7th Grade Review for Math

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7th Grade Review for Math
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Question 1
Day 1

• Johns test grades were 76, 82, 95, 82, 78, 96,
  91. His math teacher will allow John to choose
  the measure of central tendency to be used for
  his test grades. Which measure should John
  choose? Why?
• Mean because it is the highest value

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Question 1 Explanation

• Calculate the mean, median, mode, and range to
  determine which has the highest value
• Remember the mean is the average add all of the
  numbers and divide by how many there are
• Remember the median is the number in the middle
  (put them in order first)
• Remember the mode is the number that is the most
  often
• Remember the range is the highest minus the lowest

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Question 2
Day 2

• If y gt 2x 7 and y gt 2x 7 were each graphed a
  number line, explain the difference between the
  two graphs.
• y gt 2x 7 will have an open circle,
• y gt 2x 7 will have a closed circle

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Question 2 Explanation

• Graphing inequalities
• less than (lt) and greater than (gt) signs are an
  open circle because the number is NOT included in
  the solution set
• less than or equal to (lt) and greater than or
  equal to (gt) are a closed circle because the
  number IS included in the solution set

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Question 3 and 4
Day 3

• Name at least two 3-dimensional figures for which
  a circle could be the base.
• Cone and Cylinder
• Translate into an equation and solve
• Eight more than a number is twenty seven.
• n 8 27 n 19

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Question 3 and 4 Explanation

• Question 3
• The base of both a cone and a cylinder is a
  circle
• Question 4
• Replace the following words with the correct
  symbol
• The words more than mean add
• The words a number mean a variable
• The word is means equal
• Re-write the statement using the numbers and
  symbols
• Solve the equation by doing the inverse operation

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Question 5
Day 4

• A basket of 25 peaches weighs 232 ounces. After
  10 peaches are removed, the basket weighs 9 ½
  pounds. How much does the basket weigh in
  ounces?
• 152 ounces

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Question 5 Explanation

• There are 16 ounces in a pound. Multiply the
  number of pounds that the basket weighs by 16.
  This will give you the number of ounces that the
  basket weighs.
• The 25 peaches weighing 232 ounces is extra
  information. IGNORE IT!!

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Question 6
Day 5

• In Pollville, records are kept on previous
  mayors. Here are the ages of the last 6 mayors
  when they were voted into office 45, 88, 37, 42,
  41, 44. How does the outlier affect the mean?
• The mean is 7.7 points higher with the outlier
  than without.

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Question 6 Explanation

• First identify the outlier the number that is a
  lot bigger or a lot smaller than the other
  numbers. In this case the outlier is 88.
• Using all of the numbers find the mean (add all
  of the numbers and divide by how many there are).
  Write that number down.
• Cross out the outlier. Find the mean again
  without the outlier. Write that number down.
• Subtract the 2 means. That is the affect of the
  outlier.

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Question 7 and 8
Day 6

• A triangle is graphed on a coordinate grid on
  which each unit is a centimeter. It has vertices
  at points (2, -8), (2, 5), and (-4, 5). Find its
  area.
• 39 centimeters squared
• Translate into an equation and solve
• A number added to eight equals five.
• 8 n 5 n -3

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Question 7 and 8 Explanation

• Question 7
• Draw a coordinate plane and graph the triangle.
• Find the area of the triangle (1/2 base x height)
• To find the base and the height, count the number
  of units across (base) and up (height).
• Question 8
• Replace the following words with the correct
  symbol
• The word added means add
• The words a number mean a variable
• Re-write the statement using the numbers and
  symbols
• Solve the equation by doing the inverse operation

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Question 9
Day 7

• Mrs. Adams is building a miniature table for a
  dollhouse. The table will be a scale model of
  her dining room table. The top of her table
  measures 36 inches wide and 72 inches long. If
  the width of the miniature table will be 1.5
  inches, what will be its length?
• Length 3

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Question 9 Explanation

• Make a table
• Write the information as a proportion.
• Cross multiply and divide

  Table Model
Length 72  
Width 36 1.5
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Question 10 and 11
Day 8

• Unit Five starts on page 126 and ends on page
  241. How many pages long is the unit?
• 115 pages long
• Translate into an equation and solve
• The product of five hundredths and a number is
  11
• .05n 11 n 220

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Question 10 and 11 Explanation

• Question 10
• The words how many long mean subtract
• Subtract the two numbers to find the length of
  the unit
• Question 11
• Replace the following words with the correct
  symbol
• The words product of mean multiply
• The words a number mean a variable
• The word is means equal
• Re-write the statement using the numbers and
  symbols
• Solve the equation by doing the inverse operation

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Question 12
Day 9

• Write an algebraic expression to explain the
  pattern
• 2, 5, 11, 23, ____. ____, ____
• 2x 1

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Question 12 Explanation

• Ask yourself how am I getting from each number
  to the next?
• Make a list of all of the ways you can get to the
  next number
• Are you adding, subtracting, multiplying,
  dividing or a combination of the operations?
• The answer is the one that works EVERY time!

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Question 13
Day 10

• The lengths of the sides of a 5 m by 5 m square
  are increased by 3 m. The area of the square has
  increased by what percent?
• 156

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Question 13 Explanation

• This is a Percent of Change Question!
• Find the area of the square.
• Add three to each side.
• Find the area of the square again.
• Subtract the two areas put that number as the
  numerator
• Put the first area as the denominator
• Convert the fraction to a percent
• Divide bottom into top and move the decimal point
  2 places to the right.

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Question 14
Day 11

• The supply purchasing agent for Carowinds has a
  formula which tells her how much sugar to buy
  when she knows how much cotton candy will be
  sold s 40 0.125c
• c cotton candy sales s pounds of sugar
• On a day when 8,000 people purchase cotton
  candy, how much sugar should be purchased?
• 1040 pounds

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Question 14 Explanation

• Write the formula that they give you
• Replace the variable with the given numbers
• Solve the equation by doing the inverse operation

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Question 15 and 16
Day 12

• Which is a better buy a 14 ounce box of popcorn
  for 1.98 or a 36 ounce box of popcorn for 2.59?
  
• 36 ounces for 2.59
• Translate the equation into words
• 15x 11 56
• Eleven more than fifteen times a number is fifty
  six

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Question 15 and 16 Explanation

• Question 15
• Find the unit price
• Divide the price by the number of ounces
• The lower price is the better buy
• Question 16
• Replace the symbols with the correct words
• When a number is right next to a variable it
  means multiply, so use a multiplication key word
• Use the words a number for the variable
• Use an addition key word
• Use a key word for equals
• Re-write the equations using words

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Question 17 and 18
Day 13

• A soccer ball is usually priced at 16. It is on
  sale for 25 off and a 6 sales tax must be added
  to the price. How much will the customer pay for
  the soccer ball?
• 12.72
• Write and solve the equation
• The cost, c, of a CD is twice the cost of a 7
  tape. What is the price of the CD?
• c 2(7) c 14

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Question 17 Explanation

• When an item is on sale
• Multiply the price and the percent off (remember
  to change the percent to a decimal by moving the
  decimal point 2 places to the left)
• The answer will be the amount of money saved
  subtract this number from the original price
• To find sales tax
• Multiply the price and the tax (change the
  percent to a decimal)
• The answer will be the amount of tax add it to
  the original price

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Question 18 Explanation

• Replace the following words with the correct
  symbol
• The c is the variable
• The word twice means 2 times
• Re-write the statement using the numbers and
  symbols
• Solve the equation

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Question 19 and 20
Day 14

• A number has been decreased by 12. The result is
  5. Find the original number.
• 7
• Mrs. Math asked her student, Molly, to tell which
  was greater 80 or 4/5 or 0.8
• Molly said that they were all equal. Explain
  why or why not Molly is correct.
• If you convert them to the same type of rational
  number they are equal

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Question 19 and 20 Explanation

• Question 19
• The words a number means a variable
• The words decreased by means subtract
• Re-write the statement using the numbers and
  symbols
• Solve the equation by doing the inverse operation
• Question 20
• Convert each unit to the same unit a fraction, a
  decimal, or a percent.
• Put them in numerical order and compare

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Question 21
Day 15

• The scale on a map is 1 inch30 miles. Westboro,
  Malden, and Oxbridge are all located on Route 2
  and Malden is between Westboro and Oxbridge. On
  the map, the distance from Westboro to Malden is
  2.5 inches and the distance fro Westboro to
  Oxbridge is 5.75 inches. How far, in miles, is
  Malden from Oxbridge?
• 247.5 miles

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Question 21 Explanation

• This is a scale factor question!
• You are converting from a small unit to a large
  unit so you are going to divide
• Divide the distance between the two cities (in
  this case 8.25 inches you have to add the two
  distances they give you) by the scale factor (in
  this case 1/30.
• Remember the scale factor is a fraction so you
  need to Keep Change Flip!
• This will give you the total distance in miles.

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Question 22
Day 16

• A stadium seats 40,000 people. Tickets were 12
  each and 24,000 seats were sold. What percent of
  the stadium was full? How much money was
  collected?
• 60 full and 288,000 collected

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Question 22 Explanation

• This is a ratio/percent question
• Write the number of seats as a ratio
• Number of seats full Total number of seats
• Convert this ratio to a percent by dividing
  bottom into top and moving the decimal point 2
  places to the right
• To find the amount of money collected
• Multiply the number of full seats (24,000) by the
  cost of the ticket (12)

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Question 23
Day 17

• Investigate the Data
• Ages of 24 Night Class Students
• 2 3 5 5 8
• 3 0 1 2 2 4 4 4 4 5 6 6 7 8 8
  9
• 4 1 3 3 8
• A) Find the mean, median, and mode of the data
  set.
• B) Name the range, lower extreme, upper extreme,
  first quartile, and third quartile of the data.
• C) What percent of the data is represented by
  the box in the box-and-whisker plot?
• A) 34.6, 34, 34
• B) 25, 23, 48, 31, 38
• C) 56.5

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Question 23 Explanation

• A)
• Calculate the mean by adding all of the numbers
  and dividing how many numbers there are
• Find the median (the number in the middle) and
  the mode (the number that is most often)
• B)
• Calculate the range by subtracting the biggest
  and smallest numbers
• Find the lower extreme (the smallest number) and
  the upper extreme (the largest number)
• Find the first quartile (the median of the bottom
  half of data, or the numbers before the median)
  and the third quartile (the median of the upper
  half of data, or the numbers after the median.

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Question 23 Explanation Continued

• C)
• To find the percent of the data represented by
  the box in a box and whisker plot
• Count how many numbers there are from the first
  quartile to the third quartile write this number
  as the numerator.
• Write the total number of values as the
  denominator
• Convert the fraction to a percent by dividing
  bottom into top and moving the decimal point 2
  places to the right.

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Question 24
Day 18

• Tammy was paid 5 an hour for washing cars. She
  worked 3 hours on Friday, 9 hours on Saturday,
  and 5 hours on Sunday. Materials cost her
  32.75. How much money did she make after
  expenses?
• 52.25

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Question 24 Explanation

• Calculate the total number of hours that Tammy
  worked
• Add the number of hours for each day
• Multiply the number of hours by the amount of
  money that she earns per hour
• Subtract the amount of money needed for expenses
  from the amount of money she earned
• This will be her earnings after expenses.

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Question 25
Day 19

• Jason bought a car for 3,500. He sold his truck
  for 1,500 which he used as a down payment. The
  remaining amount was borrowed at 4.5 interest
  for 5 years. How much interest will he pay?
• How much will his total repayment be?
• 450 2,450

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Question 25 Explanation

• This is a Simple Interest Question
• First you have to find the Principle amount
• Subtract the cost of the truck and his down
  payment
• Write the formula I P x R x T
• Replace the letters with the values from the
  question and do the math.
• This will be the interest
• Add the interest to the principle to find the
  total amount he has to repay to the bank

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Question 26
Day 20

• The surface area, SA, of a sphere is found using
  the formula SA 4?r² , where r is the radius of
  the sphere. Find the surface area of a sphere
  with a radius of 2.5 inches.
• 78.5 square inches

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Question 26 Explanation

• On the EOG you will be given formulas that you
  are not familiar withdont worry, just replace
  the letters with the numbers they give you and do
  the math!

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Question 27
Day 21

• Martha entered the elevator and went down seven
  floors, up ten floors, up two floors, then down
  five floors. She was then on the eleventh floor.
  On what floor did she enter the elevator?
• Eleventh floor

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Question 27 Explanation

• This is a Negative Numbers Question
• Re-write it as a number sentence and do the math
  (remember down is a negative number and up is a
  positive number)
• -7 10 2 5
• This number sentence equals 0 so the elevator is
  still on the same floor!

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Question 28
Day 22

• The Jones family rented a car for 3 days of their
  vacation. The rental charge was 21.95 per day
  plus 0.17 per mile. If the bill was 96.96
  before taxes, write and solve an equation to find
  the number of miles, m, they drove
• 3(21.95) 0.17m 96.96 183 miles

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Question 28 Explanation

• Replace the following words with the correct
  symbol
• The word per means multiply
• The word was means equal
• Re-write the statement using the numbers and
  symbols
• Solve the equation using inverse operations

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Question 29
Day 23

• A brownie pan has dimensions of 8 inches by 4
  inches by 2 3/5 inches. Compute the volume of
  the pan. Express your answer in decimal form.
  If the batter is 1.75 inches deep, what percent
  of the pan is filled with brownie batter?
• 83.2 cubic inches 67.3 full

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Question 29 Explanation

• First find the volume of the pan by using the
  formula Bh (the area of the base x the height or
  length x width x height)
• Next find the volume of the batter by multiplying
  the area of the base of the pan (length x width)
  by the height of the batter
• Finally write a fraction using the volume of the
  batter as the numerator and the volume of the pan
  as the denominator
• Convert the fraction to a percent by dividing
  bottom into top and moving the decimal point 2
  places to the right.

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Question 30
Day 24

• The Wiley family went to Pizza Place for dinner.
  They bought two pizzas for 12.95 (tax included)
  each. Mr. Wiley wanted to add a 20 tip to the
  bill. What was the total cost of the dinner?
• 15.54

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Question 30 Explanation

• To find the amount of a tip
• Multiply the cost of the meal and the percent
  (remember to change the percent to a decimal by
  moving the decimal point 2 places to the left)
• To find the total cost of the meal add the cost
  of the meal and the tip

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Question 31 and 32
Day 25

• A goat is tied to a corner of a 60 ft by 75 ft
  barn in the center of a grassy field. His rope
  is 50 ft long. Approximately how much area does
  he have to graze?
• 7,850 square feet
• Roger babysits 4 ¾ hours each Saturday and each
  Sunday. He plans to babysit for 3 ½ weekends
  next month. What is the total number of hours he
  will babysit next month?
• 33 ¼ hours

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Question 31 Explanation

• Question 31
• This is the area of a circle question
• Write the formula 3.14 x radius x radius
• Replace the words with the numbers and do the
  math
• The size of the barn is extra information IGNORE
  IT!!

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Question 32 Explanation

• A weekend it 2 days Saturday and Sunday so a
  half of a weekend would be 2 day.
• Calculate the number of hours worked in a weekend
  by adding the number of hours for Saturday and
  Sunday.
• Multiply by 3 ½ to get the total number of hours
  for 3 ½ weeks

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Question 33
Day 26

• Ali is going to paint her schools basketball
  court. How many square feet of area does she
  need to paint if the court is 384 inches long and
  108 inches wide?

408 square feet
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Question 33 Explanation

• To find area of a rectangle multiply length
  times width HOWEVER- the question wants the
  answer in feet so you have to divide each
  measurement by 12 first
• 384/12 32 feet
• 108/12 15 feet
• After you have converted the measurements then
  multiply
• 32 x 15 408 square feet

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Question 34
Day 27

• The 7th grade students were voting on locations
  for a class trip. Two-ninths voted to go to the
  zoo and four-sevenths voted to go to an amusement
  park. If there are 250 students How many
  voted to go to the zoo? How many voted to go to
  an amusement park? How many students did not
  vote?

56
143
51
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Question 34 Explanation

• To find fractional parts multiply the total
  number of students by each fraction
• 250 x 2/9 55.555 about 56 students
• 250 x 4/7 142.857 about 143 students
• So 56 students voted for the zoo 143 students
  voted for an amusement park
• To find the number of students who have not
  voted add 56 143 199 then subtract 199 from
  250 250 199 51
• So 51 students did not vote

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Question 35
Day 28

• Stan has just started a new job. In the first
  week he is paid 7 an hour plus a 50 bonus. How
  much money does he make in the first week if he
  works 32 hours?

274
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Question 35 Explanation

• Stan makes 7 an hour for each of the 32 hours so
  multiply the number of hours by the dollar
  amount
• 32 x 7 224
• Then add the bonus 224 50 274
• So Stan makes 274 the first week

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Question 36
Day 29

• Monica makes 3 times as much money as George. If
  Monica make 5.52 an hour how much does George
  make. Write an equation to solve this problem.

1.84
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Question 36 Explanation

• Equation 3g 5.52
• Monica make 3 times George which is equal to
  5.52
• Solve the equation
• Divide both sides by 3 to get the g by itself
• 5.52/3 1.84
• So George makes 1.84

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Question 37
Day 30

• A 52 foot light post casts a shadow that is 72
  feet long. At the same time a lighthouse casts a
  shadow of 180 feet long. How tall is the
  lighthouse?

130 feet tall
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Question 37

• Write a proportion
• Height of lamp post Height of lighthouse post
  shadow lighthouse shadow
• Plug in the numbers
• 52 ? 72 180
• Cross multiply and divide
• 180 x 52 9360
• 9360/72 130
• So the lighthouse is 130 feet tall