Transcript 7th Grade Review for Math

th
7
Grade Review for Math
Day 1
Question #1
 John’s 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
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
Day 2
Question #2
 If y > 2x + 7 and y > 2x + 7 were each
graphed a number line, explain the
difference between the two graphs.
 y > 2x + 7 will have an open circle,
y > 2x + 7 will have a closed circle
Question #2 Explanation
 Graphing inequalities:
 less than (<) and greater than (>) signs are an
open circle because the number is NOT
included in the solution set
 less than or equal to (<) and greater than or
equal to (>) are a closed circle because the
number IS included in the solution set
Day 3
Question #3 and #4
 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
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
Day 4
Question #5
 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
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!!
Day 5
Question #6
 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.
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.
Day 6
Question #7 and #8
 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
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
Day 7
Question #9
 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
Question #9 Explanation
 Make a table:
Table
Length
72
Width
36
Model
1.5
 Write the information as a proportion.
 Cross multiply and divide
Day 8
Question #10 and #11
 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
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
Day 9
Question #12
 Write an algebraic expression to explain
the pattern:
2, 5, 11, 23, ____. ____, ____
 2x + 1
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!
Day 10
Question #13
 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%
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.
Day 11
Question #14


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
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
Day 12
Question #15 and #16
 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
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
Day 13
Question #17 and #18
 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
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
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
Day 14
Question #19 and #20
 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
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
Day 15
Question #21


The scale on a map is 1 inch:30 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
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.
Day 16
Question #22
 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
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)
Day 17
Question #23




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%
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.
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.
Day 18
Question #24


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
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.
Day 19
Question #25
 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
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
Day 20
Question #26
 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
Question #26 Explanation
 On the EOG you will be given formulas
that you are not familiar with…don’t worry,
just replace the letters with the numbers
they give you and do the math!
Day 21
Question #27
 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
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!
Day 22
Question #28
 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
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
Day 23
Question #29
 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
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.
Day 24
Question #30
 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
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
Day 25
Question #31 and #32
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
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
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!!
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
Day 26
Question #33
 Ali is going to paint her school’s 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
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
Day 27
Question #34
 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? 56
How many voted to go to an
amusement park? 143
How many students did not vote? 51
Question #34 Explanation
 To find fractional parts: multiply the total number

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
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
Day 28
Question #35
 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
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
Day 29
Question #36
 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
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
Day 30
Question #37
 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
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