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Math Pentathlon 24-25 > Practice Problems > Flashcards

Practice Problems Flashcards

1
Q

When a coin is flipped, what is the probability of it showing heads?

A

50%, 0.5, 1/2, 1:2

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2
Q

When choosing cards from a standard deck of cards, what is the probability of drawing a face card?

A

23.1%, 0.231, 3:13, 3/13

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3
Q

When rolling a dice, what is the probability of rolling a number divisible by 3?

A

1/3, 1:3, 33%, 0.33

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4
Q

A dice is rolled 50 times. It rolls a 4 a total of 10 times. Is this experimental or theoretical probability? (if it was asking for the probability)

A

Experimental Probability

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5
Q

A dice is rolled 50 times. It rolls a 4 a total of 10 times. What is the probability of rolling a 4?

A

20%, 1/5, .20

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6
Q

What is P(A’), given that P(A) = 1/6?

A

P(A’) = 5/6

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7
Q

What is P(A), given that P(A’) = 4/5?

A

P(A) = 1/5

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8
Q

A dice is rolled 2 times. Are these independent or dependent events?

A

Independent, the first roll doesn’t affect the second one

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9
Q

What is the probability of winning a game, if you have to roll a 6 on a dice and a 6 from a deck of cards?

A

P(A) * P(B) = 1/6 * 1/13 = 1/78
1/78

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10
Q

The probability of drawing two kings from a deck of cards without replacing the first. Are these independent or dependent events?

A

Dependent, because the first card is not being replaced

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11
Q

What is the probability of drawing 2 kings from a deck of cards without replacing them?

A

P(A) = 1/13, P(B|A) = 1/17
1/13 * 1/17 = 1/221

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12
Q

The probability of drawing two green marbles out of a bag without replacing them. Are these events independent or dependent?

A

Dependent, because the first marble is not being replaced

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13
Q

What is the probability of drawing two green marbles out of a bag without replacing them? The bag has 6 green marbles and 8 red marbles.

A

P(A) = 3/7. P(B|A) = 5/13
3/7 * 5/13 = 15/91

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14
Q

What type of event is this? The probability of drawing a queen or a king.

A

mutually exclusive events

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15
Q

What is the probability of drawing a king or queen?

A

P(A or B) = P(A) + P(B)
1/13 + 1/13 = 2/13

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16
Q

Keywords like arrangement, ordered, and unique indicate usually indicate permutations or combinations?

A

permutations

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17
Q

Keywords like choose, pick, and select indicate permutations or combinations?

A

combinations

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18
Q

An ice cream shop offers 12 flavors of ice cream and 8 different topping options. How many ice creams can you make with 1 flavor and 1 topping?

A

m * n = 12 * 8
96 different ice creams

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19
Q

You can choose between 2 types of bread, 3 types of meat, and 3 types of cheese. How many different sandwiches can you make with 1 bread, 1 cheese, and 1 meat?

A

m * n * l = 2 * 3 * 3
18 different sandwiches

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20
Q

Calculate 2!

A

2

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21
Q

Calculate 3!

A

6

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22
Q

Calculate 4!

A

24

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23
Q

Calculate 5!

A

120

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24
Q

Calculate 6!

A

720

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25
Q

Calculate 7!

A

5040

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26
Q

Calculate 8!

A

40320

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27
Q

Calculate 9!

A

362880

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28
Q

Calculate 10!

A

3628800

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29
Q

Calculate 6!/4!

A

30

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30
Q

Calculate 8!/4!

A

1680

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31
Q

How many different ways can Maria, Josh, Sara, and Olivia be awarded 1st, 2nd, and 3rd in a race?

A

4P3 = 24
THIS IS A PERMUTATION

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32
Q

Naomi has 10 horses and she wants to ride 6 of them in a specific order. How many different ways can Naomi ride 6 of the 10 horses each day?

A

10P6 = 151,200

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33
Q

You have 5 friends but can only take 3 to the concert. How many different ways can you choose a group of friends?

A

5C3 = 10

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34
Q

A coach has 9 players signed up, but can only choose 5. How many different teams sets of teams can he have?

A

9C5 = 126

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35
Q

If a dice is rolled, what is the probability of it rolling 2 or less?

A

1/3, mutually exclusive events: 1/6 + 1/6

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36
Q

What is the probability of a coin showing heads both times if it is flipped twice?

A

1/36, independent events, 1/6*1/6

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37
Q

A restaurant offers 3 salads, 7 main dishes, 4 sides, and 6 desserts. How many different 4-course meals can be selected?

A

504, fundamental counting principle, 436*7

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38
Q

How many different groups of 3 people can be chosen from 9?

A

84, combinations, 9C3

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39
Q

A student scores 73%, 88%, 79%, 81%, 93%, and 96%. What is the mean of these scores?

A

73+88+79+81+93+96 = 510, 510/6=85
85% is the mean test score

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40
Q

What is the median of {52, 14, 23, 36, 60, 14, 45, 39}?

A

37.5

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41
Q

What is the mode of {2, 2, 3, 4, 6, 7, 7, 7, 7, 8, 9, 9}?

A

7

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42
Q

What is the mode of {53, 56, 92, 4, 88, 3, 10, 0.00001, 3, 50, 0.00019}?

A

3

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43
Q

A clothing store sold 16, 22, 14, 32, 28, 46, and 52 shirts over 7 days. What is the range?

A

38

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44
Q

A clothing store sold 16, 22, 14, 32, 28, 46, and 52 shirts over 7 days. What is the median?

A

28

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45
Q

A clothing store sold 16, 22, 14, 32, 28, 46, and 52 shirts over 7 days. What is the mode?

A

there is no mode

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46
Q

A clothing store sold 16, 22, 14, 32, 28, 46, and 52 shirts over 7 days. What is the mean?

A

30

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47
Q

What is the outlier in this data set? {104, 102, 108, 101, 107, 42, 110}

A

42

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48
Q

What is the outlier in this data set?
{53, 56, 52, 54, 58, 63, 60, 01, 63, 50}?

A

1

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49
Q

In my book club, I asked the students their ages. They were 18, 18, 20, 21, 58, 27, 24, and 28. Which age is the outlier?

A

58

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50
Q

In a stem-and-leaf plot, what would 6 | 3, 6, 8, 9 be?

A

{63, 66, 68, 69}

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51
Q

In a stem-and-leaf plot, what would 10 | 0, 4 be?

A

{100, 104}

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52
Q

In a stem-and-leaf plot, what would 7 | 4, 5, 9 be?

A

{74, 75, 79}

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53
Q

In a stem-and-leaf plot, what would 8 | 1, 4, 4, 8 be?

A

{81, 84, 84, 88}

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54
Q

In a stem-and-leaf plot, what would 9 | 0, 2, 5, 5, 5, 7 be?

A

{90, 92, 95, 95, 95, 97}

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55
Q

What is the mode of this set? 3|5, 6, 6, 6, 7, 7, 8, 8, 9, 9

A

36

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56
Q

What is the IQR when Q1 = 80 and Q3 = 125?

A

IQR = 45

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57
Q

What is the IQR when Q1 = 70 and Q3 = 90?

A

IQR = 20

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58
Q

What is the range when the upper extreme is 95 and the lower extreme is 65?

A

30

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59
Q

What is the correlation if the line of best fit is going down?

A

negative correlation

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60
Q

What is the correlation if the line of best fit is going up?

A

positive correlation

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61
Q

What is the correlation if there is no line of best fit?

A

no correlation

62
Q

Each day, the height of a plant increases. What type of correlation is represented in this situation?

A

positive correlation

63
Q

Each day, the height of a plant increases. What would x represent in this scenario?

A

the number of days

64
Q

Each day, the height of a plant increases. What would y represent in this scenario?

A

the height of the plant

65
Q

What is the next term in this sequence: 3, 6, 9, 12, …?

A

15

66
Q

What is the next term in this sequence: 1, 3, 9, 27, …?

A

81

67
Q

What type of sequence is this sequence: 1, 3, 9, 27, …?

A

a geometric sequence

68
Q

What type of sequence is this sequence: 3, 6, 9, 12, …?

A

an arithmetic sequence

69
Q

Write the next 4 terms in this sequence. 4, 7, 11, 15, ….

A

19, 23, 27, 31

70
Q

Write the next 3 terms in this sequence. 256, 128, 64, …

A

32, 16, 8

71
Q

What is the mean of this set of data? {19, 5, 9, 12, 10, 5}

A

10

72
Q

What is the median of this set of data? {19, 5, 9, 12, 10, 5}

A

9.5

73
Q

What is the mode of this set of data? {19, 5, 9, 12, 10, 5}

A

5

74
Q

What is the range of this set of data? {19, 5, 9, 12, 10, 5}

A

14

75
Q

What is the mean of this set of data? {4, 8, 17, 16, 23, 7, 16, 7, 19}

A

13

76
Q

What is the median of this set of data? {4, 8, 17, 16, 23, 7, 16, 7, 19}

A

16

77
Q

What is the mode of this set of data? {4, 8, 17, 16, 23, 7, 16, 7, 19}

A

7 and 16

78
Q

What is the range of this set of data? {4, 8, 17, 16, 23, 7, 16, 7, 19}

A

19

79
Q

What is the median of this set of data? {38, 47, 56, 38, 56, 44, 48, 55, 42, 38, 36, 38}

A

43

80
Q

What is the mode of this set of data? {38, 47, 56, 38, 56, 44, 48, 55, 42, 38, 36, 38}

A

38

81
Q

What is the range of this set of data? {38, 47, 56, 38, 56, 44, 48, 55, 42, 38, 36, 38}

A

20

82
Q

What is the median of this set of data? {3, 56, 75, 68, 81, 82, 4, 54}

A

62

83
Q

What is the range of this set of data? {3, 56, 75, 68, 81, 82, 4, 54}

A

79

84
Q

What is the mode of this set of data? {3, 56, 75, 68, 81, 82, 4, 54}

A

none

85
Q

What is the outlier of this data set? {80, 84, 92, 98, 81, 51, 87, 88, 95, 98}

A

51

86
Q

What would you write to say 6 is an element of {3, 6, 9}?

A

6 ∈ {3, 6, 9}

87
Q

{1, 2, 3} ∪ {3, 4, 5} = ?

A

{1, 2, 3, 4, 5}

88
Q

{1, 2, 3} ∩ {2, 3, 4, 5} = ?

A

{2, 3}

89
Q

{2, 4, 6, 8, 10, 12} ∩ {3, 6, 9, 12} = ?

A

{6, 12}

90
Q

What types of numbers are these: π and sqrt3?

A

irrational numbers

91
Q

What types of numbers are these: 12/18, -0.522, 2/3?

A

rational numbers

92
Q

Place these numbers from least to greatest. -0.9, 1/2, 0.834, 4/6, 4/18

A

-0.9, 4/18, 1/2, 4/6, 0.834

93
Q

Which of the following from this set is rational? {sqrt2, π, 1/2, sqrt8, 0.03030030003}

A

1/2

94
Q

Select the numbers that are prime: 17, 18, 19, 20, 21, 22, 23, 24, 25.

A

17, 19, 23

95
Q

Select the numbers that are composite: 31, 32, 33, 34, 35, 36, 37, 38, 39, 40.

A

32, 33, 34, 35, 36, 38, 39, 40

96
Q

What is the prime factorization of 20?

A

225

97
Q

What is the prime factorization of 36?

A

223*3

98
Q

What is the GCF of 24 and 36?

A

12

99
Q

What is the base of 5^3?

A

5

100
Q

What is the base of 4^9?

A

4

101
Q

What is 5^0?

A

1

102
Q

What is 200^0?

A

1

103
Q

What is 3^4?

A

81

104
Q

What is 5^4?

A

625

105
Q

What is 8^2?

A

64

106
Q

What is 6^-2?

A

1/36

107
Q

What is 5^2 * 5^4? (answer in exponent form)

A

5^6

108
Q

√36?

A

6

109
Q

√144

A

12

110
Q

√36a^2b^8

A

6ab^4

111
Q

Simplify √27

A

3√3

112
Q

Cube root of 64?

A

4

113
Q

Write the algebraic expression for the sum of 3 and a number.

A

x + 3

114
Q

Write the algebraic expression for a number multiplied by 5.

A

5x

115
Q

Solve 2 + 3x if x = 4.

A

14

116
Q

Solve 6m + 8/n if m = 3 and n = 4.

A

20

117
Q

Solve x - 6 = 24.

A

x = 30

118
Q

Solve 3x + 4 = 19.

A

x = 5

119
Q

Solve for Q when QP - X = Y.

A

Q = (Y + X)/P

120
Q

What is the slope of this equation? y = 5x + 8

A

5

121
Q

What is the y-intercept of this equation? y = 5x + 8

A

8

122
Q

If 7 is to 21 as x is to 12. Solve for x.

A

x = 4

123
Q

If it takes 4 eggs to make 48 cookies, then how many cookies can be made with 5 eggs?

A

60 cookies

124
Q

What type of algebraic expression is 9x?

A

monomial

125
Q

What type of algebraic expression is 4a^2?

A

monomial

126
Q

What type of algebraic expression is 3mpxz?

A

monomial

127
Q

Simplify (-9m^2)s + (5m^2)s.

A

(-4m^2)s

128
Q

Simplify (a + b)(c + d).

A

ac + ad + bc + bd

129
Q

Simplify (3x - 1)(2x + 7).

A

6x^2 + 19x - 7

130
Q

What is the greatest common monomial factor of 5x^5 - 70x^3?

A

5x^3

131
Q

Factor 5x^5 - 70x^3.

A

5x^3 * (x^2-14)

132
Q

Factor x^2 - 144.

A

(x - 12)(x + 12)

133
Q

Factor 4x^7 - 64x^5.

A

4x^5 * (x - 4)(x + 4)

134
Q

Factor 12x^3 - 60x^2 + 75x.

A

3x * (2x- 5)^2

135
Q

Factor x^2 - 3x + 2.

A

(x - 1)(x - 2)

136
Q

Factor 3x^3 - 6x^2 - 45x.

A

3x * (x - 5)(x + 3)

137
Q

Factor 7x^2 + 9x + 2.

A

(x + 1)(7x + 2)

138
Q

Factor 18x^3 - 39x^2 - 15x.

A

3x * (2x - 5)(3x + 1)

139
Q

Solve x^2 - 6x = 16. x^2 - 6x -16 = 0

A

x = 8, x = -2

140
Q

Solve for x when 2x + 4 > 6.

A

x > 1

141
Q

Is 20% rational or irrational?

A

rational

142
Q

Is 70 prime or composite?

A

composite

143
Q

Is 80 prime or composite?

A

composite

144
Q

What is the GCF of 75 and 100?

A

25

145
Q

{4, 5, 6, 7} ∩ {6, 7, 8, 9, 10, 11} =

A

{6, 7}

146
Q

Simplify 7^-3.

A

1/7^3

147
Q

Simplify √50.

A

5√2

148
Q

Express five increased by three times x algebraically.

A

5 + 3x

149
Q

Find the slope of this line: y = -4x + 8.

A

-4

150
Q

Find the y-intercept of this line: y = -4x + 8.

A

8, or (0,8)

Math Pentathlon 24-25 (4 decks)

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