076

119.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

What is the approximate probability that a product will last between 12 and 15 days?

a)

.68

b)

.34

c)

.16

d)

.025

120.

Which is NOT true about the standard normal distribution?

a)

It is bell-shaped.

b)

It is not skewed left or right.

c)

The total area under the curve is 1.

d)

It is asymmetrical.

121.

The mean July daily rainfall in Hulu Kinta is 10 mm and the standard deviation is 1.5 mm

Assume that this data is normally distributed.

How many days in July would you expect the daily rainfall to be less than 8.5 mm? (Find the z-score, and look it up. Then, multiply by 31 days!)

a)

5

b)

6

c)

7

d)

10

122.

If the value we are looking for is smaller than the mean, the value of z is:

a)

Not enough information

b)

Negative

c)

Positive

d)

0

123.

If the value we are looking for is the same as the mean, the value of z is:

a)

Not enough information

b)

Positive

c)

Negative

d)

0

124.

What's the probability x < 13?

(Mean = 10, Variance = 4)

a)

0.9332

b)

0.2266

c)

0.7734

d)

0.0668

125.

What's the probability x > 17?

(Mean = 15, Standard dev = 3)

a)

0.7486

b)

0.7454

c)

0.2514

d)

0.2546

126.

According to an investigation, the probability of rainfall on Mountain X in May is 0.45.

Calculate the probability that Mountain X will have two consecutive rainy days in May.

a)

0.90

b)

0.55

c)

0.3025

d)

0.2025

127.

A box contains 12 bulbs where two of the bulbs are burnt. Two bulbs are selected at random from the box.

Calculate the probability of getting two burnt bulbs.

a)

1/36

b)

1/66

c)

15/22

d)

25/36

128.

The probability of Kam Seng passing his Physics and Chemistry tests are 0.58 and 0.42 respectively.

Calculate the probability that

a) Kam Seng passes both tests.

a)

0.2345

b)

0.2436

c)

0.2433

d)

0.2536

129.

The probability of Kam Seng passing his Physics and Chemistry tests are 0.58 and 0.42 respectively.

Calculate the probability that

b) Kam Seng passes only one test

a)

0.4128

b)

0.5

c)

0.5128

d)

0.5118

130.

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

a)

462

b)

55440

c)

55

d)

1000

131.

There are 125 juniors at the high school. How many ways can they elect a president, vice president,and secretary?

a)

1906500

b)

317750

c)

375

d)

1953125

132.

Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choose three?

a)

336

b)

56

c)

24

d)

100

133.

There are 14 candy bars for sale. How many ways can Andy choose five of them?

a)

240240

b)

2002

c)

87178291200

d)

70

134.

There are 12 kinds of Girl Scout cookies for sale. How many ways can Rachel choose three different kinds to buy?

a)

220

b)

36

c)

1320

d)

100

135.

Brianna’s school day consists of six classes. How many different ways can her schedule be arranged?

a)

720

b)

36

c)

100

d)

500

136.

If Lucas owns 11 hoodies,how many ways can he choose four to bring on vacation?

a)

44

b)

7920

c)

330

d)

121

137.

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

a)

324

b)

4896

c)

816

d)

54

138.

Rob is one of seven children in his family. How many ways can his parents choose four siblings to do chores?

a)

35

b)

28

c)

840

d)

10

139.

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?

a)

84

b)

504

c)

9!

d)

3!

140.

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

a)

6!

b)

120

c)

20

d)

3!

141.

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!

142.

Members of 6 different school organizations decorated floats for the homecoming parade. How many different ways can first, second, and third prize be awarded?

a)

18

b)

120

c)

36

d)

18

143.

A shelf can hold 7 trophies. How many ways can the trophies be arranged if there are 10 trophies available?

a)

60,480

b)

10,000,000

c)

604,800

d)

100

144.

How many ways can you listen to 3 songs from a CD that has 12 selections?

a)

1320

b)

33

c)

36

145.

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

a)

324

b)

4896

c)

816

d)

54

Algebra 2 Spring 25 Review

Total questions: 145

Worksheet time: 24hrs 10mins

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