7th Grade Math Review 1-Freeman

​Q1 & Q2 Review-Math 7

By Jessica Freeman

​7.G.A.1-Scale Drawings

Multiple Choice

Pam drew a scale drawing of a game room. She used the scale 1 inch : 2 feet. If the air hockey table is 5 inches in the drawing, how long is the actual air hockey table?

• 10 Feet

• 2.5 Feet

• 5 Feet

• 15 Feet

Multiple Choice

Desmond measured a city park and made a scale drawing. The scale he used was 1 centimeter : 9 meters. The actual width of the soccer field is 54 meters. How wide is the field in the drawing?

• 6 cm

• 486 cm

• 9 cm

• 54 cm

Multiple Choice

Alan drew a scale drawing of a house and its lot. The scale he used was 1 millimeter : 5 meters. In the drawing, the lawn in the backyard is 10 millimeters long. What is the length of the actual lawn?

• 50 m

• 2 m

• 10 m

• 5 m

Multiple Choice

Brody drew a scale drawing of a campsite. He used the scale 1 inch : 3 feet. If the actual width of the tent is 6 feet, how wide is the tent in the drawing?

• 2 in

• 1 in

• 3 in

• 18 in

Multiple Choice

Kenny drew a scale drawing of a swimming pool. The scale of the drawing was 2 centimeters : 1 meter. If the pool is 26 centimeters in the drawing, how wide is the actual pool?

• 13 m

• 2 m

• 1 m

• 52 m

Multiple Choice

Spencer measured a house and its lot and made a scale drawing. He used the scale 3 inches : 2 feet. In the drawing, the deck is 90 inches long. What is the length of the actual deck?

• 60 ft

• 6 ft

• 180 ft

• 270 ft

Multiple Choice

Jonathan drew a scale drawing of a house. The scale of the drawing was 1 millimeter : 2 meters. If the actual width of the garage is 8 meters, how wide is the garage in the drawing?

• 4 mm

• 16 mm

Multiple Choice

Edgar drew a scale drawing of the town library. The scale of the drawing was 5 centimeters : 2 meters. The parking lot is 34 meters wide in real life. How wide is the parking lot in the drawing?

• 85 cm

• 68 cm

Multiple Choice

A building is 360 feet tall. On a scale drawing, 1/4 inch = 10 feet. What is the height of the building in the scale drawing?

• 15 in

• 9 in

• 7 in

• 13 in

Multiple Choice

Norris is doing renovations in the living room of his home. The length of the room is 22 feet, and the width of the room is 19 feet. A proportional scale drawing of the room was created that has width of 38 inches. What is the length in the scale drawing?

• 51 in

• 44 in

• 50 in

• 59 in

Multiple Choice

A flagpole is 1 in.= 4 ft. If the pole measures 12 inches, how tall is the actual pole?

• 16 feet
• 3 feet
• 48 feet
• 9 feet

Multiple Choice

A blueprint was using a scale of 3cm=4.5m. Find the actual length if it is 5cm on the drawing.

• 7.5
• 13.5
• 1.5
• 1.7

Multiple Choice

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, how far apart are they?

• 87 km
• 216 km 
• 33 km
• 192 km

Multiple Choice

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

• 14 in 
• 7 in
• 42 in
• 56 in

Multiple Choice

The windows in the drawing are 1¾ cm apart, how many meters apart are the actual windows if the scale is 2 cm=10 m?

• 8¾ m

• 7½ m

• 5 m

• 2¼ m

Multiple Choice

The scale of a mug in a picture is ½ in.=3 cm. Find the actual length of the 4 in. coffee mug.

• 24 cm
• 6 cm
• 30 cm
• 13 cm

Multiple Choice

A scale drawing of a house shows 9cm ×10cm. If 6cm=12 ft, what are the actual dimensions?

• 9ft x 10ft
• 1ft x 2ft
• 12ft x 6ft
• 18ft x 20ft

Multiple Choice

If the actual dimensions of the kitchen are 24 ft. by 24 ft., what is the scale of the drawing?

• 1cm : 9ft
• 1cm : 8ft
• 4cm : 1ft
• 1cm : 4ft

Multiple Choice

The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?

• 12 feet
• 16 feet 
• 10 feet
• 4 feet

Multiple Choice

From Denver to Chicago = 3 in. If the scale is 1 in = 300 miles, find the actual distance.

• 300 miles
• 1000 miles
• 900 miles
• 600 miles

​7.RP.A.1-Unit Rates

Multiple Select

Find the unit rate - $112 in 8 hours

• $12 per h

• $14 per h

• $13 per h

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound

• $35 per pound

• $5 per pound

• $0.125 per pound

Multiple Choice

A store has 120 customers in 6 hours. What is the unit rate in customers per hour?

• 16 customers per hour

• 12 customers per hour

• 20 customers per hour

• 15 customers per hour

Multiple Choice

Will spent $3.75 for 3 pounds of granola. What is his unit rate in dollars per pound?

• $.50 per pound

• $1.25 per pound

• $3 per pound

• $2.50 per pound

Multiple Choice

If Antonia can type 408 words in 4 minutes, how many words can she type per minute?

• 408 words per minute

• 100 words per minute

• 400 words per minute

• 102 words per minute

Multiple Choice

• 20

• 36/5

• 1/20

• 60/3

Multiple Choice

• 7/100

• 35/20

• 7/4

• 21

Multiple Choice

• 6/5

• 5/6

• 15/128

• 15/16

Multiple Choice

Simplify the complex fraction shown.

• 9/40
• 40/9
• 10/36
• 5/18

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound
• $5 per pound
• $35 per pound
• 0.125 pounds per dollar

Multiple Choice

8.  Find the unit rate of $97.50 for 15 pizzas.

• $6 per pizza
• $82.50 per pizza
• $5.50 per pizza
• $6.50 per pizza

Multiple Choice

Sasha can mow 3/8 of an acre of grass in 3/4 an hour. How many acres of grass does Sasha mow per hour?

• 2  ac./hr.
• 1/2  ac./hr.
• 9/24  ac./hr.

Multiple Choice

Which is the better deal?
Oreos
$2.98 for 15 oz
OR
Chips Ahoy
$2.50 for 14 oz

• Oreos
• Chips Ahoy
• They are the same

Multiple Choice

A unit rate is

• a rate with the numerator of one.

• a rate with the denominator of one.

Multiple Choice

Identify the best deal.
27 ounces of nacho chips for $3.51
10 ounces of nacho chips for $1.30

• 27 ounces of nacho chips for $3.51
• 10 ounces of nacho chips for $1.30
• Neither

Multiple Choice

An eight pack of juice boxes costs $4.79, and a 12 pack of juice boxes cost $6.59. Use this information to calculate the better buy.

• 8 pack
• 12 pack

Multiple Choice

Which option is the better deal?
Doritos
$4.39 for 11.5 oz
or
Cheetos
9.75 oz for $3.24

• Doritos
• Cheetos

Multiple Choice

Which statement best describes the relationship between x and y in the table?

• Proportional
• Not Proportional

Multiple Choice

Does the table represent a proportional relationship?

• Yes.
• No.

Multiple Choice

What is the total cost of tickets if there are 7 adults?

• $600
• $75
• $500
• $525

Multiple Choice

Find the unit rate: $3.60 for 3 pounds of apples.

• $1.00 per pound

• $3.60 per pound

• $1.20 per pound

• $1.10 per pound

Multiple Select

Find the unit rate - 49 points in 7 games

• 6 points per game

• 8 points per game

• 7 points per game

Multiple Select

Find the unit rate - 120 problems in 5 hours

• 24 problems per h

• 22 problems per h

• 10 problems per h

Multiple Select

Find the unit rate - 150 miles in 6 gallons

• 20 miles per gallon

• 25 miles per gallon

• 22 miles per gallon

Multiple Select

Find the unit rate - 105 students in 3 classes

• 33 students per class

• 32 students per class

• 35 students per class

Multiple Select

Find the unit rate - 549 vehicles on 9 acres

• 61 vehicles per acre

• 60 vehicles per acre

• 62 vehicles per acre

Multiple Select

Find the unit rate - 88 students for 4 classes

• 20 students per class

• 21 students per class

• 22 students per class

Multiple Select

Find the unit rate - $920 for 40 hours

• $20 per h

• $22 per h

• $23 per h

Multiple Select

Find the unit rate - $11.49 for 3 packages

• $3.85 per package

• $3.83 per package

• $3.88 per package

Multiple Select

Find the unit rate - 13 apples for 2 pies

• 6 apples per pie

• 6.25 apples per pie

• 6.5 apples per pie

​7.RP.A.2-Proportional vs. Non-Proportional Relationships

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

Multiple Choice

Which line shows a proportional relationship between x and y?

• Line L
• Line M

Multiple Choice

What is the unit rate in this proportional relationship?

• 60 miles/1 hour
• 120 miles/ 2 hours
• 1 mile/ 1 hour

Multiple Choice

Which statement best describes the relationship between x and y in the table?

• Proportional
• Not Proportional

Multiple Choice

The cost of 4 pounds of grapes is $24.36. What is the constant of proportionality the relates cost in dollars, y, to the number of pounds of grapes, x?

• 6.09
• 20.36
• 8.12
• 28.36

Multiple Choice

What is a Ratio?

• A comparison of two quantities 
• To multiply two fractions 
• A number over another number
• Two decimals that can be multiplied

Multiple Choice

What makes a graph proportional?

• Straight Line
• The line goes through (0,0)
• Curvy line
• Straight line and passes through (0,0)

Multiple Choice

Is this table proportional?

• yes
• no
• I'm not sure, I need extra help!

Multiple Choice

Josh bought a pizza with eight slices of pizza for $12. What is the cost of a slice of pizza?

• $12
• $1.50
• $3
• $1

Multiple Choice

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, what is the actual distance between the 2 cities?

• 87 km
• 216 km 
• 33 km
• 192 km

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y
• x
• 14
• y=14

Multiple Choice

What is the constant of proportionality?

• 15
• 5
• 75
• 25

Multiple Choice

What is the constant of proportionality (in miles per hour) based on the table?

• 45
• 90
• 135
• 2

Multiple Choice

What is the equation y=kx for the table?

• y=1/3x
• y=3x
• y=5x
• y=1/5x

Multiple Choice

Which equation matches the graph?

• y = 8x
• y = 1x
• y = 3x
• y = 16x

Multiple Choice

The cost of 4 pounds of grapes is $24.36. What is the constant of proportionality that relates cost in dollars, y, to the number of pounds of grapes, x?

• 6.09
• 20.36
• 8.12
• 28.36

Multiple Choice

A machine packs boxes at a constant rate of 2/3 a box every 1/2 a minute.  What is the number of boxes it packs per minute?

• 1/3
• 3/4
• 7/6
• 4/3

Multiple Choice

Does this equation represent a proportional relationship?

• Yes
• No

Multiple Choice

What is the scale factor?

• 3
• 18/6
• 1/3

Multiple Choice

These figures are similar.  Solve for x.

• 3
• 5
• 4
• 2

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

​7.NS.A.1-2-Combining Integers

Absolute Value and Additive Inverse Review

Lesson 1.1
Integers and Their Opposites

Rules of Integers

Rules for Adding and Subtracting Integers

• When two numbers are positive, the rules you have always used still apply.

• When two or more numbers that are negative, add the numbers together and keep the negative sign.

   (Example: - 5 - 7 = - 12)

• When you have one positive and one negative number, subtract the numbers and keep the sign of the larger number. (Example: - 10 + 3 = - 7)

• When two negative signs are right next to each other, replace the negative signs with a positive sign.

  (Example: -6 - (- 4) becomes - 6 + 4 = - 2)

  
  

Rules for Multiplying and Dividing Integers

• If two integers are positive, the answer will be a positive integer.

  Example: 2 x 5 = 10

• If two integers are negative, the answer will be a positive integer.

  Example: -2 x -5 = 10     -10/-2 = 5

• If there is one positive and on negative integer, the answer will be negative.

  Example: -2 x 5 = -10     or   2 x -5 = -10

• If you are multiplying or dividing more than two integers, if there is an even amount of negative integers, the answer will be positive.  If there is an odd amount of negative integers, the answer will be negative.

  Example: -2 x -2 x 5 = 20 because there are two negative integers.

  Example: -2 x -2 x -5 = -20 because there are three negative integers

  
  

  
  

Fill in the Blank

$$\frac{-36}{3}$$  

Fill in the Blank

$$-22\times10$$  

Fill in the Blank

$$-24+27\ =$$  

Fill in the Blank

-14 - (-11) =

Fill in the Blank

27 - 36 =

Fill in the Blank

-412 - (-400)

Fill in the Blank

$$180\ \div\ \left(-12\right)$$  

Fill in the Blank

-2 x -4 x -6 =

Fill in the Blank

If you have an odd number of negative numbers to be multiplied, will your answer be positive or negative?

Fill in the Blank

If you have 2 positive numbers and two negative numbers to be multiplied, will your answer be positive or negative?

Fill in the Blank

If you are combining (adding or subtracting) two negative numbers, will your answer be positive or negative?

Fill in the Blank

-6 x 5 x (-5)

Definitions:

Opposite Integers: An opposite integer is an integer that shares the same distance from 0 as its opposite.
Ex: -1 and 1 or -5 and 5 or -10000000 and 10000000
Absolute Value: The absolute value of a number is the distance that number has from 0. Note: if two numbers share the same absolute value, they will be opposite integers.
Ex: |5| = 5 or |-10| = 10

​Visual:

​Today's Goal:

​Today we are going to learn to identify and use opposite integers. We will do this using number lines, counters and common sense.

​Ex: Use counters to find the opposite integer of 3.

Multiple Choice

What is the opposite integer of 4?

• 0

• -4

• 4

• 8

Multiple Choice

What is the opposite integer of -6?

• -5

• -6

• 0

• 6

​Ex: Use a number line to find the opposite integer of -7.

Draw

Find the opposite integer of -2 and use the number line to show this.

​Quantities combining to make zero:

1. ​Mr. Carbone has $5 in his pocket and spent $5. How much money does he have left?

2. Mr. Carbone is bad at keeping friends. Last year he made 4 friends and lost 4 friends. What was his net change in friends.

3. Class Example?

4. Pair and share:

Multiple Choice

Which statement best describes a situation where quantities combine to make 0?

• A scuba diver swam to a location 20 feet below sea level, then she swam 10 feet deeper.

• A hot air balloon used propane to fly 50 feet higher, then used weights to fly 50 feet lower.

• A child grew 1.5 inches taller one year, then 1.5 inches taller the next year.

• A farmer mowed 4 inches off his grass one week, then it grew 7 inches the next week.

​Conclusion: Write two complete sentences about what you learned.

​I learned that opposite integers share _______.

I can use tools like _____ or _____ to show opposite integers.
I know two quantities will combine to zero if they are _____.

Multiple Choice

Which is the least integer?

• 1

• -1

• -2

• -8

Multiple Choice

Which is the greatest integer?

• -33

• -31

• -28

• -17

Multiple Choice

Which answer has the integers in order from least to greatest?

• − 9, -5, -3, 0, 4, 3

• − 9, -5, -3, 0, 3, 4

• − 5, -9, -3, 0, 4, 3

• 3, 4, 0, -3, -5, -9

Multiple Choice

Compare: 6 ? -3

• =

• >

• <

Multiple Choice

Compare: -3 ? -5

• >

• <

• =

Multiple Choice

What is the absolute value of 87?

• -87

• 87

Multiple Choice

What is the absolute value of -77?

• 77

• -77

Multiple Choice

What does the absolute value symbol look like?

Multiple Choice

• -13

• 13

Multiple Choice

• -50

• 50

Multiple Select

What does absolute value mean? Choose ALL that are correct.

• The number itself

• The number needed to make zero when you add

• A number's distance from zero

• The opposite of a number

Multiple Choice

What is the additive inverse of -13?

• -13

• 13

Multiple Choice

What is the additive inverse of 8?

• 8
• 0
• -0
• -8

Multiple Select

What does additive inverse mean? Choose ALL that are correct.

• The number itself

• The number needed to make zero when you add

• A number's distance from zero

• The opposite of a number

Multiple Choice

What is the difference between additive inverse and absolute value?

• Nothing. They are the same thing.

• One is a distance so it's always positive.

• One is more difficult than the other.

Multiple Choice

______________ are the set of whole numbers, their opposites, and zero.

• Rational Numbers

• Opposites

• Integers

• Absolute Values

Multiple Choice

______________ is the distance between a number and zero.

• Additive inverse

• Opposites

• Integers

• Absolute value

Multiple Choice

Additive Inverse example

• -5 + 5 = 0

• |-4| = 4

• -2 + -2 = -4

Multiple Choice

What is the additive inverse of -77?

• 77

• -77

Multiple Choice

|-3| - |1| =

• -4
• 2
• -2
• -4

Multiple Select

Which pair(s) of numbers are opposites? Choose ALL correct answers.

• 4 and -4

• 3.6 and -6.3

• 9/11 and -9/11

Multiple Choice

• -44

• 44

• I have no idea.

Multiple Choice

• <

• >

• =

Multiple Choice

• <

• >

• =

Fill in the Blank

You start 5 feet below sea level. You walk 12 feet up a hill. You then trip and fall 10 feet down the hill. What integer represents your height in relation to sea level?

Multiple Choice

A) Which city is the closest to sea level (0 ft)?

B) Which city has the coldest average temperature?

• A) New Orleans and B) Cleveland

• A) Cleveland and B) Miami

• A) Miami and B) Burlington

• A) Miami and B) Cleveland

Absolute Value and Additive Inverse Review

​7.EE.A.1-Combining Like Terms

Multiple Choice

Simplify by combining like terms:
5a + 2b - 3a + 4

• 8a + 2b + 4
• 2a + 2b + 4
• 8ab
• 4ab + 4

Multiple Choice

A coefficient is __________.

• the variable
• a constant
• an exponent
• the number that comes before the variable

Multiple Choice

How many terms does this expression have?
-18y + 7yz - 4z

• -18
• 3
• 7
• -4

Multiple Choice

Simplify: x + 3x + 6x + x

• 9x

• 11x

• 2x + 9x

• Can't be simplified

Multiple Choice

Simplify: 7t - 3t + t - 3t

• 2t

• 8t - 6t

• 14t

• Can't be simplified

Multiple Choice

Simplify: 4q + 4t + 3q + t

• 12tq

• 3q + 4t

• 7q + 5t

• Can't be simplified

Multiple Choice

Simplify: 10w + 3d + 3w + d

• 13w + 4d

• 17wd

• 13w + 3d

• Can't be simplified

Multiple Choice

Simplify: m + m + m + m

• 4m

• m⁴

• m

• Can't be simplified

Multiple Choice

A variable can be _______?

• Any number

• Any letter of the alphabet

• only X

• only 1

Multiple Choice

Simplify the expression: 7v + 2 + 12 + 2v

• 23
• 23v
• 9 + 14v
• 9v + 14

Multiple Choice

Simplify by combining like terms.
m + 9 - 4m

• 5m
• m + 5m
• -3m + 9
• 4m

Multiple Choice

Which expression is equivalent to  $$8c\ +\ 6\ -\ 3c\ -\ 2?$$  

• $$5c+4$$  

• $$5c+8$$  

• $$11c+4$$  

• $$11c+8$$  

Multiple Choice

Simplify by combining like terms.
-14w + 8 + 9w - 2

• 23w + 6
• -23w + 6
• -6w + 7
• -5w + 6

Multiple Choice

Combine Like Terms

30 + 80k + 9k + 27

• 57 + 89k

• 57 + 720k

• 30 + 80k

Multiple Choice

Simplify: x + 3x + 6x + x

• 9x

• 11x

• 2x + 9x

• Can't be simplified

Multiple Choice

Simplify: 5 + 11y + 2

• 5 + 11y

• 18y

• 11y + 7

• 11y + 3

Multiple Choice

Simplify: 15x + 19 + 2x + 4

• 17x + 15

• 17x + 23

• 30x + 15

• 13x + 15

Multiple Choice

5(a + 6)

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

6 (x + y + 7)

• 6x + 6y + 42

• 12xy + 42

• 6x + 6y + 7

• 6x6y + 42

Multiple Choice

Which of the following is equivalent to 4(2x + 3)

• 8x + 12
• 8x + 3
• 8x - 12
• 20x