Download Seventh Grade FSA Review Packet Proportions

Name______________________
Date: ______________________
Math 7, period _____
FSA Review Packet
Seventh Grade FSA
Review Packet
Proportions
Rules
Word
Problems
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Examples_____________
1. A recipe uses 4 cups of flour to make
12 cookies. If you want 60 cookies, how
much flour will you need?
Set up a proportion consistently.
Cross multiply.
Divide by the number with the
variable.
2. I took a random sample of 100
students and 42 buy lunch. How many
students out of the 600 at school will buy
lunch?
Constant
Rate of
Rate

Using the table, divide column y
by column x.


1. Find the constant rate of change for the
table below.
Number of
Cost
Students
2
30
4
60
6
90
Divide the distance by the time.
Use the A b/c key on the
calculator for fractions.
1. I drove 120 miles in 2 ½ hours. What
was my average speed?
2. A sprinter runs 200 m. in 27 seconds.
What is the average running rate?
Constant of
Proportionality



Divide the dependent row by the
independent row to find the
constant of proportionality.
k = constant of proportionality.
Put that in the equation y = kx.
The number times k = cost.
Items
Cost
2
20
4
40
a. Find the constant of proportionality.
b. Use the constant of proportionality to write
an equation in y = mx form.
c. How much would 6 items cost?
Practice for Proportions
1. I made punch with 3 parts ginger ale to 2 parts Hi-C. I need 20 oz. of punch. How
much Hi-C do I need?
2. I ran 13 miles in 2 ¼ hours. What was my average speed?
3a. What is the constant rate of change for the table below?
Minutes
Number of Pages Read
10
60
20
120
30
180
3b. Use the constant rate of change to write an equation in y = mx form.
3c. How many pages would you read in 60 minutes?
Geometry
Rules
Circumference 
of a Circle


Multiply the radius by 2 and then by
the pi key on the calculator.
Round to the nearest tenth.
If being asked for the radius, the
number in front of pi is the diameter.
Divide by 2 to get the radius.
Examples_____________
1. If you wrap lace around a circle with a
radius of 10 m., how much lace do you need?
2. Find the radius of a circle with a
circumference of 9π ft.
Area of a
Circle



Divide the diameter by 2.
Multiply the resulting radius by itself,
then by the pi key on the calculator.
Round to the nearest tenth.
The diameter of a pizza is 12 inches. What is
the area of the pizza?
Practice for Geometry
1. Find the circumference of a circle with a radius of 20 m.
2. Find the area of a circle with a diameter of 10 m.
3. Find the radius of a circle with a circumference of 15π m.
Probability
Rules
Simple
Probability


Find the total.
Put the favorable outcomes over the
total.
Examples_____________
1. There are 3 red marbles, 4 blue marbles, and
6 green marbles. Find the probability you
choose a red marble.
2.
Flavor
# of
Students
Vanilla
Chocolate
Strawberry
10
15
5
Find the probability of chocolate being the
favorite flavor of a student.
Independent
Probability

Find the probability of each event and
multiply them together.

Dependent Events do effect each
other.
Outcomes


Find the probability of the event.
Multiply it by the number of times the
event is occurring.
Counting
Principle

Find the number of outcomes from
each event and multiply them together.
Dependent
Probability
What is the probability of tossing two coins and
having both land on heads?
Name two dependent events.
If you roll a die 40 times, how many times would
you expect it to come up odd?
How many outcomes are possible if you choose
a letter from the word MATH and a letter from
the word FINAL?
Practice for Probability
1. What’s the probability of picking a dime if you have 3 dimes, 4 pennies, and 5
quarters?
2. What is the probability a student will choose math as their favorite subject if you have
conducted a survey and found 6 like SS, 10 like science and 15 like math?
3. What’s the probability of tossing a pair of dice and having both come up even?
4. Name two dependent events.
5. You roll a die 60 times. How many should come up the number 1?
6. How many outcomes are possible if you chose one letter from the word FUN and
another letter from the word NOT.
Algebra
Rules
Distribution
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

Simplifying
Expressions
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
Inequalities
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Two-Step
Equations
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
Examples_____________
Multiply the number outside the
parentheses by both terms inside the
parentheses.
If it is an equation, subtract the number
from both sides of the equation.
Divide by the number next to the
variable on both sides of the equation.
1. Simplify: 2(-3x – 4).
Find like terms.
Add or subtract the like terms by
adding/subtracting the coefficients and
keeping the variables.
In cases of (), line them up. Remember
to subtract all terms.
1. -15x + 6 + 6x – 3
When solving inequalities, the final step
is to divide by the number with the
variable and reverse the inequality sign
if that number is negative.
Otherwise, simply divide by the number
with the variable.
When graphing, <,> are open circles
and <, > are closed.
Shade in the appropriate direction.
Add the number by itself to both sides
of the equation.
Divide by the number with the variable
on both sides of the equation.
2. Solve: 2(x + 1) = -14
2. (-4x + 6) – (8x – 10)
1. What is the last step in solving -3x + 2 < 10?
2. Solve and graph 4x < 20
1. Solve: 3x – 9 = 15
2. Solve: 6 + 4m = -26
Patterns


Divide the numbers in the two columns
to determine the coefficient.
Multiply that number by the given
number of minutes.
Time
1
2
3
Distance
150
300
450
How far would you go in 10 minutes?
Practice for Algebra
1. Simplify: 2(-4x – 3)
2. Simplify: -4x + 9 + 8x - 2
3. Simplify: (-4x + 5) – (3x – 10)
4. Which operation would be last when solving the inequality -5x + 9 < -6
5. Solve: 5x – 10 = 25
6. Solve: 3(x + 2) = 90
7. Solve and graph: 9x < 72.
8. If the pattern continues, how far will it be in 10 minutes?
Time (min.)
Distance (ft.)
1
20
2
40
3
60
Algebra continued
Rules
Distribution/
Combining
Like Terms
Equation





Variables on
Both Sides
of the Equal
Sign
Equation
Writing/
Solving Two
Step
Equations


Examples_____________
Multiply the number outside the
parentheses by both terms inside the
parentheses.
Combine like terms.
Add the number to both sides of the
equation.
Divide by the number next to the
variable on both sides of the equation.
Do the inverse of +/- to the smaller
variable on both sides of the equation.
Add the constant to both sides of the
equation.
Divide by the number with the variable
on both sides of the equation.




Write an equation as: cost=price of 1
item +cost of other itemx
Subtract the constant on both sides of
the equation.
Divide by the coefficient on both sides
of the equation.
The solution of an equation is the value
that makes the equation true. In other
words, what is x?
1. Solve: 2(x – 1) + 4x = 46
1. Solve: 12x – 9 = 9x + 15
Write and solve an equation for the
following: A granola bar costs $2 and
candy is $.50 each. You have $5.
How many pieces of candy can you
get?
Create a two-step equation with a
solution of 5. Prove your solution is
correct.
Practice for Algebra continued
1. Solve: 8x – 4 = 12x + 12
2. Solve: 7(x – 2) + 3x = 46
3. Write and solve an equation for the following: A flower shop charges $3 per rose
plus a $5 delivery fee. You spent $59 on roses. How many roses did you order?
Percents
Rules
Percent of a
Number

Change the percent to a decimal by
moving the decimal point 2 places left.
Multiply the decimal by the number.

Examples_____________
1. 81% of all ticket sales were to adults. If there
were 500 tickets sold, how many were to adults?
2. Last year, there were 200 students in 6 th
grade. This year, there is 150% of that number.
How many 6th graders are there this year?
Discount

Change the percent to a decimal by
moving the decimal point 2 places left.
Multiply the decimal by the price.
Subtract your answer from the original
price.


Interest
Percent of
Change


Interest = principal • rate • time
First change the percent to a decimal
by moving the decimal point 2 places
left.





Markup



Subtract the numbers.
Divide by the ORIGINAL number.
Multiply by 100.
If the numbers went up, it is an
increase.
If the numbers went down, it is a
decrease.
Shirts are $40. They are on sale for 10% off.
What is the sale price?
How much interest would there be on a $1000
loan at 6.25% for 10 years?
Last year, there were 25 students in a class.
This year, there is 30. What is the percent of
change? Is it an increase or decrease?
A $40 item is marked up 50%. What is the
Change the percent to a decimal by
selling price of the item?
moving the decimal point 2 spaces left.
Multiply the decimal by the cost.
Add the product to the cost.
Practice for Percents
1. There were 400 students in attendance. 51% are boys. How many are boys?
2. A $30 watch is discounted 15%. What is the sale price?
3. You invested $5000 for 20 years at 7.25%. How much interest did you earn?
4. A $50 watch was marked up to $60. What is the markup rate? Is it an increase or
decrease?
5. You bought an item for $25 on Ebay and plan on marking it up 65%. What price will
you sell your item for to the nearest dollar?
Rational Numbers
Rules
Properties

When you switch terms, you are using
the commutative property.
When you multiply the term outside the
parentheses by all terms inside the
parentheses, you are using the
distributive property.

To find the distance between two
integers, subtract the numbers, and
take the absolute value of the answer.
It was -15 degrees at 10 AM. By 2 PM, the
temperature was 30 degrees. How much did the
temperature rise?


Substitute the number for the variable.
Multiply. If the signs are the same, the
answer is positive. If the signs are
different, the answer is negative.
Divide. If the signs are the same, the
answer is positive. If the signs are
different, the answer is negative.
Evaluate if x = 9 and y = 4: xy ÷ 2
If the signs are the same, multiply and
make the answer positive.
Product means multiply.
For fractions, multiply the numerators,
multiply the denominators, and simplify.
Find the product of (-1/9)(-1/2).

Distance
Evaluating

Multiplying



Fractions to
Decimals
Ordering
Rational
Numbers
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
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

Writing/
Solving
Rational #
Problems
Examples_____________
Give an example of the commutative property.


Divide numerator ÷ denominator in
calculator.
Repeating decimals repeat.
Put the repeating sign over the
numbers that repeat.
Change all numbers to a decimal.
Move the decimal point on a percent 2
places left.
For fractions, divide numerator ÷
denominator on the calculator.
Place in order.
If one digit is repeating, it is larger than
the same number not repeating.
Create an expression where you are
adding all of the numbers.
Use your calculator to complete the
problem.
Give an example of the distributive property.
1. What is the decimal 31/45?
2. What is 1/3 as a decimal?
Put in order from least to greatest:
62.5%, .0625, 5/9
You start at a distance above sea level of 50
feet. You hike down 40 feet, up 5 feet, down 30
feet, and up 20 feet. Where do you end your
hike?
Practice for Rational Numbers
1. What property is demonstrated by 6 + -6 = 0?
2. You started hiking at 31.3 feet below sea level. At the end of your hike, you
were at 56.2 feet above sea level. How many feet did you climb?
3. If x = 3 and y = -1, what is the value of xy ÷ -3?
4. What is the product of (-2/7)(-5/6)?
5. What is the decimal equivalent of 23/45?
6. Put the following numbers in order from least to greatest:
12.5%, .125, 1/6
7. Change 1/6 to a decimal.
8. You have a bank account balance of $305. You withdraw $40, deposit $25, withdraw
$60 and deposit $10. What is your account balance at the end of the month?
Statistics
Rules
Examples_____________


Check the middle line-it’s the median.
Subtract the ends of the boxes. The
larger difference has the greater
variation.

Put the numbers in order from least to
greatest.
Cross off one from each end. The
middle number is the median.
Find the median: 93, 45, 45, 100, 38.

The number that occurs the most is the
mode.
Find the mode: 93, 45, 45, 100, 38.
Mean


Add all the numbers.
Divide by the number of numbers.
Find the mean: 93, 45, 45, 100, 38.
Range

Highest number – lowest number
Find the range: 93, 45, 45, 100, 38.
Biased
Sample

Biased samples ask people of a certain
population the question regarding their
own population.
Comparing
Populations
Median
Mode

Compare the populations:
What’s a biased sample for finding out the
most popular instrument at a school?
Practice for Statistics
1. Find the mean, median, range, and mode using the following data:
1, 2, 3, 3, 4, 5, 6, 7, 8.
2. What would be a biased sample if you wanted to know the most popular sport?
3. Compare the populations.