Free Printable Semester 2 Final Review

Worksheets

Semester 2 Final Review

Total questions: 162

Worksheet time: 5hrs 1mins

Name

Class

Date

Find the probability of drawing a 10 from a standard deck of 52 cards.

1 out of 52

13 out of 52

26 out of 52

4 out of 52

Mrs. Elder has a box containing 6 cracker, 3 peppermints, 6 bubble gums, and 3 licorice sticks. If she randomly chooses one piece from the box, what is the probability that she will grab a cracker or a peppermint?

peppermint

1/6

1/2

1/3

Mrs. Moreno has a box containing 6 lipsticks, 4 eye shadows, 6 eye liners, and 5 mascaras. If she randomly chooses one item from the box, what is the probability that she will grab a lipstick?

3/7

15/21

5/7

6/21

If 33% of the students at Harnett Central have a pet, then what is the probability of the complement of this event?

33%

77%

67%

50%

Event A has a probability of 0.3. What is the probability of the complement of Event A?

30%

3/100

7/100

0.7

What is the complement of spinning purple on this spinner?

Not green

Purple

Not purple

Orange, red, or yellow

What is an outcome?

The result of an experiment

The chance or likelihood of an event

A fraction, decimal, or a percent

An activity that gives various results

A set of all possible outcomes is known as -

a list

a complement

a sample space

an event

The letters that form the word MATHEMATICS are placed in a bowl. What is the probability of choosing a letter that is a vowel?

8/121

4/11

2/11

4/121

10.

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”?

2/7

5/49

5/7

10/49

11.

The probability of an event occurring, P(A), can be expressed as a fraction, decimal, or percent.

True

False

12.

If you choose from the following M & M colors, what is the probability that you choose blue?
5 green
6 yellow
8 blue
7 brown

8/26

4/13

8/25

1/3

13.

What is the probability of spinning green or blue?

5/12

1/2

3/4

14.

What is the probability of spinning red?

5/12

1/2

3/4

15.

What is the probability of spinning green?

1/4

1/2

3/4

16.

What is the probability of spinning red?

1/2

3/4

17.

Probability can be between what two numbers?

10 and 20

0 and 100

0 and 1

All Numbers are possible

18.

Find the probability of rolling a 7 on a single die.

1/6

7/6

7/7

19.

Find the probability of rolling greater than a 1 on a single die.

6/6

5/6

4/6

1/6

20.

What is the probability of spinning an even number?

16 2/3%

33 1/3%

50%

75%

21.

Clara brings a box of donuts to work that contains one donut in each flavor. First the secretary chooses one. Then the office manager makes a selection.

Dependent

Independent

22.

Allie downloads a song from an online service. A few minutes later, a customer in another city searches for a song on the same site.

Dependent

Independent

23.

Reid picks a card at random. Without putting the first card back, he picks a second card at random.

Dependent

Independent

24.

During P.E. class, one team is picking softball gloves from the class bucket. Lindsey chooses a glove first, followed by Megan.

Dependent

Independent

25.

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement.P(both marbles are purple)

2/9

1/3

1/2

1/4

26.

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.
P(white, then purple, then black)

1/36

2/39

5/41

6/43

27.

Christopher picks a marble at random. Without putting the first marble back, he picks a second marble at random.

Independent

Dependent

28.

Pablo chooses a colored marble from a mixed bag and writes down the color. Pablo leaves it out and then draws another.

Independent

Dependent

29.

Clara picks a card at random, puts it back, and then picks another card at random.

Independent

Dependent

30.

Clare picks a marble at random, puts it back, and then picks another marble at random.

Dependent

Independent

31.

Rolling a 15 on a number cube is

Impossible

Certain

Unlikely

Equally Likely

32.

P(not A) =
*Remember to simplify.*

6/8

3/4

2/8

1/4

33.

A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a lemon?

1/10

3/10

30%

34.

Determine the likelihood of the following event:
Drawing a red card from a standard deck of cards

1/2

13/52

1/4

4/52

35.

What is the probability of selecting an orange candy?

25%

50%

100%

36.

What is the probability of flipping a coin and getting heads?

1/2

1/3

1/4

Never, Tails never fails.

37.

Experimental Probability is:

What Will happen

What actually happens

What should happen

What I think Happens

38.

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?

3/10

3/9

1/9

1/3

39.

The chart below represents the number of marbles in a jar.
P(green) =

5/19

10/28

5/14

40.

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

5/6

1/2

1/3

1/6

41.

Gabriel has these cans of soup in his kitchen cabinet.

• 2 cans of tomato soup

• 3 cans of chicken soup

• 2 cans of cheese soup

• 2 cans of potato soup

• 1 can of beef soup

Gabriel will randomly choose one can of soup. Then he will put it back and randomly choose another can of soup. What is the probability that he will choose a can of tomato soup and then a can of cheese soup?

2/5

1/25

2/45

1/5

42.

A bag contains:

• 5 red marbles

• 6 blue marbles

• 3 green marbles

• 4 black marbles

• 2 yellow marbles

A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction for the number of times a green or black marble will be drawn? (Hint: Use a Proportion)

43.

Melissa rolled a number cube that has sides labeled 1 to 6. What is the probability that she rolled a 2 or a 3?

1/6

1/3

1/2

3/4

44.

A bag contains 3 red marbles, 2 blue marbles, and 10 green marbles. If Sam draws a marble from the bag, what is the probability that it is a blue marble?

2/15

1/5

2/3

1/7

45.

Tamara can choose between 5 pairs of earrings and 7 pairs of necklaces. How many outcomes are in the sample space?

46.

Alex flips a coin 3 times. What is the probability that he flips tails all three times?

1/2

1/6

1/8

1/4

47.

Giselle rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that both number cubes show a 4?

1/24

1/12

1/6

1/36

48.

A bag has 2 yellow marbles and 8 brown marbles. Nancy takes out two marbles without replacing the marbles. What is the probability that they will both be yellow?

2/19

1/10

1/25

1/45

49.

Jorge flips a coin and rolls a number cube that has the numbers 1 through 6. What is the probability that Jorge will flip a heads on the coin and an odd number on the number cube?

1/4

2/3

1/6

1/12

50.

Matt spins a spinner that has equally sized blue, red, green, and yellow sections. What is the probability of spinning a pink?

1/2

1/4

51.

The experimental probability that Lily will win a game is 4/9. if she plays the game 90 times, how many times can she expect to win? (HINT Set up a proportion: Part/Whole = Part/Whole)

52.

Christopher flipped a coin fifteen times. She flipped heads 8 times and tails 7 times. What is the experimental probability that Christopher will flip tails on his next flip?

8/15 or about 53%

7/15 or about 47%

1/2 or 50%

1/4 or 25%

53.

The probability that Morgan misses a free throw is 12%. If she makes 85 free throws, about how many of them can she expect to miss?

54.

John conducted an experiment will total number of 50 trials. The results are shown on the table. If he decided to conduct the trails again at 5000, what is the probability that John would draw a blue card?

200

1,000

2,000

100

55.

Kim will spin the spinner twice. What is the probability it will land on red both times?

25/144

5/12

10/24

1/2

56.

Growth or Decay? Increase

Growth

Decay

57.

Growth or Decay? Decrease

Growth

Decay

58.

Growth or Decay? Half-Life

Growth

Decay

59.

Growth or Decay? The population of HomeTown is 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%.

Growth

Decay

60.

Growth or Decay? Newtons Law of Cooling states that the rate of cooling of an object is

proportional to the temperature difference between the object and its surroundings.

A roast turkey is taken from the oven when tis temperature has reached 185 F

and is placed on a table in a room where the temperature is 75 F.

Growth

Decay

61.

Growth or Decay? A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable environment. Six hours later, he measures 450 bacteria.

Growth

Decay

62.

Growth or Decay? Carbon-14 has a half-life of 5730 years. You are presented with a document which purports to contain the recollections of a Mycenaean soldier during the Trojan War. The city of Troy was finally destroyed in about 1250 BC, or about 3250 years ago. Carbon-dating evaluates the ratio of radioactive carbon-14 to stable carbon-12. Given the amount of carbon-12 contained a measured sample cut from the document, there would have been about 1.3 × 10–12 grams of carbon-14 in the sample when the parchment was new, assuming the proposed age is correct. According to your equipment, there remains 1.0 × 10–12 grams. Is there a possibility that this is a genuine document? Or is this instead a recent forgery? Justify your conclusions.

Growth

Decay

63.

Growth or Decay? A certain type of bacteria, doubles in population every 6.5 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?

Growth

Decay

64.

Growth or Decay? Radio-isotopes of different elements have different half-lives. Magnesium-27has a half-life of 9.45 minutes. What is the constant for Magnesium-27? Round to five decimal places.

Growth

Decay

65.

Growth or Decay? A strain of bacteria growing on your desktop doubles every 5 minutes. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 96 minutes?

Growth

Decay

66.

Growth or Decay? Some people are frightened of certain medical tests because the tests involve the injection of radioactive materials. A hepatobiliary scan of my gallbladder involved an injection of 0.5 cc's (or about one-tenth of a teaspoon) of Technetium-99m, which has a half-life of almost exactly 6 hours. While undergoing the test, I heard the technician telling somebody on the phone that "in twenty-four hours, you'll be down to background radiation levels." Figure out just how much radioactive material remained from my gallbladder scan after twenty-four hours.

Growth

Decay

67.

Growth or Decay? A patient is given a 300 mg dose of medicine that degrades by 25% every hour. What is the remaining drug concentration after a day?

Growth

Decay

68.

Simplify

(x-9)/(x+9)

1/(x-9)

(x+9)

1/(x+9)

69.

Multiply and Simplify

4(x+3)/(x+2),

(x+2)/4(x+1)

(x+2)/4(x+3),

4(x+1)/(x+2),

70.

Multiply and Simplify

2(x+8) / (x-2)

(x-2)

(x+4) / (x-6)

(x-4) / (x+8)

71.

Divide and Simplify

1/6

x+10/ 6x+60

x+8/ 6x+60

(x+10)(x+8)/ 6x+60

72.

Simplify:

-1

Can't be simplified

73.

Add

74.

Who is this?

Jake Swallow

Jack Sparrow

Jake the Pirate

Panama Jack

75.

Solve

76.

Simplify the given complex fraction.

(1-x)/(x+3)

(3-x)/(x+1)

1/(x+3)

3-x

77.

Solve for x. Make sure the x-value(s) does not make the denominators zero.

No Solution

x = 3

x = 2

x = 0

78.

log₅25 = ?

125

79.

Evaluate log₄1

undefined

80.

Rewrite as a single log: 4 log g - 2 log h

log (4g/2h)

log (g⁴/h²)

log (g⁴ - h²)

log (2gh)

81.

Write as a single log: log 12 + 2 log x

log (12 + 2x)

log (14x)

log (12 * 2x)

log (12x²)

82.

Rewrite log_vn = a in exponential form.

v^a = n

n^a = v

vⁿ = a

aⁿ = v

83.

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

84.

Rewrite log_pt = m in exponential form.

p^t = m

t^m = p

m^t = p

p^m = t

85.

Rewrite log₂8 = 3 in exponential form/

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

86.

Condense

87.

Write as a single log: log 12 + 2 log x

log (12 + 2x)

log (14x)

log (12 * 2x)

log (12x²)

88.

Solve:
_{log (−2a + 9) = log (7 − 4a)}

-5

-1

89.

Solve:
log x + log 8 = 2

12.5

17.5

90.

Solve:
log₂2x = -0.65

0.32

0.23

0.45

0.54

91.

Which of the following numbers is/are rational?
I. sin 30⁰ II. cos 45⁰ III. tan 60⁰

I only

II only

I and III only

II and IV only

92.

If sin θ = 1 - cos 60⁰, where θ is an acute angle, then θ =

30⁰

45⁰

60⁰

90⁰

93.

If cos θ = 3/5, where θ is an acute angle, find the value of 2tan θ.

3/4

3/2

4/3

8/3

94.

Simplify (1 - sin² θ)/ cos³ θ

cos θ

- cos θ

1/cos θ

-1/cos θ

95.

96.

97.

98.

99.

100.

101.

Rewrite log₂8 = 3 in exponential form

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

102.

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

103.

Write in logarithmic form

2^-4 = ¹/₁₆

log₂(¹/₁₆) = -4

log_-4(¹/₁₆) = 2

log_-4 2 = ¹/₁₆

log₂(-4) = ¹/₁₆

104.

Write in exponential form

log₂32 = 5

2^-5 = 32

2³² = 5

2⁵ = 32

32⁵ = 2

105.

Solve for x:
log_x25 = 2

-5

1/5

-1/5

106.

Solve for x.
3^x = 27

107.

Evaluate.
log₃81

¹/₄

-4

-¹/₄

108.

Evaluate log₄1

undefined

109.

Evaluate.
3 log₂4

110.

State the property (s) used to simplify the expression

6log 2 = log 64

Product Property

Quotient Property

Power Property

Product and Power Property

111.

State the property (s) used to simplify the expression

log₄20 - 3log₄x = log₄(20/x³)

Power Property

Quotient Property

Quotient and Power Property

Product and Power Property

112.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

log₅7

log₅12

log₇5

3log₅4

113.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

log₆125

log₅20

log₆5

log₆30

114.

Write the logarithm expression as a single logarithm

log₄60 - log₄4 + log₄x

log₄15

log₄15x

log₄56x

xlog₄30

115.

Write the logarithm expression as a single logarithm

2log 4 + log 2

log 8

log 16

log 32

log 8²

116.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

-1

117.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

-1

118.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

log₆5

log₆1

119.

Expand the logarithm expression

log 6x³y

log 6x³ + log y

log 6 + log x³ + log y

3 log 6 + log x + log y

log 6 + 3log x + log y

120.

Expand the logarithm expression

log 5x/4y

log 5x + log 4y

log 5x - 4log y

(log 5 + log x) - (log 4 + logy)

5log x - 4 logy

121.

Find the 22nd term of the following sequence:
5, 8, 11, ...

122.

Identify the common difference.
97, 86, 75, 64, ...

-11

-8

123.

Identify the common difference.
3, 7, 11, 15, ...

124.

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

127

356

125.

Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...

-34

-146

-225

126.

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

127.

The next two terms of the sequence 4,7,10,13 are ....

16 and 19

15 and 19

16 and 18

15 and 18

128.

The next term of the sequence 2,4,8,16 is

108

129.

The next two terms of the sequence 4,7,10,13 are ....

16 and 19

15 and 19

16 and 18

15 and 18

130.

Find the common difference 10, 20, 30, 40.........

Multiply by 10

Add 10

Multiply by 2

131.

What is the next term in the sequence 1, 4, 9, 16, 25, ...?

132.

What is the 15th term of the sequence an = -3n+50

-5

-95

133.

What is the 10th term of the sequence an = 20-2n

-20

134.

Find the common difference: 29, 21, 13, 5, ...

d = -10

d = -9

d = -8

d = -7

135.

Find the common difference: -18, -23, -28, -33, ...

d = -5

d = 5

d = -3

d = 3

136.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

-515

-490

-535

460

137.

Is the sequence arithmetic: 37, 31, 25, 19, ...

Yes

138.

Find the first term of the given sequence:
a₁₄=68
d=3

139.

Identify the common difference.
3, 7, 11, 15, ...

140.

What is the distance from one number to the next in a sequence of numbers that is represented by a (d) in an arithmetic sequence?

Common denominator

Common opposites

Common domain

Common difference

141.

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? (Hint: Use a list, tree diagram, or Fundamental Counting Principle.)

192

40,320

51,200

142.

How many outfits are possible with 2 pairs of jeans, 5 t-shirts, and 2 pairs of shoes? (Hint: Use a list, tree diagram or the Fundamental Counting Principle.)

143.

A bag contains:

• 5 red marbles

• 6 blue marbles

• 3 green marbles

• 4 black marbles

• 2 yellow marbles

A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction for the number of times a green or black marble will be drawn? (Hint: Use a Proportion)