7th Grade Review Packet
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University of West Alabama *
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Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
24
Uploaded by MasterMoose2829
© 2018 The Math Cafe
7
th
Grade Math Review Packet: Study Guide & Test Practice
Page 1
© 2018 The Math Cafe
Study Guide: 1. Rational number:
numbers that can be expressed as ratios (fractions); the decimal form is either a terminating
decimal (0.567) or a repeating
decimal (
0.13
̅
= 0.133333 …
); includes integers. 2. Operations with Integers:
3. Additive Inverse:
Adding the opposite of a number to return to zero; [
Example: 9 + (−9) = 0
, −
2
3
+
2
3
= 0
] 4. Multiplicative Inverse: Multiplying a number by its reciprocal
to produce 1; [
Example: 4 ×
1
4
= 1
, 2
5
×
5
2
=
10
10
= 1
] 5. Properties of Operations: 6. Converting Fractions to Decimals: Divide the numerator by the denominator: ?
?
= 1 ÷ 2 = 2 1.0 = ?. ?
Operations with
Rational Numbers 0.5
1
What is the additive inverse of ?
?
? A
2
5
B
−
2
5
C
5
2
D
−
5
2
2
What is the additive inverse of −?. ?
? A
+3.2
B
−3.2
C
+2.3
D
−2.3
4
Sara had a balance of $350
in her bank account. Her electric bill was $375.
After she pays the electric bill, what amount of money should she deposit to bring her bank account back to $0
? A
$375
B
$350
C
$25
D
$50
3
What number will complete the equation? −? + ? + ____ = ?
A
+3
B
−4
C
−7
D
−1
5
A scuba diver reached a depth of −14 feet (below sea level). The diver descended another −12
feet. How many feet will the diver have to travel to return to sea level? A
+26 ??.
B
−26 ??.
C
+14 ??.
D
+2 ??.
Page 2
© 2018 The Math Cafe
6
Which expression best represents the number line below? A
(−4) + (+3)
B
(−4) − (+3)
C
(−4) − (+7)
D
(−4) + (+7)
7
Which expression best represents the number line below? A
−6 + (−4)
B
−6 − (−4)
C
−6 + (−10)
D
−4 + (−6)
8
Which number line shows the additive inverse property? A
B
C D
9
On Tuesday morning, the temperature was recorded at 5°?
. Over the course of the day, the temperature dropped 7°
. After this drop, what temperature will be recorded? A
12° ?
B
2°?
C
−2° ?
D
−12° ?
10
Which expression is equivalent to −??
? A
9 − (−12)
B
9 + (−12)
C
−9 + 12
D
−9 − 12
11
What is the distance
(in units) between 4
and −9
on a number line? A
5 ??𝑖??
B
−5 ??𝑖??
C
13 ??𝑖??
D
−13 ??𝑖??
A helicopter is flying directly above a submarine at a position of ??? ????
above sea level. The submarine is located at −?? ????
below sea level. 12 What expression will calculate the distance
between the two vehicles? A
125 − 70
B
|125 − 70|
C
|125 − (−70)|
D
|125| − | − 70|
13 What is the distance
between the two vehicles? A
55 ????
B
−195 ????
C
−55 ????
D
195 ????
14
Evaluate using properties of operations when appropriate. ?
?
+ (
?
?
−
?
?
)
A
5
7
B
−
5
7
C
2
5
8
D
41
56
15
Which property of operations is demonstrated in the equation below? ?
?
+ (
?
?
−
?
?
) = (
?
?
+
?
?
) −
?
?
A
????????𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
B
𝐴????𝑖??𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
C
𝐼????𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
D
?𝑖???𝑖???𝑖?? 𝑃???????
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Page 3
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16
Lindsey was the scorekeeper for a card game that included both negative and positive scores. She has to find the total of the following scores: (+?) + (−??) + (+?) + (−?)
Lindsey decides to calculate the scores in the following order: (+?) + (+?) + (−??) + (−?)
Which property of operations justifies her decision? A
????????𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
B
𝐴????𝑖??𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
C
𝐼????𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖??
D
?𝑖???𝑖???𝑖?? 𝑃???????
17
Which equation properly demonstrates the 𝐼????𝑖?? 𝑃??????? ?? 𝐴??𝑖?𝑖???
A
8 + (−8) = 0
B
2
3
+ 0 =
2
3
C
1
4
×
4
1
= 1
D
−8 × 1 = −8
18
Evaluate: −?. ? × ?
A
−2.9
B
2.9
C
−10.5
D
10.5
19
Evaluate: −
?
?
× (−
?
?
)
A
−
16
21
B
16
21
C
−
7
12
D
7
12
20
Which expression will have a positive product?
A
(−1) × (−1) × (−1)
B
(1) × (−1) × (1)
C
(−1) × (1) × (−1)
D
(1) × (1) × (−1)
21
Which expression is equivalent to the expression below? −?(? − ?)
A
−1??
B
−? + ?
C
−? − ?
D
? + ?
22
Which scenario might be represented by the expression below? ?(−??)
A Making three payments of $20 each to total paying $60. B Making 20 payments of $3 each to total paying $60. C
Three friends giving you $20 each, totaling $60. D
Paying $3 for each of 20 arcade games, totaling $60 spent on games. 23
Evaluate: ??? ÷ (−?)
A
45
B
0.02
̅
C
−45
D
−0.02
̅
24
Which expression is NOT equivalent to the expression −
??
??
? A
−45
67
B
45
−67
C
− (
45
67
)
D −45
−67
25
Which scenario might be represented by the expression below? −???
?
A Owing $100 on a credit card and making four equal payments totaling $25 each. B Spending $100 on each of four friends, totaling $400 spent. C
Receiving $100 in birthday money each year for four years, totaling $400 in birthday money. D
Receiving $100 in total from four different friends who have given $25 each. 26
Evaluate using properties of operations when appropriate. −
?
?
× ? ×
?
?
A
1
B
−1
C
2
3
D
−
2
3
Page 4
© 2018 The Math Cafe
27
Which property does the equation below demonstrate? ?(−? ∙ ??) = (−? ∙ ??)?
A
????????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
B
𝐴????𝑖??𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
C
𝐼????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
D
?𝑖???𝑖???𝑖?? 𝑃???????
28
Which property does the equation below demonstrate? −
?
?
× ? = −
?
?
A
????????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
B
𝐴????𝑖??𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
C
𝐼????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
D
?𝑖???𝑖???𝑖?? 𝑃???????
29
Which property justifies ???? ?
shown below? (
?
?
×
?
?
) ×
?
?
[???? ?: ] ?
?
× (
?
?
×
?
?
)
[???? ?: ] ?
?
× ?
[???? ?: ] ?
?
A
????????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
B
𝐴????𝑖??𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
C
𝐼????𝑖?? 𝑃??????? ?? 𝑀???𝑖??𝑖???𝑖??
D
?𝑖???𝑖???𝑖?? 𝑃???????
30
Convert ?
??
to a decimal number.
A
0.425
B
0.16
C
6.25
D
0.08
31
What is −
?
?
expressed as a decimal number?
A
−0.29
B
−0.2 C
0.2
D
−0. 2
̅
32
Which decimal number below is not
considered to be a rational number? A
−0.125
B
0. 3
̅
C
1.73
D
3.14159 …
33
Evaluate: ?. ? + [(−?) × (
?
?
+
?
?
)] ÷
?
?
A
0
B
1 C
3
D
−1.5
34
Evaluate: ? + (−?) × ? − ?? ÷ ?
A
0
B
−4. 3
̅
C
−13
D
−5. 6
̅
The menu at the local pizza shop is shown below:
35
Sadie’s family orders a medium pizza with one topping, a large pizza with three toppings, two salads, and an order of breadsticks. What is the cost of the bill before tax and tip? A
$40.25
B
$43.00 C
$44.00
D
$39.25
36
Ben and his friend share a taxi to work. The taxi driver charges a $2.50 flat fee as well as $0.40 for every 1
5
of a mile traveled. The total distance of the taxi ride was 4.2 miles. Ben and his friend split the final bill. How much did each friend pay?
A
$5.45
B
$10.90
C
$4.18
D
$6.70
Page 5
© 2018 The Math Cafe
Expressions &
Equations Study Guide: 1. Expression:
A mathematical sentence containing numbers and/or variables, and operators →
Examples: “
?? − ?"
or "? + ? × ?"
2.
Equation
: A mathematical sentence containing numbers, and/or variables, operators and an equal
sign →
Examples: ? + ? = ??
or ?? − ? = ??
3. Term:
A unit of an expression or equation; each new term begins with a +
or –
→
Example: 2? − 7 + 5?
→
There are three
terms in the expression above: “
2?
”, “
−7
” and “
+5?
”
→
2?
and +5?
are made up of a coefficient
(the 2 and 5)
and a variable (the x and y) →
−7
is considered a constant
term as it is not multiplied or divided by a variable. 4. Like Terms: Terms with the same
variable can be combined by adding their coefficients →
Example: ?? − ? + ?? − ?? + ?? + ??
→
Use commutative property
to re-order the expression: ?? − ?? + ?? + ?? − ? + ??
→
Simplify the expression by combining like terms
: −?? + ?? + ?
→
Since none of the remaining terms have like variables, the expression is as simple as it can be. 5. Factoring Expressions: Expressions can be separated into two different factors
(multipliers) →
Example: 12? + 24
→
Check the two terms for their GCF (Greatest Common Factor), in this case “12”
→
Divide both terms by the GCF: 12?
12
+
24
12
= ? + 2
→
Write your factored expression as two factors: (1) the GCF multiplied by (2) the resulting expression →
12? + 24 = ??(? + ?)
6. Expanding Expressions: Same as “distributive property” (page 1)
→
Example: −3(? − 10)
= −?? + ??
7. Adding Expressions: Add (?? + ?) ??? (−? + ??)
→
(2? + 3) + (−? + 10)
→
2? + 3 − ? + 10
→
? + ??
8. Subtracting Expressions: Subtract
(?? + ?) ???(−? + ??)
→
(2? + 3) − (−? + 10)
→
2? + 3 + ? − 10)
→
?? − ?
9. Solving Equations with One Variable: Apply the inverse
operation to both sides of the equal sign until one side is left with 1 (positive) ?
(or variable), and then other side is left with a number. Example: 2? − 3 = 11
10. Solving Inequalities with One Variable: Solve an inequality in one variable using the same steps as solving an equation, with these two differences:
→
The inequality symbol (
<, >, ≤, ≥)
takes the place of the equal sign →
When multiplying or dividing
both sides of an inequality by a negative number
, flip
the inequality symbol [When graphing an inequality: >, <
use open circles; while
≥, ≤
use closed circles
]
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Page 6
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1
Simplify the expression below. ?? + ?? − ?? + ?
A
7? + 10
B
7? + 11
C
11? + 11
D
22?
2
What is the sum of (5? − 10)
and (−? + 8)
? A
2?
B
4? − 18
C
6? − 2
D
4? − 2
3
What is the difference of (−2? + 9)
and (3? − 4)
? A
−5? + 5
B
? + 5
C
−5? + 13
D
? + 13
4
Simplify the expression below: −(? + ?)
A
−? − ?
B
−??
C
−? + ?
D
? − ?
5
Which expression could NOT be a factored form of the expression below? ??? − ??
A
10(? − 2)
B
5(2? − 4)
C
2(5? − 20)
D
−2(−5? + 10)
6
At the movies, the cost of popcorn and the cost of soda can be represented by the expressions shown below. In terms of ?
, how could the price of one order of popcorn and two sodas be expressed in simplest form? 𝑷??????: 3? + 5
????: 2?
A
5? + 5
B
10?
C
7? + 5
D
12?
7
At a restaurant, Toby knew he would tip his server 20% of whatever the cost (c) of the final bill was. He knew he could use the strategy ? + ?. ??
to calculate his final cost after paying the 20% tip. Which other process could Toby use to calculate his cost after tip? A
? + 20
B
1.2?
C
0.8?
D
?
0.2?
8
Which expression could NOT be used to calculate the perimeter
of the rectangle below? A
2?(? + 10)
B
2(2? + ? + 10)
C
2(2?) + 2(? + 10)
D
2? + 2? + ? + 10 + ? + 10
9
When calculating the price (?)
of an item that has been marked down by 25%
, Denise states that the expression ? − ?. ???
will calculate the sale price. Kristal says that a shorter way to calculate the sale price would be to use the expression ?. ???
. Who is correct? A
Denise is correct. B
Kristal is correct. C
Both Denise and Kristal are correct. D
Neither Denise nor Kristal are correct. 10
When hanging a 2
7
8
??
long wall hanging in the middle of a wall that is 11 ??
long, approximately
how far from each end of the wall should it be hung to be in the center of the wall? A
Approximately 6 ft from each end. B
Approximately 3 ft from each end. C
Approximately 2 ft from each end. D
Approximately 4 ft from each end.
Page 7
© 2018 The Math Cafe
16
Which equation represents the description below? ??? ?????????? ?? ? ?????? ??? ?? ?? ?????????? ?? − ? ??? ??? ?????? ?? − ??.
A
? − 15 × (−3) = −30
B
? − [15 × (−3)] = −30
C
−3(? − 15) = −30
D
−3? − 15 = −30
17
Solve for x: −?? + ?? = −??
A
? = 12
B
? = −12
C
? = 3.5
D
? = −3.5
18
Solve for x: ?
?
? = ??
A
? = 18
B
? = 16
C
? = 24
D
? = 25
19
Solve for x: ? −
?
?
=
?
?
A
? = −
9
20
B
? =
4
9
C
? =
19
20
D
? = −2
Use the situation below to answer questions 20 and 21. Collin’s
bowling team practices on a night when the bowling alley offers a special deal of $2 per game. The shoe rental fee is $3.50. 20 Which equation would calculate how many games (?)
of bowling Collin played if his final cost was $17.50
? A
2? + 3.5 = 17.5
B
7.5? = 17.5
C
2? − 3.5 = 17.5
D
2? + 3.5? = 17.5
21 How many games did Collin bowl? A
5 ?????
B
7 ?????
C
6 ?????
D
8 ?????
Use the situation below to answer questions 11 and 12. Lin, Mark, and Sara were assigned to read a book for Language class. The book has a total of 250 pages. The current progress of each student is shown in the table below. 11
How many more
pages has Mark read than Sara? A
150 pages B
55 pages C
105 pages D
45 pages 12
How many pages have the three students read combined? A
350 pages B
305 pages C
295 pages D
195 pages Use the situation below to answer questions 13 and 14. Avery is currently making $??
per hour at her job. Her boss gives her a ??%
raise for showing good work ethic.
13
If she works 40 hours every week, how much will her weekly paycheck be at this new rate of pay? A
$161.00
B
$644.00
C
$560.00
D
$1,160.00
14
If Avery works 40 hours per week, how much more
per week will Avery be making than before her 15%
raise? A
$15.00
B
$280.00
C
$84.00
D
$116.00
15
Which equation represents the descriptions below? 𝑭??? ???? ???? ??? ????? ? ?????? ?? ??.
A
2(? + 5) = 11
B
2? + 5 = 11
C
5(? + 2) = 11
D
5? + 2 = 11
Page 8
© 2018 The Math Cafe
27
Solve the inequality for ?.
−?? + ?? > −?
A
? < 6
B
? > 6
C
? < −6
D
? > −6
28
Which number line represents the solution to the inequality shown below? ?
?
? ≤ ??
A
B
C
D
Use the situation below to answer questions 29 and 30. George has $??
saved. He knows he can make $??
for each lawn (?)
he mows. He would like his savings account balance to be at least $???
by the end of the summer.
29
Which inequality represents George’s summer savings goal? A 75 + 20? ≥ 500
B
75 + 20? ≤ 500
C 75? + 20 ≥ 500
D 75? + 20 ≤ 500
30
How many lawns will George have to mow to reach his savings goal? A 21 ?????
B
22 ?????
C 6 ?????
D 7 ?????
Use the situation below to answer questions 22 and 23. Marlee had a certain amount of money (?)
in her bank account. She deposited $??. ??
from her grandmother for her birthday. She then spent ?
?
of the money in her account on rent that totaled
$???
. 22 Which equation represents this situation? A
1
4
? + 60 = 550
B
1
4
(? − 60) = 550
C
? + 60 ×
1
4
= 550
D
1
4
(? + 60) = 550
23 How much money (?)
did Marlee have in her account to begin with? A
$2,140.00
B
$2,440.00
C
$1,960.00
D
$790.00
24
Which sequence of steps will solve the equation below for ?
? ?
?
+ ? = −?
A
???? 1:
Subtract 8 from both sides of the equation ???? 2: Divide both sides of the equation by 3 B
???? 1:
Subtract 8 from both sides of the equation ???? 2: Multiply both sides of the equation by 3 C
???? 1:
Divide both sides of the equation by 3 ???? 2: Add 8 to both sides of the equation D
???? 1:
Add 8 to both sides of the equation ???? 2: Divide both sides of the equation by 3 Use the situation below to answer questions 25 and 26. A rectangle has an area of ??? ??
?
. Its width is ?? ??.
25 Which equation will calculate the length (?)
of the rectangle?
A
195 × ? = 13
B
13 × ? = 195
C
2(? + 13) = 195
D
?
13
= 195
26 What is the length (?)
of the rectangle? A
84.5 ??.
B
2,535 ??.
C
15 ??.
D
26 ??.
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Page 9
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Ratios &
Proportional Relationships Study Guide: 1. Rate/Ratio:
A relationship between two different types of quantities →
Examples: 3 boys to 2 girls (3 to 2, 3:2, 3
2
) 2. Unit Rate
: A rate/ratio describing “how many in just 1”; the denominator of a unit rate is always “1” →
Examples: 55 ?𝑖???
1 ℎ???
, $1.99
1 ??
→
Calculating Unit Rate: To calculate a unit rate, (1) set up a ratio of the two given quantities, making sure that the unit you “want 1 of” is in the denominator. (2) Divide the numerator by the denominator.
For example, “Painting 1
3
of a wall in 1
4
of an hour; how many walls can be painted in 1 hour?”
1
3
????
1
4
𝐻???
=
1
3
÷
1
4
=
1
3
×
4
1
=
?
?
?? ? ???? ?? ? ???? ??
?
?
????
? ????
3. Proportional Relationship:
Two quantities have a proportional relationship if their ratios are equal
to each other
(a) Graphs: Graphs show proportional relationships if they show a straight line traveling through (0,0)
(origin)
→
Examples: NON
-Examples: 5. Tables: Tables show a proportional relationship if the ratios of ?: ?
reduce to be equal (or if cross-products are equal) →
Example: NON
-Example: 6. Equations: Equations have proportional relationships if they are in the form of ? = ?? ?? ? =
?
?
where ? is the constant of proportionality
(see below). (
?
and ?
can be different variables) →
Examples: ? =
1
2
?
NON
-examples: ? =
?
?
? + ?
? = 4?
? =
?
?
? =
?
3
? = ? − ?
7. Constant of Proportionality
: The constant of proportionality (?)
is the number which ?
is multiplied by to produce ?
. Calculate the constant of proportionality by dividing: ?
?
; This is the same idea as calculating the scale factor
and unit rate. 8. Percent Terms
: Terms that will increase
the final value: ?𝑖?, ?????𝑖??, ???, 𝑖???????, ??????, ????𝑖??𝑖??
Terms that will decrease
the final value: ????, ?𝑖??????, ????????
9. Scale Drawings
: A drawing of a real-life object that has been enlarged or shrunk by multiplying the dimensions of the original figure by the same number (
scale factor).
10. Scale Factor
: To calculate the scale factor used to make a scale drawing, divide the NEW dimensions by the OLD dimensions: ???
???
Page 10
© 2018 The Math Cafe
1
Theo can run 1
2
?𝑖??
in 1
10
ℎ???
. If Theo continues at this rate, how far can he run in 1
hour? A
4 ?𝑖???
B
2.5 ?𝑖???
C
5 ?𝑖???
D
5.5 ?𝑖???
2
Lindsey used 2
3
????
of sugar to make 1
2
????ℎ
of cookies. How much sugar should she use to make a full batch of cookies? A
1
1
3
???? B
1
2
3
????
C
1 ???
D
1
1
2
????
3
Robbie has a 1 acre lawn. When he mows the lawn, it takes him 1
5
ℎ???
to mow 1
8
????. How long will it take Robbie to mow the full acre? A
5
8
ℎ???
B
1
3
5
ℎ???
C
1
1
2
ℎ???
D
1 1
4
ℎ???
4
How can the graph below be described? A The graph shows a proportional relationship between ?
and ?
. B
The graph does NOT show a proportional relationship between ?
and ?
. C The graph shows both a proportional and a non-proportional relationship between ?
and ?
. D
There is not enough information to determine if ?
and ?
have a proportional relationship. 5
Which graph shows a proportional relationship between ?
and ?
? A
B
C
D
6
How can the table below be described? A The table shows a proportional relationship between ?
and ?
. B
The tables does NOT show a proportional relationship between ?
and ?
. C The table shows both a proportional and non-
proportional relationship between ?
and ?
. D
There is not enough information to determine if ?
and ?
have a proportional relationship. 7
Which table does NOT show a proportional relationship between ?
and ??
A
B
C D
8
What is the constant of proportionality of the table below? A
0
B
1
C
1
2
D
2
9
What is the constant of proportionality in the equation below? ? =
?
?
?
A
1
3
B
1
C
3
D
?
Page 11
© 2018 The Math Cafe
16
Which equation best represents the relationship between hours worked (ℎ)
and money earned (𝑀)
as shown in the graph below? A
𝑀 = 10ℎ + 175
B
𝑀 = 175ℎ + 10
C
𝑀 = 17.5ℎ
D
𝑀 = 25ℎ
17
Which equation best represents the relationship between pounds (?)
and total cost (?)
as shown in the table below? A
? = 1?
B
? = 0.99? + 1
C
? = 1.98? + 2
D
? = 0.99?
Use the situation below to answer questions 18 and 19. The graph below shows a proportional relationship between the amounts of sugar needed to make different amounts of cupcakes. 18
Interpret the coordinate (5, 60).
A For every 5 cupcakes made, 60 cups of sugar are used. B
For every 60 cupcakes made, 5 cups of sugar are used. C If 5 is multiplied by 60, the product will be the final amount of cupcakes that are made. D
If 5 is divided by 60, the quotient will be the final amount of cupcakes that are made.
19
For the situation above, what would be the value of ?
in the coordinate
(1, ?)
? A
? = 1
B
? = 12
C
? = 6
D
? = 2
10
What is the constant of proportionality in the diagram below? A
3
B
2
C
3
2
D
2
3
11
What is the constant of proportionality in the graph below? A
4
3
B
3
4
C
1
2
D
2
12
Sara makes $255
for working 15 ℎ????
and makes $680
for working 40 ℎ????.
What is the constant of proportionality (unit rate) of Sara’s rate of pay per hour? A
15
B
2. 6
̅
C
17
D
12
13
Which equation shows a proportional relationships between ℎ
and ?
? A
? = 55ℎ
B
? = 12ℎ + 1
C
? = ℎ − 1
D
? =
4
ℎ
14
Mike purchased 1.35
pounds of steak for $13.50
. Which equation represents the relationship between the cost per pound? A
? = 13.50?
B
? = 10?
C
? = 3.5?
D
? = 16.5?
15
When Julie jogs, she burns 255 calories in 15 minutes and 340 calories in 20 minutes. Which equation represents how many calories (?)
she can burn per minute (?)?
A
? = 17?
B
? = 15?
C
? = 85?
D
? = 20?
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Page 12
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21
On tax-free weekend, Ben buys school supplies totaling $47.50
. He has a sale coupon for 15%
off his entire purchase. What will Ben’s final cost be after the 15% discount? A
$7.13
B
$42.35
C
$40.38
D
$32.50
22
Wendy and two friends went out to eat and decided they would split the bill. The total bill was $35.40
. They also decided to leave a 20%
tip. What is the price that each person paid? A
$7.08
B
$42.48
C
$21.24
D
$14.16
23
What is the final cost of a TV that has a price of $699.00
after an 8%
tax? A
$643.08
B
$754.92
C
$707.00
D
$559.20
24
A salesman makes $13.00
per hour, plus 10%
commission on all sales that he makes. One week, he worked 40 hours and sold $1,250.00
worth of merchandise. How much money did he earn in that week? A
$645.00
B
$560.00
C
$616.00
D
$1,810.00
25
Maggie takes out a loan from the bank for $7,500.
The simple interest on the loan is 5%
. She agrees to pay the loan back over the course of 3 years. What is the total
amount of money that Maggie will pay back after 3 years? 𝑰 = ???
A
$11,250
B
$8,625
C
$7,875
D
$1,125
26
A department store purchases certain tennis shoes for $48.00
and applies a markup of 30%
. What is the retail price that the customer will pay at the department store? A
$78.00
B
$14.40
C
$62.40
D
$59.00
27
John purchased a pair of headphones on sale for $32.50
that were originally priced at $50.00
. What was the percent decrease
from the original price to the sale price? A
30%
B
17.5%
C
25%
D
35%
28
A car salesman purchased a car at an auction for $8,550.
He will re-sell the car at a markup of $11,970.
What is the percent increase
of the markup? A
40%
B
35%
C
30%
D
45%
Use the situation below to answer questions 29 and 30. Anne sketched a scale drawing of the small garden she is planning with dimensions shown below. She plans to use a scale of ? ??: ? ??.
29
What will the length
of the real garden be? A
12 ??.
B
9 ??.
C
6 ??.
D
4 ??.
30
What will the area
of the real garden be? A
18 ??
2
B
36 ??
2
C
27 ??
2
D
40.5 ??
2
20
The graph below shows the speed of the future “Hyperloop” with the coordinate (8, 6,080)
labeled on the line. Which choice best completes and describes the coordinate (1, ?)
? A (?, ???); The coordinate (1, 760)
describes the unit rate of the graph stating that the “Hyperloop” will have a speed of 760
miles per hour. B
(?, ???); The coordinate (1, 760)
describes how long it will take the “Hyperloop” to travel 1 mile. C (?, ???)
; The coordinate (1, 600)
describes the unit rate of the graph stating that the “Hyperloop” will have a speed of 600 miles per hour. D (?, ???); The coordinate (1, 600)
describes how long it will take the “Hyperloop” to travel 1 mile.
Page 13
© 2018 The Math Cafe
(1) What is the measure of the missing angle ?°?
85° + 40° + ?° = ???°
125° + ?° = ???°
-125
o
-125
o
?° = ??°
(2) If the triangle shown is NOT an isosceles triangle, what is one possible side length for side ?
? A. 5 B. 7 C. 9 D. 11 Geometry Study Guide: 1. Triangles:
Triangles have two conditions that must be met, 1 regarding the three interior angles and 1 regarding the length of the sides: →
ANGLES: (Triangle Sum Theorem)
→
The three interior angles of any triangle ALWAYS add up to 180°
; if a set of 3 angles sums to 180
o
, the measures could form many triangles
(same angles, proportional side lengths) →
SIDE LENGTHS: (Triangle Inequality Theorem)
→
The sum of any 2 side lengths of a triangle must be greater than the measure of the third side; If a set of 3 sides
meets these conditions, only ONE triangle can be formed Example: 2. Cross-Sections of 3D Figures
: A cross-section of a 3D figure is produced when a 3D figure is cut by a flat plane. The cross-section that is produced is described as a 2D shape of the flat surface that appears after the cut. →
Examples: 3. Circles:
Vocabulary →
Radius (?)
: The distance half-way
across the center of a circle. →
Diameter (?)
:
The full
distance across the center of a circle. →
Pi (𝜋) : The ratio of the circumference to the diameter; Estimated value
: 𝝅 ≈ ?. ??
→
Circumference (𝑪)
: The distance around the outside of a circle; Formula
: 𝑪 = 𝝅?
→
Area (𝑨)
: The amount of space in square units covered by the circle; Formula:
𝑨 = 𝝅?
?
5. Angle Relationships: Two sets of equal angles are formed every time one line crosses another line. →
Complementary Angles:
Angles that sum to 90
o
→
Supplementary Angles: Angles that sum to 180
O
[Angles like A & B or B & C]
→
Adjacent Angles: Angles that share a side and vertex [Angles like A & B or D & C]
→
Vertical Angles: Angles that only share a vertex (always equal to each other); [Angles like A & C and B & D]
6. Composite Figures: Figures that are made up of one or more shapes. To calculate the area, surface area, or volume of a composite figure, calculate the individual areas/surface areas/volumes and then add together for a total. Volume of Prism: 𝑽 = ???? ?? ???? × ??????
Area of Circle: 𝑨 = 𝝅?
?
Area of Square: 𝑨 = ?
?
Area of Triangle: 𝑨 =
?
?
??
OR 𝑨 =
?×?
?
Area of Rectangle: 𝑨 = ? × ?
Area of Trapezoid: 𝑨 =
?
?
+?
?
?
× ?
A plane slices through the square pyramid parallel
to the base of the pyramid. The cross-section
that is produced is in the shape of a square. A plane slices through the square pyramid
perpendicular to the base of the pyramid. The cross-section
that is produced is in the shape of a triangle.
Page 14
© 2018 The Math Cafe
1
Which set of angles could NOT be the measures of the interior angles of a triangle? A
90°, 45°, 45°
B
60°, 70°, 80°
C
50°, 60°, 70°
D
100°, 30°, 50°
2
What is the missing angle of the triangle? A
149°
B
31°
C
41°
D
24°
3
Which set of values could create only one unique triangle? A
8 ??, 7 ??, 10 ??
B
1 ??, 2 ??,3 ??
C
50°, 40°, 90°
D
90°, 90°, 90°
4
Which set of values could create many triangles? A
8 ??, 7 ??, 10 ??
B
1 ??, 2 ??,3 ??
C
50°, 40°, 90°
D
90°, 90°, 90°
5
Which TWO sets of values would create NO triangles? A
8 ??, 7 ??, 10 ??
B
1 ??, 2 ??,3 ??
C
50°, 40°, 90°
D
90°, 90°, 90°
6
Brad, Jamie, and Iris were attempting to predict which straw lengths would create a triangle. The straws they are using are number 1-5 (shown below) and their lengths are labeled in centimeters. Which student did NOT predict correctly? A Brad predicts straws 1, 2, and 3 will create a triangle. B
Jamie predicts straws 1, 3, and 4 will create a triangle. C
Iris predicts straws 2, 4, and 5 will create a triangle. D
All three predictions are correct.
7
What is the cross-section of the cylinder shown below with a plane slicing it parallel to the base of the cylinder? A Circle B Square C Rectangle D
Oval
8
Liam is attempting to create a triangular cross-
section by slicing the cone below with a plane. Which direction should he use to slice the cone in order to create this cross-section? A Parallel to the base in any spot B Perpendicular to the base in any spot C Perpendicular to the base directly through the vertex D
Diagonally in any spot
9
Which cross-section could NOT be created from the square prism below? A Oval B Triangle C Rectangle D
Square
10
Find the approximate area of the circle shown below. Use 3.14 ≈ 𝜋
. 𝑨 = 𝝅?
?
A
81 ??
2
B 254 ??
2
C 243 ??
2
D
57 ??
2
11
Find the approximate circumference of the circle shown below. Use 3.14 ≈ 𝜋
. 𝑪 = 𝝅?
A
18 ??
B 54 ??
C 28 ??
D
57 ??
12
A circle has a circumference of 47.1 𝑖?.
What is the circle’s diameter?
Use 3.14 ≈ 𝜋
. 𝑪 = 𝝅?
A
44 𝑖?
B 130.9 𝑖?
C 15 𝑖?
D
7.5 𝑖?
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Page 15
© 2018 The Math Cafe
Use the situation below to answer questions 13 and 14. Figure 1 shows a circle divided into 20 equal parts. Figure 2 shows those same 20 parts rearranged to form an approximate parallelogram. 13
Which part of the circle in Figure 1 will have the same measure as the height
in Figure 2? A
?𝑖??????
B ???𝑖??
C ?𝑖???????????
D
1
2
?𝑖???????????
14
Which part of the circle in Figure 1 will have the same measure as the
length
in Figure 2? A
?𝑖??????
B ???𝑖??
C ?𝑖???????????
D
1
2
?𝑖???????????
15
In the figure below, what is the measure of ?°
and ?°
? A
?° = 75°, ?° = 105°
B ?° = 105°, ?° = 75°
C ?° = 75°, ?° = 115°
D
?° = 115°, ?° = 75°
16
Two angles are complementary
. The measure of one of the angles is 37°
. What is the measure of the second angle? A
37°
B 53°
C 90°
D
143°
17
Two angles are supplementary
. The measure of one of the angles is 37°
. What is the measure of the second angle? A
37°
B 53°
C 90°
D
143°
18
Two angles are vertical
. The measure of the first angle is 37°
. What is the measure of the second angle? A
37°
B 53°
C 90°
D
143°
19
In the figure below, what is the value of ?
? A
40
B 70
C 20
D
140
20
In the figure below, what is the value of ?
? A
121
B 59
C 11
D
31
21
In the figure below, what is the value of ?
? A
4
B 5
C 3
D
12
22
Find the area of the figure below. A
48 ??
2
B 80 ??
2
C 64 ??
2
D
112 ??
2
23
Find the area of the shaded region in the figure below. A
7 ??
2
B 84 ??
2
C 14 ??
2
D
77 ??
2
Page 16
© 2018 The Math Cafe
Use the situation below to answer questions 24 and 25. Marcus needs to paint a large wall with a window centered in the middle of the wall (shown below). 24
What is the area (in square feet) that Marcus will need to paint? A
336 ??
2
B 256 ??
2
C 300 ??
2
D
264 ??
2
25
Marcus can expect 1 gallon of paint to cover 350 square feet of wall. If he needs to paint two coats on this wall, how many gallons of paint can he expect to use? A
1 ??????
B 1.8 ???????
C 1.5 ???????
D
2.2 ???????
Use the figure below to answer questions 26 and 27. 26
What is the surface area of the figure? A
532 𝑖?
2
B 484 𝑖?
2
C 460 𝑖?
2
D
414 𝑖?
2
27
What is the volume of the figure? A
632 𝑖?
3
B 434 𝑖?
3
C 584 𝑖?
3
D
19,200 𝑖?
3
Use the figure below to answer questions 28 and 29. 28
What is the surface area of the figure? A
1,296 ??
2
B 1,086 ??
2
C 1,254 ??
2
D
876 ??
2
29
What is the volume of the figure? A
630 ??
3
B 11,340 ??
3
C 1,890 ??
3
D
2,520 ??
3
Page 17
© 2018 The Math Cafe
Inferences Study Guide: Vocabulary: 1) Population –
the entire group of individuals or objects that is the topic of a data collecting study 2) Sample –
a group of individuals or objects that data is actually collected on (normally because the population will be too large to collect data on every single individual/object). 3) Representative Sample –
a sample that is generally proportional in diversity to its population. 4) Biased Sample –
a sample that does not
represent the diversity of the population
.
5) Random Sample –
A sample where every member of the sample has the same chance of being selected to participate in the data collection (normally generates a representative sample). It is the BEST KIND of sample to use when collecting data. 6) Valid Sample –
a sample is valid if enough individuals/objects were involved in order to make sure the sample is representative of the population. When analyzing data: 7) Mean –
the average
of the data (add all data, divide by the number of numbers) 8) Median –
the middle
number when the data is in order from least to greatest
. If there is no middle number, take the average of the two middle numbers. 9) Mode –
the number that occurs most
in a set of data 10) Range –
the difference
between the highest number and lowest number in a set of data 11) Interquartile Range –
the difference
between the upper quartile (quarter) and the lower quartile Data Displays:
1) Box-and-Whisker Plot (or Box Plot) –
Divides data up into quarters (25%) with only FIVE (5) of the data points plotted: (1) Lower Extreme, (2) Lower Quartile, (3) Median, (4) Upper Quartile, (5) Upper Extreme Example: In the box plot to the right, 25% of the data collected was between 15 and 20, 25% was between 20 and 30, 25% was between 30 45, and 25% was between 45 and 60
. 2) Stem-and-Leaf Plot –
An abbreviated way to record each specific piece of data in an organized way. Will have a key to tell the reader how to interpret the data. Example: In the stem-and-leaf plot to the right, the stem represents the tens place, the “leafs” represent the ones place in which each number represents a new piece of data; there were two pieces of data that fell into the 30’s: 31 and 34
3) Dot Plot - places a dot or x for each piece of data that belongs to a category (see below).
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Page 18
© 2018 The Math Cafe
Use the situation below to answer questions 1 –
4.
Randy is going to survey a sample of his school in order to determine if there is enough support for purchasing new PE equipment. There are a total of 700 students at Randy’s school. 1
Which group of people represents the population
of this situation? A The specific group of students that Randy chooses to survey. B The entire student body (all 700 students).
C The portion of students who vote “yes” for new PE equipment.
D
The portion of students who vote “no” for new PE equipment.
2
Which group of people represents the sample of this situation? A The specific group of students that Randy chooses to survey. B The entire student body (all 700 students).
C The portion of students who vote “yes” for new PE equipment.
D
The portion of students who vote “no” for new PE equipment. 3
Which sampling method would NOT be a method that produces valid data for Randy’s survey?
A Surveying every 5
th
student in the cafeteria. B Surveying every 7
th
student that enters the school in the morning.
C Surveying every student in PE class who looks like they are enjoying class.
D
Drawing 3 letters from a hat and surveying the students who have the last name beginning with those letters. 4
Randy chooses to survey every 5
th
student in the cafeteria. He surveys a total of 140 students and finds that 84 students support buying new PE equipment. If this is a representative sample, how many total students could he predict would support the purchase of new PE equipment out of the entire student body? A 280 students
B 84 students C 588 students D
420 students Use the situation below to answer questions 5 - 8.
Shae is interested in finding out how many of the registered voters in her town will vote to elect her uncle as the new mayor. She knows there are 2,000 registered voters in her town, but does not want to poll all 2,000 voters. 5
Which group of people represents the population
of this situation? A The group of 2,000 registered voters. B Every person who lives in the town.
C Every person who chooses to vot
e for Shae’s uncle.
D
The portion of voters that Shae ultimately surveys.
6
Which group of people represents the sample of this situation? A The group of 2,000 registered voters. B Every person who lives in the town.
C Every person who chooses to vote for Shae’s uncle.
D
The portion of voters that Shae ultimately surveys. 7
Which sampling method would be BEST and produce a representative sample for Shae’s data?
A Polling every other person who shops at the local clothing boutique on a Monday. B Calling every 10
th
person on the registered voter list and asking who they intend to vote for.
C Calling all of her uncle’s friends and asking them who they intend to vote for.
D
Polling every 5
th
person at the senior citizen center. 8
After surveying a re
presentative sample, Shae’s data reports that 4 out of every 7 voters intend to vote for Shae’s uncle. About how many voters can Shae predict will actually vote for her uncle if all 2,000 registered voters decide to vote in the mayoral election? A About 1,224 voters
B About 1,500 voters C About 1,143 voters D
About 1,017 voters
Page 19
© 2018 The Math Cafe
Use the situation below to answer questions 9 - 12 .
The box plots below show the scores of two different classes on the same assessment. 9
Which class has a greater interquartile range? A Class #1 B Class #2
C Both classes have the same interquartile range.
D
There is not enough data to determine which class has the greater inter-quartile range.
10
Which classes data shows 50% of the students scoring a 70 or above? A Class #1 B Class #2
C Both classes have 50% of the students scoring a 70 or above.
D
There is not enough data to determine which class has 50% of the students scoring a 70 or above. 11
Which statement about the data above is TRUE?
A Twenty-five percent of each class scores between a 60 and 70. B Class #2 has a higher median score than Class #1.
C The interquartile range of Class #1 is 5 points greater than the interquartile range of Class #2. D
The lowest 50% of Class #2 is equivalent to the lowest 25% of Class #1. 12
Which statement about the interquartile range of Class #1 is TRUE?
A The interquartile range of Class #1 is twice as large as the difference between the medians of the two classes. B The interquartile range of Class #1 is three times as large as the difference between the medians of the two classes.
C The interquartile range of Class #1 is 20 points greater than its median.
D
The interquartile range of Class #1 is 60. Use the situation below to answer questions 13 - 16 .
Anna decided to collect data on the ages of her classmates in months. She then decided to divide the class alphabetically to compare the data. The dot plots below show two sections of Anna’s class and their ages in months. 13
Which section of the class has a greater age range (in months)? A Section A - F B Section G - Z
C Both sections have the same age range.
D
There is not enough data to determine which class has the greater age range.
14
Which statement about the mean age in months is TRUE? A Section A –
F has a higher mean age than Section G –
Z. B Section A –
F has a lower mean age than Section G –
Z.
C Section A –
F has an equal mean age then Section G –
Z.
D
There is not enough data to determine which section of the class has a greater mean age.. 15
What is the difference
of the medians between Section A –
F and Section G –
Z? A 2 B 3
C 4
D
5 16
As Anna looks at the data, she decides that if your last name is towards the 2
nd
half of the alphabet, you are likely to be older than friends who have last names towards the first part of the alphabet. Is Anna’s thinking justified?
A Yes, the data clearly backs up Anna’s theory.
B No, this is a coincidence. C Maybe, but there is no way to prove one way or the other.
D
Maybe, but Anna should collect more data from the other classrooms in the school because one class is not a large enough sample to make this conclusion.
Page 20
© 2018 The Math Cafe
Use the situation below to answer questions 17 - 20 .
The stem-and-leaf plots below show two data sets. 17
Which statement is TRUE about the medians of the data sets? A Data Set 1 has a greater median than Data Set 2. B Data Set 1 has a lesser median than Data Set 2.
C Data Set 1 has an equal median to Data Set 2.
D
There is not enough data to determine which data set has the greater median.
18
Which statement is TRUE when comparing the means
of the two data sets? A The mean of Data Set 1 is equal to the mean of Data Set 2. B The mean of Data Set 1 is less than the mean of Data Set 2 by approximately 4.
C The mean of Data Set 1 is less than the mean of Data Set 2 by approximately 6.
D
The mean of Data Set 1 is greater than the mean of Data Set 2 by approximately 2. 19
Which statement about the data above is TRUE?
A The range of Data Set 1 is 7 greater than the range of Data Set 2. B The range of Data Set 1 is 9 greater than the range of Data Set 2.
C The range of Data Set 2 is 7 greater than the range of Data Set 1. D
The range of Data Set 2 is 9 greater than the range of Data Set 1. 20
Which statement about the interquartile range of the data sets is TRUE?
A The interquartile range of Data Set 1 is 22. B The interquartile range of Data Set 2 is 24.
C The difference is between the medians is two times the difference between the interquartile ranges. D
All of the above answers are true. Scratch Work
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Page 21
© 2018 The Math Cafe
Study Guide: Vocabulary: 1) Probability –
the chance of an “event” happening; Is always a number between 0 and 1 (can be expressed as a fraction or decimal). 2) Event –
The particular outcome or set of outcomes that occur in an experiment. 3) Outcomes –
All of the possible outcomes that could
happen during an experiment. 4) Sample Space –
A list or diagram of all of the possible outcomes for an experiment. 5) Theoretical Probability –
The probability that an event should occur “in a perfect world” or “in theory.”
6) Experimental Probability –
The probability that actually
occurs when the experiment is attempted in real life. The more the experiment is performed, the closer the experimental probability should get to the theoretical probability. 7) Simulation –
A simulation is an experiment that you can model on a smaller scale that will represent an event in real life that may be too difficult or time-consuming to measure. For example, if you wanted to know the probability of a family having two boys and two girls, you could use flipping a coin to aid you in this experiment because the probability of having either a boy or girl is the same probability as landing on heads or tails (the alternative would be tracking down families with four children and recording how many have two boys and two girls). Calculating Probability - use a ratio to show the number of times the desired outcome is available out of the total number of outcomes. For example: Find the probability of rolling a 3 on a 6-sided die: # ?? ???𝑖??? ????????
# ?? ????? ????????
=
1
6
Since there is only one “3” on a 6
-sided die, the probability of rolling a 3 is 1
6
. This can also be notated as : 𝑷(?) =
?
?
Calculating Compound Probability: find the probabilities of the two separate events, and multiply them together. For example: Find the probability of rolling two fives when rolling two 6-sided dice: 𝑷(? ??? ?) =
1
6
×
1
6
=
?
??
Likelihood: How “likely” an
event is to happen is purely based on its numerical value. See the number line diagram below: Probability
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Page 22
© 2018 The Math Cafe
1
When rolling a 6-sided number cube, what is the likelihood that an odd number will be rolled? A Certain B
Likely C Neither likely nor unlikely D
Unlikely 2
When drawing a marble at random out of the bag below, what is the likelihood of drawing a white marble? A Certain B
Likely C Neither likely nor unlikely D
Unlikely 3
The probability of spinning an even number on this spinner is 0.6. Which word describes the likelihood of this event? A Certain B
Likely C Neither likely nor unlikely D
Unlikely 4
Using the same spinner, calculate the probability of spinning a 4. A 0.4 B
0.2 C 0.5 D
0.1 5
What is the probability of rolling a 1 or a 2 on a 6-
sided number cube? A 1
6
B 1
2
C 1
4
D
1
3
6
Shown below is a Punnett square combining genetics for eye color: Bb (brown eyes with a recessive gene for blue eyes) and bb (blue eyes). What is the probability that the offspring of these two eye genes will be blue eyes (bb)? A 1
4
B 1
2
C 3
4
D
1
7
Mia decided to experiment with probability by rolling a 6-sided number cube. She knows that theoretical probability states that if you roll the cube six times, each number should appear once. Mia rolled the cube six times and got the following results: Because Mia did not roll a 3 or a 4 at all, she has decided that theoretical probability is not true. Is Mia’s decision justified? A No, Mia’s decision
is not justified. If she rolled the number cube more times, she would find that the more she rolled, the closer her experimental probability would get to theoretical probability. B No, Mia’s decision
is not justified. She should know that theoretical probability is a mathematical concept and should not argue with it. C Yes, Mia’s decision is justified. Her experiment proved that the theory was wrong. D
Yes, Mia’s decision is justified. It is common knowledge that you will never produce one of each number if you roll six times. 8
If the spinner below is spun 300 times during an experiment, how many times could you expect it to land on “Blue”?
A ??????? 200 ?𝑖??? B 𝐴?????𝑖?????? 200 ?𝑖???
C ??????? 100 ?𝑖???
D
𝐴?????𝑖?????? 100 ?𝑖???
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9
Josh conducted an experiment with the bag of marbles shown below. He will draw a marble out of the bag, record the result, return the marble to the bag, and draw another marble, continuing the process. If he completes this process 600 times, about how many times should he expect to draw a striped marble? A 𝐴?????𝑖?????? 400 ?𝑖??? B 𝐴?????𝑖?????? 250 ?𝑖???
C 𝐴?????𝑖?????? 200 ?𝑖???
D
𝐴?????𝑖?????? 150 ?𝑖???
10 Ruby flipped the coin and spun the spinner below. What is the probability that the coin will land on heads AND the spinner will land on either a 2 or a 3? A 1
2
B 1
4
C 1
10
D
1
3
11 Dante rolled both six-sided number cubes at the same time. What is the probability of him rolling double sixes? A 1
6
B 1
3
C 1
12
D
1
36
12 The sample space for flipping a coin and rolling a six-sided number cube is shown below. What is the probability of flipping “tails” and rolling an even number? A 1
4
B 1
3
C 1
2
D
1
12
13 A coin is flipped and the spinner below is spun. Which tree diagram correctly represents the sample space for all of the possible outcomes of this event? A
B
C
D
14 Maggie had four colored pencils in a bag: blue, yellow, pink, and
green.
She also had the spinner shown below. Maggie wants to make a table to show the sample space of drawing one colored pencil out of the bag at random as well as spinning the spinner. Which table will show the correct sample space for Maggie’s experiment? A
B
C
D
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