Mrs. Moroney's Math Final Review

A box of five ice cream sandwiches costs $1.05. What is the unit price?

$1.05 / 5 = $0.21 per ice cream sandwich

90% of what is 18?

20

-3 x -8 = ?

24

What is 30% of 100?

30

If B = 50 degrees, what is the value of A?

40 degrees

Percent

A ratio that compares a number to 100

Numeric Expression

Contains numbers and at least one operation

What is d?

Diameter

Random Sample

Each member of the population has an EQUAL chance of being included.

There are 25 tomato seeds and 35 sunflower seeds in a gardening kit. The manager of the gardening shop wants to divide the kits into bags of the same size, where each bag has the same number of tomato seeds and sunflower seeds. If he creates the greatest number of teams possible, how many sunflower seeds will be in each bag?

GCF = 5 bags 35 sunflower seeds / 5 bags = 7 sunflower seeds per bag

What is the divisibility rule for 6?

If the number is divisible by 2 and 3

How do you divide fractions?

KCF (Keep, Change, Flip)

Is 6 a factor of 35v + 50? (Divide all numbers by 6)

No

The temperature on Feb. 2 in Lake City was 14 degrees. The temperature in Ellenville the same day was -6 degrees. Gabby subtracted 14 - (-6) and got 8 degrees. Is she correct?

No. The answer should have been 20 degrees, not 8 degrees, because subtracting a negative number is the same as adding its opposite.

Bernard polled the 2 fastest swimmers on the swim team. Is this a random sample of the swimmers on the swim team?

No. The pick was not random.

Like terms

Terms that contain the same variable

Divisibility

The ability to divide a number into another number evenly (no remainders)

Brooke earns 5% commission as a salesperson. She sold a rug that cost $53. How much commission did Brooke earn?

$2.65

A 2-foot piece of copper pipe costs $3.62. What is the unit price?

$3.62 / 2 = $1.81 per foot

Maura has $40,000 in a savings account. The interest rate is 14% per year and is not compounded. How much will she have in total in 3 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

$56,800

Tammy has $50,000 in a savings account that earns 9% interest per year. The interest is not compounded. How much will she have in total in 3 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

$63,500

-9.5 x 1 / 5 = ?

-1.9

3 + -5.5 = ?

-2.5

Every week during the summer, Manny records the change in the water level of the pond in his backyard. Last week, the change in the water level was -14 centimeters. This week, the change in the water level was -14 centimeters. What is the total change in the water level over the past two weeks?

-28 (-14 + -14 = 0)

k/2>-1

-2>5

-¼ divided by ⅔ = ?

-3/8

-32 / 8 = ?

-4

-1 - 4

-5

-3/10 - 3/10 = ?

-6/10

Write 7/40 as a decimal number.

.175

Write 5/8 as a decimal number.

.625

Fill in the blanks 18r+1=1 18r=___ r=______

0, 0

3.56 / 10 to the power of 2?

0.0356

2+2h=4

1

Subtract. (8j + 7) - (8j + 6)

1

What is 13 to the power of 0?

1

Victoria measured a neighborhood park and made a scale drawing. In real life, the volleyball court is 8 meters wide. It is 2 centimeters wide in the drawing. What scale did Victoria use for the drawing?

1 centimeter : 4 meters

If you flip a coin 2 times, what is the best prediction possible for the number of times it will land on tails?

1 time

With sales tax, it costs $60.60 to buy a $60 wooden bench. What is the sales tax percentage?

1%

Chad planted 8 sunflowers along the edge of his garden. The seed packet stated that each sunflower has an 80% chance of growing to be six feet tall, which is taller than him! How likely is it that at least 7 of the sunflowers will grow to be six feet tall? Which simulation could be used to fairly represent the situation? 1. Use a computer to randomly generate 8 numbers from 1 to 10. If the number is at most 8, it represents a sunflower that is six feet tall. 2. Put 8 brown marbles and 7 yellow marbles in a bag. Pick a marble, then return it to the bag, 8 times. Each time a yellow marble appears, it represents a sunflower that is six feet tall. 3. Create a spinner with 5 equal sections, each labeled with a different number from 1 to 5. Spin the spinner 7 times. Each time the spinner lands on 1, 2, 3, or 4, it represents a sunflower that is six feet tall.

1.

During the summer, Whitney goes fishing at Cobalt Basin Lake every weekend. She catches a sunfish 90% of the time, but she really wants to catch a new type of fish. How likely is it that at least 1 of the next 3 fish she catches will be something other than a sunfish? Which simulation could be used to fairly represent the situation? 1. Create a spinner with 10 equal sections, each labeled with a different number from 0 to 9. Spin the spinner 3 times. Each time it lands on 0, it represents Whitney catching something other than a sunfish. 2. Roll a six-sided die 3 times. Each time a 1 appears, it represents Whitney catching something other than a sunfish. 3. Use a computer to randomly generate a pair of numbers from 1 to 100. Each time a multiple of 10 appears, it represents Whitney catching something other than a sunfish.

1.

Which set of numbers shows a proportional relationship? 1. 1x = 5y, 2x = 10y, 4x = 20y or 2. 5x = 1y, 10x = 2y, 15x = 3y

1.

What is the probability of flipping heads on a coin and rolling a one on a six-sided die?

1/12

At the annual Haunted Harvest Festival, Nolan is running a spider game. Depending on where the spinner lands on, guests can win one of these small toys: spider, skull, bat, monster, or skeleton. Before the guests arrive Nolan spins the spinner 12 times to try it out. Here are his results: Bat, spider, skull, bat, skeleton, monster, spider, bat, skull, bat, monster, skull Based on the data, what is the probability of the spinner landing on bat? (simplify fractions)

1/3

What is the probability of rolling a three on the first die and a three on the second die?

1/36

Put 20 plants in 2 rows how many plants will be in each row?

10

Admission to the Chesterfield County Fair is $10. Once you are inside, it costs x dollars to go on each ride. When Isabelle went to the fair last weekend, she went on 4 rides. What 2 expressions represent how much Isabelle spent at the fair?

10 + 4x; 10 + x + x + x + x

Simplify the expression: 2(5 + 4p)

10 + 8p

Mr. Morgan's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. What 3 expressions represent Mr. Morgan's profit last month from these two ice cream flavors.

10(x+y)-4(x+y), 6x+6y, 10x+10y-4x-4y

Write an expression equivalent to 5(2j)

10j

You roll a die and flip a coin. How many outcomes are possible?

12

The probability that a student guesses the correct answer to a four-choice multiple choice question is P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 48 four-choice multiple choice questions?

12 correct answers

The radius of a circle is 2 feet. What is the circle's circumference?

12.56 feet

The radius of a circle is 2 feet. What is the circle's circumference? (Use 3.14 for pi)

12.56 square miles

Simplify the expression: 5c + 6c + 1 + c

12c+1

Judy and her friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Judy and her friends spend sailing, x, and their distance from shore (in miles), y. After sailing for 8.6 hours, they are 103.2 miles from shore. Write the equation for the relationship between x and y.

12x

Every month, Midtown Grocery Store donates 8-ounce cans of vegetables to a food bank. The food bank's volunteers fill bags with these cans and deliver the bags to families in need. There is a proportional relationship between the number of bags the food bank's volunteers can fill, x, and the total number of cans they deliver, y. With 65 cans, the volunteers can fill 5 bags. Write the equation for the relationship between x and y.

13x

Add. (7r + 8) + (8r + 9)

15r + 17

What is the opposite of -16

16

You have a deck of 7 cards. You pick a card and flip a coin. How many outcomes are possible?

16

Cooper has 16 math problems to do for homework. He already finished p of them. Write an expression that shows how many problems Cooper has left.

16 - p

A rectangular prism is 13.5 yards long and 10.9 yards wide. Its volume is 2,501.55 cubic yards. What is the height of the rectangular prism?

17 yards high

2m = ? when m = 9

18

1.8 x 10 to the power of 4

18000.0

10=6+2y

2

At soccer practice, Mike asked each of his teammates to write down their shoe size. I--IIIIIIII-----I I--I--I--I--I--I--I--I--I--I--I 2 4 6 8 10 12 What is the interquartile range for Mike's teammates' shoe sizes?

2 sizes

4(z-18)=8

20

Of the balloons recently sold by a party store, 4 were purple and 8 were other colors. Considering this data, how many of the next 66 balloons sold would you expect to be purple?

22

Rafi took a total of 12 quizzes over the course of 4 weeks. After attending 9 weeks of school this quarter, how many quizzes will Rafi have taken in total? Solve using unit rates.

27

Simplify the expression: (d + 1)(2)

2d + 2

Subtract. (5v + 4) - (3v + 4)

2v

Evaluate 2 to the 5th power.

2×2×2×2×2

This morning, the temperature rose 2 degrees in 2/3 of an hour. At what rate did the temperature rise?

3 degrees per hour

Write an expression equivalent to 2(3p)

3(2p)

Write 30u-60v in factored form.

30(u-2v)

Evaluate when t = 10, 25 50 - 2t

30, 0

After visiting the Needleton Natural Museum, Irma was so fascinated by the reptile exhibit that she got her own pet lizard. Irma bought a terrarium shaped like a rectangular prism for her lizard to live in. The terrarium is 20 inches long, 15 inches wide, and 12 feet tall. What is the volume of the terrarium?

3600 cubic inches

A school staff meeting had 78 teachers in attendance, 50% of whom were first-year teachers. How many first-years were in the meeting?

39

What is 60% of $66.40?

39.84

Camilla took a survey to find out how many students in her school have a pet. There are 620 students in the school. 65% of them have a pet. How many students in Camilla's school have a pet?

403

15 - (5 x 2)

5

3, 5, 8, 5, 5, 8, 9 What is the median?

5

Estimate 20% of 24.93

5

Find the GCF of 30, 25, and 90.

5

What is I -5 I (Absolute value)

5

Find the prime factorization of the number 175

5, 5, 7

-1 ½ x -3.8 = ?

5.7

4 - -2

6

Lauren's Auto Wash had revenues of $40 from 5 customers. In all, how many customers does Lauren's Auto Wash need to serve in order to have a total of $48 in revenue? Solve using unit rates.

6

What is the surface area?

6 square cm

In the circus, a tiger has been trained to jump through a ring of fire that has a radius of 1 yard. What is the ring's circumference? (Use 3.14 for 𝜋)

6.28 yards

What is the percent of decrease from 94.1 to 35.1?

62.7%

Mr. Kline planned a field day for the seventh-grade students at Sherman Middle School. He set up 6 stations and planned for the students to spend the same amount of time at each one. On the day of the event, there was a fire drill, and they lost 30 minutes. Only 90 minutes were left for the field day, so each station got cut short. Write an equation you can use to find how long, x, each station was originally supposed to last?

6x-30=90

Evaluate the expression for r = 2 and s = 5. r + s =

7

The Riverview Classic Car Club is hosting its annual parade of classic cars through the center of town. Frank loves classic cars and comes to watch the parade every year. These are the cars he has seen so far in this year's parade: hot rod, convertible, sedan, convertible, sedan, hot rod, hot rod, convertible, sedan Based on the data, estimate how many hot rods will be among the next 20 cars Frank sees in this year's parade. (If necessary, round your answer to the nearest whole number.)

7

Find the prime factorization of the number 56

7, 2, 2, 2

Marvin made a scale drawing of a house. The scale of the drawing was 7 millimeters = 1 meter. What is the scale factor of the drawing?

7/1,000

What is the percentage change from 20 to 36?

80% increase

Rosanne paid for an Introduction to Painting course at Cool Canvas Art Studio. The cost of the course covers 8 painting classes. She also bought a beginner's painting kit for $42. Rosanne paid $186 in all. Write an equation you can use to find the cost, c, of each painting class?

8c + 42 = 186

Add. (6h + 9) + (2h + 2)

8h + 11

63 out of the 70 teachers in a school staff meeting were first-year teachers. What percentage of the teachers were first-year teachers?

90%

Find the LCM of 14 and 49.

98

Which expression is equivalent to 8x + x + 2

9x + 2 (add like terms)

Identify the cross-section of the cylinder.

A circle

Identify the cross-section of the sphere.

A circle

Ratios

A comparison of two quantities using division

Expression

A mathematical phrase that contains operations, numbers, and/or variables.

Subject

A member of a sample

Composite number

A number with more than 2 factors

Constant

A number without a variable

Sample

A part of a population. Samples are used when you do not have the resources to study every member of a population.

Statistical Question

A question that investigates an aspect of the world and can have more than one possible answer

Unit Rate

A rate in which the second quantity in the comparison is one unit (ex. 60 seconds per 1 minute)

Variable

A symbol (usually a letter) standing in for an unknown value

Bias

A tendency TOWARD A PARTICULAR PERSPECTIVE that is different from the overall perspective of the population.

Power

A way to write a repeated multiplication

How to add/subtract like terms

Add/subtract their coefficients

Integer

All whole numbers (both positive and negative) and zero.

Linear expression

An algebraic statement where each term is either a constant or a variable

Proportions

An equation stating that two ratios are equal

Prime factorization

Any composite number can be written as a product of its prime factors

Zero Power Property

Any number raised to the power of 0 is one

Rational Numbers

Any number that can be expressed as a fraction

Diameter

Any straight line segment that passes through the center of the circle and whose endpoints lie on the circle

What is the formula for finding the circumference from the radius?

C = 2 x 𝞹 (pi) x r

What is the formula for finding the circumference from the diameter?

C = 𝞹 x d

Which team has a higher median number of points per game? Points Scored by Boys' Basketball Team 35, 41, 39, 50, 43, 38, 36, 45, 49 Points Scored by Girls' Basketball Team 44, 41, 42, 42, 43, 43, 44, 47, 42

Girls, 43

Draw a rectangle that is not a square.

I-------------------I I-------------------I

Draw a rectangle that is not a rhombus.

I----I I----I

What is the divisibility rule for 2?

If a number is divisible by 2 if the number is even.

What is the divisibility rule for 3?

If a number is divisible by 3 if the sum of the digits is divisible by 3.

What is the divisibility rule for 4?

If the last 2 digits are divisible by 4

What is the divisibility rule for 10?

If the number ends in 0

What is the divisibility rule for 5?

If the number ends in 5 or 0

What is the divisibility rule for 9?

If the sum of digits is divisible by 9.

How are two expressions equivalent?

If they are the same when written in standard form

Simple Interest

Interest earned only on the original principal amount invested

What does it mean if the value is closer to 1?

It is more likely the outcome will happen

One package of burger patties contains ten patties. One package of burger buns contains 8 buns. You are having a party and serving burgers. When you start grilling, you open a package of each. When is the next time you will open a new package of each at the same time?

LCM = 40

Do the ratios 3/2 and 6/5 form a proportion?

No -- 3/2 and 6/5 are not equivalent ratios

Prime number

Only factors are 1 and itself

Isaac made cookies for a bake sale. So far, he has sold 74 cookies, including 10 cookies in the shape of a diamond. What is the experimental probability that the next cookie sold will be in the shape of a diamond? (Put into fraction form)

P(diamond) = 5/37

Carrie will roll a number cube with sides labeled 1 to 6 What is the probability she will roll a number less than 7?

P(less than 7) = 1

There are 15 children in Lola's preschool class. During free time yesterday, 1 of them chose to play at the water table. What is the probability that a randomly selected child chose to play at the water table yesterday?

P(play at water table) = 1/15

P E MD AS

Parentheses (evaluate group symbols) Exponents (evaluate powers) Multiplication / Division (whichever comes first) Addition / Subtraction (whichever comes first)

How to solve percent problems using proportions:

Part / Whole = Percent / 100

Is -1 + 3 positive or negative?

Positive

Is 59 + -45 positive or negative?

Positive

Experimental Probability

Repeat an experiment many times and use this ratio: P(event) = number of times event occurs / total number of trials

Factor tree

Shows the prime factorization of a number

What is the rule for dividing a decimal by 10 to the power of x

Slide the decimal in the number to the left x number of times

What is the rule for multiplying a decimal by 10 to the power of x

Slide the decimal in the number to the right x number of times

Based on the medians, which population had the most screen time? Adults Median: 28 IQR: 4 Teens Median: 23.5 IQR: 16

The adults

Population

The complete set of items being studied

Absolute Value

The distance a number is from zero on a number line. ALWAYS POSITIVE

Circumference

The distance around a circle

Radius

The distance from the center of a circle to any point on its circumference

Greatest Common Factor (GCF)

The largest factor that two or more numbers have in common.

Probability

The likelihood that a particular event will occur

Compare the mean values of the data sets. Camp 1 22, 23, 25, 25, 27, 27, 27, 28, 32, 33, 34 Camp 2 18, 21, 22, 22, 22, 24, 24, 26, 29, 30, 30 What can you infer from the mean values?

The mean values tell you that participants in Camp 1 are taller.

Coefficient

The number in front of the variable in a term

Biased sample

The number of subjects in the sample with the trait being studied is NOT PROPORTIONAL to the number of members in the population with that trait.

Representative Sample

The number of subjects in the sample with the trait being studied that is proportional to the number to the number of members in the population with that trait (ACCURATE)

Outcome

The possible result of an action

P(outcome)

The probability of the outcome is equal to _____

Scale Factor

The ratio between corresponding measurements of an object

Least Common Multiple (LCM)

The smallest multiple (other than zero) that two or more numbers have in common.

Triangle rules

The sum of the length of any two sides of a triangle has to be greater than the length of the third side

Evaluate

To find the value of an expression

Substitution

To replace a variable with a number

How to solve for a variable:

Use inverse operations to undo the operations in the inequality. Be sure to do the same operation to both sides of the inequality.

Theoretical Probability

When all outcomes of an action are equally likely, then use this ratio: P(event) = number of favorable outcomes / number of possible outcomes

Harper threw some printed pages into the air and grabbed 2 as they fell. Is this sample of the printed pages likely to be representative?

Yes. The selection is random.

Does this graph represent a proportional relationship?

Yes; if a straight line is passing through the origin (0,0), it is a proportional relationship

Compare the two data sets. What can you infer from the number of curl-ups last year and this year? Curl-Ups Completed Last Year Mode: 24 Range: 7 Curl-Ups Completed This Year Mode: 28 Range: 9

You can infer that the students this year could do more curl-ups than last year (larger mode).

Solve for c. 2c-3>9

c>9

k/4 ≥ 5

k ≥ 20

In a number line, when multiplying by a negative, does it go left or right?

left

Solve for m. 4(m-3)>8

m>5

Is 5 x -12 positive or negative?

negative

Negative multiplied by a positive =

negative

Can the sides of a triangle have lengths 1, 2, and 4?

no

Can the sides of a triangle have lengths 1, 2, and 9?

no

n+16≤18

n≤2

Negative multiplied by a negative =

positive

Positive multiplied by a positive =

positive

This number line shows an unknown letter b. Is 3b positive or negative?

positive

is -50 divided by -10 positive or negative?

positive

Solve for q. 2(q + 4) > 10

q > 1

6+2r>10

r>2

Solve for t. t+5>17

t>12

True or False: The rules for integer multiplication is the same for division

true

Opposite Integers

two integers that are the same distance away from zero

Write an equation for the relationship between x and y: 1x=5y, 2x=10y

y=5x

Are the angles a and b complementary?

yes