Name______________________Date: ______________________Math 7, period _____FSA Review Packet

Seventh Grade FSA Review Packet

Proportions

Rules Examples_____________ Word Problems

Constant Rate of

Rate

Constant ofProportionality

Set up a proportion consistently.

Cross multiply. Divide by the number with the

variable.

1. A recipe uses 4 cups of flour to make 12 cookies. If you want 60 cookies, how much flour will you need?

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?

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?

Using the table, divide column y by column x.

1. Find the constant rate of change for the table below.Number of Students

Cost

2 304 606 90

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.

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?

Items 2 4Cost 20 40

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 6020 12030 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 Examples_____________ Circumferenceof a Circle

Area 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.

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.

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 Examples_____________ Simple Probability

IndependentProbability

DependentProbability

Outcomes

Counting Principle

Find the total. Put the favorable outcomes over the

total.

1. There are 3 red marbles, 4 blue marbles, and 6 green marbles. Find the probability you choose a red marble.

2.Flavor # of

StudentsVanilla 10

Chocolate 15Strawberry 5

Find the probability of chocolate being the favorite flavor of a student.

Find the probability of each event and multiply them together.

What is the probability of tossing two coins and having both land on heads?

Dependent Events do effect each other.

Name two dependent events.

Find the probability of the event. Multiply it by the number of times the

event is occurring.

If you roll a die 40 times, how many times would you expect it to come up odd?

Find the number of outcomes from each event and multiply them together.

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 Examples_____________ Distribution

Simplifying Expressions

Inequalities

Two-StepEquations

Patterns

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).

2. Solve: 2(x + 1) = -14

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

2. (-4x + 6) – (8x – 10)

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.

1. What is the last step in solving -3x + 2 < 10?

2. Solve and graph 4x < 20

Add the number by itself to both sides of the equation.

Divide by the number with the variable on both sides of the equation.

1. Solve: 3x – 9 = 15

2. Solve: 6 + 4m = -26

Divide the numbers in the two columns to determine the coefficient.

Multiply that number by the given number of minutes.

Time Distance1 1502 3003 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.)1 202 403 60

Algebra continued

Rules Examples_____________ Distribution/CombiningLike Terms Equation

Variables onBoth Sides of the Equal Sign Equation

Writing/Solving TwoStep Equations

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.

1. Solve: 2(x – 1) + 4x = 46

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.

1. Solve: 12x – 9 = 9x + 15

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?

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 Examples_____________ Percent of aNumber

Discount

Interest

Percent of Change

Markup

Change the percent to a decimal by moving the decimal point 2 places left.

Multiply the decimal by the number.

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 6th grade. This year, there is 150% of that number. How many 6th graders are there this year?

Shirts are $40. They are on sale for 10% off. What is the sale price?

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 = principal • rate • time First change the percent to a decimal

by moving the decimal point 2 places left.

How much interest would there be on a $1000 loan at 6.25% for 10 years?

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.

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?

Change the percent to a decimal by moving the decimal point 2 spaces left.

Multiply the decimal by the cost. Add the product to the cost.

A $40 item is marked up 50%. What is the selling price of the item?

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 Examples_____________ Properties

Distance

Evaluating

Multiplying

Fractions toDecimals

Ordering RationalNumbers

Writing/SolvingRational #Problems

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.

Give an example of the commutative property.

Give an example of 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).

Divide numerator ÷ denominator in calculator.

Repeating decimals repeat. Put the repeating sign over the

numbers that repeat.

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 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.

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_____________ Comparing Populations

Median

Mode

Mean

Range

BiasedSample

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.

The number that occurs the most is the mode.

Add all the numbers. Divide by the number of numbers.

Highest number – lowest number

Find the median: 93, 45, 45, 100, 38.

Find the mode: 93, 45, 45, 100, 38.

Find the mean: 93, 45, 45, 100, 38.

Find the range: 93, 45, 45, 100, 38.

Compare the populations:

What’s a biased sample for finding out the most popular instrument at a school? Biased samples ask people of a certain

population the question regarding their own population.

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.