review packet.doc

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Name: _____________________

Date: ______________________

Math 7, period _____

Final Exam Review Packet

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Proportions

Rules

Examples_____________

Word

Problems

(2 on part 1

for 2 points

each)

Constant

Rate of

Change (1

for 2 points)

Rate (2 for

2 points

each)

Constant of

Proportionality

(1 on part 2 for

5 points)

Items 2

4 Cost

20

40 

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

30

4

60

6

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.

(3)

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.

(4)

Geometry

Rules

Examples_____________

Circumference

of a Circle (2

for 2 points

each)

Area of a

Circle (1 for

2 points)



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.

(5)

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.

(6)

Probability

Rules

Examples_____________

Simple

Probability

(2 for

2 points

each)

Independent

Probability

(1 for 2

points)

Dependent

Probability

(1 for 2

points)

Outcomes

(1 for 2

points)

Counting

Principle

(1 for 2

points)



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

Students

Vanilla 10 Chocolate 15 Strawberry 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.

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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?

(8)

Algebra

Rules

Examples_____________

Distribution

(2 for 2

points each)

Simplifying

Expressions

(2 for 2

points each)

Inequalities

(2 for 2

points each)

Two-Step

Equations

(2 for 2

points each)

Patterns

(1 for 2

points)

Time

Distance

1

150

2

300

3

450 

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.

(9)

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

(10)

Algebra continued

Rules

Examples_____________

Distribution/

Combining

Like Terms

Equation

(1 for 2

Points)

Variables on

Both Sides

of the Equal

Sign

Equation

(1 for 2

points)

Writing/

Solving Two

Step

Equations

(2 on part 2

for 4 or 5

points

each)



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?

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Practice for Algebra continued

1. Solve: 8x – 4 = 12x + 12

2. Solve: 7(x – 2) + 3x = 46

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Percents

Rules

Examples_____________

Percent of a

Number

(2 for 2

points each)

Discount

(1 for 2

points)

Interest

(1 for 2

points)

Percent of

Change

(1 for 2

points)

Markup

(1 on part 2

for 2 points)



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.

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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?

(14)

Rational Numbers

Rules

Examples_____________

Properties

(1 for 2

points)

Distance

(1 for 2

points)

Evaluating

(1 for 2

points)

Multiplying

(1 for 2

points)

Fractions to

Decimals

(2 for 2

points each)

Ordering

Rational

Numbers

(1 for 2

points)

Writing/

Solving

Rational #

Problems

(1 on part 2

for 2 points)



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, the answer is positive.



If the signs are different, the answer is negative.



Product means multiply.

What is the sign of 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.

(15)

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 sign of 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.

(16)

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Statistics

Rules

Examples_____________

Comparing

Populations

(1 for 2

points)

Median

(1 for 2

points)

Mode (1 on

for 2

points)

Mean (1 for

2 points)

Range

(1 for 2

points)

Biased

Sample

(1 for 2

points)



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?

(18)

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?

(19)

Graphing Linear Equations

Rules

Examples_____________

System of

Equations

(1 for 2

points)

Solutions

(1 for 2

points)

Slope (1 on

for 2

points)

y-intercept

(1 for

2 points)

Solve for y

(1 for 2

points)



Substitute (x,y) into the equation.



Solve using the order of operations.



If the answers are the same, it is a solution.



If the answers are not the same, it is not a solution.



The number in front of the x (m) in the equation y = mx + b.



The constant (b) in the equation y = mx + b.



Subtract/Add the number on the same side of the equation as y to put it in the form y = mx + b before you begin.