SOL Rigor Review Heading:

6.1: Ratios

1. Mario has finished 35 out of 45 of his test questions. Which of the following represents how much he

has left to finish?

a. 7

9 b.

4

5 c.

3

5 d.

2

9

2. If the ratio of boys to girls is 3:2, which would be an equivalent ratio?

a. 25:20 b. 23:22 c. 15:10 d. 12:18

3. An auditorium that holds 350 students currently has 150 students seated in it. What part of the

auditorium is full?

a. 1

4 b.

1

3 c.

3

7 d.

3

5

4. Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10 glasses of milk, how many sodas

did he sell?

a. 45 b. 20 c. 25 d. 10

5. If there are 90 boys in my sixth grade team at my school and that represents 3

5 of all the students, what is

the ratio of boys to girls?

a. 90:60 b. 90:150 c. 60:90 d. 150:60

6. Using the following shapes, write the given ratios as fractions in simplest form.

a. Circles and diamonds to squares: _________ b. squares to all shapes: ___________

7. The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. How many boys were

at the dance?

a. 45 b. 50 c. 55 d. 40

6.2: Fractions, Decimals and Percents (no calculator)

1. Which number in the answer choices below is not equivalent to the other numbers?

a. 0.6 b. 60% c. 3

5 d. 6%

2. Name the fraction, decimal and percent for the shaded part of the figure below.

Fraction: ___________ Decimal: ___________ Percent: _____________

3. Which of the following has the greatest value?

a. 7

8 b.

3

4 c.

2

3 d.

1

5

4. Katie and her family ordered a pizza for dinner and ate 3

4 of it. The next day, Katie ate

1

2 of what was

leftover for lunch. What fraction of the original pizza did Katie eat for lunch?

a. 1

8 b.

1

6 c.

1

4 d.

1

2

5. Order the following rational numbers from least to greatest: 85

100, 0.085, 81%,

4

5, , 0.82

6.3: Integers

1. Order the following integers from least to greatest: -42, 31, -29, 0, -30, 18

__________________________

2. Compare the following using <, >, or =.

a. -14_____-10 b. 85____ -85 c. 0 ____|−35| d. |−78|_____|78|

3. Plot a point for |−7| and its opposite on the number line below.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

6.4 Representations of the Multiplication and Division of Fractions

1. Represent the following multiplication problem: 4

5 x

2

3. What is the product? _______

2. A recipe calls for 4 cups of flour. How many 2

3 cups can be created out of the 4 cups? Using a model,

illustrate your work.

3. Write the equation for the following model:________________What is the product?_______

4. Tamara has 5 cookies and wants to share with her friends so each get 1

2 a cookie. Will she be able to

share with 11 friends? Yes or No. Explain your answer and illustrate your work.

5. Kim is baking cookies for a large party and wants to double the recipe. The original recipe calls for 2

3 cup of sugar. How many cups should she use for the double batch? ______ Illustrate your work.

6. What multiplication problem is modeled below?

6.5: Positive Exponents and perfect squares

1. What is the value of 5(40)?________________

2. What is the square root of 225?________________

3. 53= ?

a. Write in expanded form _____________________

b. Write in standard form ________________________

4. What is 25? ___________________________

5. The square of a positive number is 49. What is the number? _____________

6. The square root of a number added to 25 is equal to 30. What is the number? ___________

6.6: Operations with fractions (no calculators)

1. Mrs. Williams did a craft project in her class using a 6 foot piece of string. The students were to cut the

string into pieces that were 1½ feet long. How many pieces of string can they cut? Draw a picture and

explain your solution.

2. Mary had 1½ pizzas. She is to split it evenly with her brother. What fractional amount will he eat?

Draw a picture and explain your solution.

3. A theater on Broadway seats 400 people. There were two performances on Saturday that were both sold

out. If 1

4of the first show bought popcorn and

4

5 of the second show bought popcorn, how many people

bought popcorn on Saturday?

4. The cheerleaders are making brownies to sell at next week’s ballgame. Each pan of brownies uses 17

8

cups of flour. They have 12 cups of flour.

a. About how many pans of brownies can be made without buying any more flour?

b. Now solve to find the actual number of pans of brownies that can be made.

c. Compare your original estimate with your answer.

5. Troy has a piece of string that is 8 feet long. For a craft project, his mother asked him to cut the string

into pieces that are 6 inches long. How many pieces of string will his mother have if each piece is 6

inches long? Draw a sketch to verify your answer.

6. This representation shows which of the expressions below?

a.

2 42

5 5

d.

4 22

5 5

b.

4 22

5 5

e.

2 42

5 5

c.

4 52

5 4

2

5

2

5

2

5

2

5

2

5

2

5

2

5

7. Circle each that shows 2

3 of 6 shaded.

8. Which product does this model represent?

a.

1 1

7 3 b.

1 2

6 3 c.

2 3

6 7 d.

2 2

6 3

⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄

⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄

⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄⁄

9. From the choices below, which one shows “How many groups of

2

3 are in

12

3?”

a)

b)

c)

d)

10. The art teacher must cut

5

6 yard of fabric into five equal pieces for his five groups of students. How

much fabric will each group of students get? Provide a drawing to illustrate your answer.

6.7: Operations with decimals (no calculator)

1. Kim timed her homework sessions. Sunday she spent 48.05 minutes on homework, Monday 28.8

minutes, Tuesday 31.25 minutes, Wednesday 49.8 minutes, Thursday 57.85 minutes, and no time on

Friday or Saturday.

a. Estimate how much time Kim spent doing her homework this week.

b. What was the actual amount of time Kim spent on homework?

2. The cost of three copies of a book is $38.85.

a. Estimate the cost of one book.

b. Do you think your estimate is higher or lower than the book’s actual cost? Explain

c. Find the actual cost of one book and compare to your thinking above.

3. Suppose you saved $444.12 in one year.

a. Estimate how much you saved each month.

b. Find the actual amount you saved each month.

4. A Big Mac contains 406.6 calories. If a person gains about one pound for every 3000 calories

consumed. About how many Big Macs would a person consume if a pound of weight was gained?

5. Lisa went to the mall and bought the following:

Music CD for $12.99

T-shirt for $9.50

Fruit smoothie for $3.25

Lisa had $30 in her purse. After she purchased these three items, how much money was left?

6. Saul worked 3 hours on Monday, 6 hours on Tuesday, 11 hours on Wednesday, and 1 hour on Thursday.

He is paid $8.97 per hour. About how much money did he earn that week?

a. $100 b. $160 c. $180 d. $220

7. Use the chart to answer the questions.

b. Johnny has $25 to buy a meal for himself and two friends.

Can he purchase 2 hamburgers,

1 cheeseburger, 1 order of fries, 2 onion rings and

medium sodas? Explain your answer.

c. Does he have enough money left to purchase anything else?

Explain your answer.

Burger Barn Menu

Hamburger $4.30

Cheeseburger $4.75

Fries $2.15

Onion Rings $2.90

Soda- Small $0.85

Medium $0.95

Large $1.05

a. Johnny ordered a hamburger, fries and a

medium soda. He handed the clerk $20. How

much change should he receive?

Explain your answer.

6.8: Order of Operations (no calculator)

1. What is the value of 24+3∙6

3 – 3 ?

2. When simplifying the following using order of operations, which operation should be performed first?

11 ÷ (12 – 8 ∙ 3) + 24

a. 11÷12 b. 12-8 c. 8∙3 d. 24

3. What number is equal to: 2 ∙ 8 – 4 ÷ 4

a. 2 b. 3 c. 14 d. 15

6.9: Ballpark comparisons of the US Customary and Metric systems

1. Which measurement would best describe the mass/weight of a textbook

a. 5 lb b. 1 Kg c. 1 g d. 8 oz

2. Which temperature would best describe when water freezes?

a. 0˚ F b. 0˚C c. 32˚C d. 30˚F

6.10: Pi, circumference & area, perimeter & area, volume & surface area

1. Mr. Jay is putting a border around a rectangular mirror. The perimeter of the mirror is 32 inches.

Identify the measurements that could be the two dimensions of the mirror.

2 3 4 8 13 15 16

2. A wheel has a radius of 46.5 meters. Which is the closest to the circumference of the wheel?

a. 146.01 b. 73.005 c. 292.02 d. 678.65

3. Which statement is true:

a. π is a ratio of a circle’s diameter to its circumference.

b. π is a ratio of a circle’s area to its diameter.

c. π is a ratio of a circle’s circumference to its diameter.

d. π is a ratio of a circle’s area to its radius.

4. Trevor covered a rectangular box for a project. It had a height of 2 inches, a width of 4 inches, and a

length of 5 inches. Which is the closest to the minimum amount of paper Trevor needed to cover the

entire box?

2in

5in

4in

a. 40 sq in b. 38 sq in c. 76 sq in d. 96 sq in

5. A powdered drink mix is stored in a rectangular container that has a length of 9 centimeters, a width of 6

centimeters, and a height of 12 centimeters. Which is closest to the maximum number of cubic

centimeters the container will hold?

a. 108 cubic cm b. 54 cubic cm c. 72 cubic cm d. 648 cubic cm

6. Billy Bob wants to paint a rectangular wall that measures 16 feet by 9 feet. The wall contains a window

with the dimensions shown.

If Billy Bob does not paint the window, what is the total shaded area he will paint?

a. 144 sq ft b. 104 sq ft c. 50 sq ft d. 40 sq ft

7.

a. 3 b. 4 c. 6 d. 8

8. Use the following to find the perimeter :

a. 11 m b. 17 m c. 33 m d. 22 m

9.

If the diameter of the rug is equal to the length of the bedroom floor, which is the closest to the area of

the rug?

a. 38 sq ft b. 75 sq ft c. 113 sq ft d. 452 sq ft

6.11: Coordinate Graphing

Locate and label points A (-2, 2), B (2, 2), C (2,-2), and D (-2, -2) on a coordinate plane. Connect the points in

order to form square ABCD.

1. Move point B up 3 units and label this point B′. What are the coordinates of B′? _______

2. Move point D down 3 units, and label this point D′. What are the coordinates of D′?____

3. What shape does AB′CD′ form? _______________

6.12: Congruence of segments, angles and polygons

1. Which of the following choices is correct for the statement, 'a straight angle is two times a right angle'?

a. Sometimes true b. Always true c. False d. None of the above

2. "The sum of two acute angles is equal to an obtuse angle." - Which of the following is correct about this

statement?

a. Always true b. Sometimes true c. False d. None of the above

3. Identify all true statements for the following figures

a. AB ≅ QR b. ∠C ≅ ∠R c. AB ≅ PQ d. ∠A ≅ ∠R

4. ∆PQR is congruent to ∆TSR. PR is the longest side of ∆PQR, PQ = 9 in and PR = 15 in. The perimeter

of ∆PQR is 36 in. What is the measure of QS?

a. 26 in. b. 24 in. c. 12 in. d. 18 in

5. Which set of the triangles are not congruent?

6. Which of the figures are congruent?

7. Which of the figures are congruent?

6.13: Quadrilaterals

1) The measure of one angle of a parallelogram is 110°. Find the measures of the other three

angles. Illustrate your answer.

2) Describe the similarities and differences between a trapezoid and a parallelogram.

6.14: Data analysis and circle graphs

1) The ages of 7 trumpet players in a band are 13, 12, 11, 12, 11, 10 and 12. What type of graph would be

appropriate for comparing the ages of these trumpet players?

2) The federal hourly minimum wage was recorded each year from 1990 to 2007. What type of graph would

best show the changes in minimum wage during this time period?

3) When asked if "antidisestablishmentarianism" has 28 letters, 50 people said yes, 35 people said no and 15

people said I don't know. What type of graph would best compare these responses to each other and with

the total?

4) The growth of 7 different plants was recorded in centimeters. What type of graph would be best for

comparing the growth of each plant?

5) In a city, the rainfall was recorded in inches each month for 12 months. What type of graph would best

display the change in rainfall?

6) Which percentage most accurately describes the shaded area of this circle?

a. 50% b. 33% c. 75% d. 66%

7) Look at the circle. Which fraction and percent correctly names the unshaded part of the circle?

a. 2/3 and 66% b. 2/3 and 33% c. 1/3 and 33% d. 3/3 and 33%

8) Color 4

5 of the circle below.

Using what you know about percentage, tell why you chose to put your lines where you did. Use mathematical

terms and/or pictures to explain your answer.

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

The following graph shows the Newspapers Recycled (in pounds) by five sections of a class of an Elementary

School Students. Study the pie graph and answer the following questions.

Recycling Circle Graph

9) What fraction of the graph is represented with sections E and D? __________________

10) Which two sections are 1

5 of the circle graph? ______________________

11) Sections B and C are what percentage greater than Sections A, E, D? __________

6.15: Measure of Center

1. Use the following data to answer the questions below.

Data set: 1, 7, 6, 6,4, 8, 6, 5, 6

a. Use the number line below and plot the points

b. What is the mean of this data set?

2. Find the balance point for this set of data.

x x x

x x x x x x

5 6 7 8 9 10 11 12 13 14

3. Mark’s last 5 math grades are 85, 90, 80, 90 and 95

a. Which measure of center best represents the average of his grades?

b. Explain why______________________________________________

4. The following data set represents the ages of children at the playground

1, 4, 3, 3, 2, 5, 3, 6, 4, 2, 3, 3, 0, 2

Which measure of center best represents the children’s ages at the playground?

Explain why:_____________________________________________ ___

5. This set of data represents the number of miles biked in one week.

22, 24, 5, 26, 27, 30

What is the outlier? _______

6. What center of measure best represent the miles biked? __________________

6.16: Independent and Dependent Events

1. Identify all statements that represent dependent probability.

a. Roll a dice; toss a coin

b. Take a marble out of a bad; replace it and take another marble out of the bag.

c. Choose a person from a group of 50, choose a second person from the same group.

d. Pick a card, do not replace it, and then pick a second card.

e. Selecting a marble and then choosing a second without replacing the first marble.

f. Rolling a number cube and spinning a spinner.

2. Josh has 8 black socks and 2 white socks. Every morning he chooses one sock at random. After he's pulled

that one sock out, he chooses another sock at random - and wears them! What is the probability that he

chooses first a white sock, then a white sock?

a. 1

10 b.

1

45 c.

1

100 d.

1

16

3. One letter is randomly selected from the word MATHEMATICS and a second letter is randomly selected

from the word PROBLEMS. What is the probability that both letters are vowels? ______

4. The letters from the word EVALUATE are written on a set of cards. Find the probability if you pick two

cards without replacing the first.

a. P ( L then A) _______________

b. P ( E then T) _______________

6.17: Geometric and arithmetic sequences

1. Determine whether the sequence is arithmetic, geometric, both or neither.

8, 14, 20, 26, ……

a. Neither b. Geometric c. Arithmetic d. Both

2. A grocery clerk sets up a display of oranges in the form of a triangle using 9 oranges at the base and 1 at

the top. How many oranges were used by the clerk to make the arrangement?

a. 45 oranges b. 40 oranges c. 47 oranges d. 44 oranges

3. Mr. Thomas’s car insurance is $500 per year. He expects it to increase by $45 each year. How much will

he pay for insurance in 5 years?

a. $590 b. $635 c. $680 d. $725

4. Identify the missing term in the pattern; 34, 27, ______, 13, 6

a. 21 b. 19 c. 20 d. 17

5. What is the 7th term in this sequence?

3, 6, 9, 12, ……

a. 15 b. 21 c. 18 d. 24

6. What rule describes the sequence shown?

1, 4, 16, 64

a. Multiply by 4 b. Divide by 4 c. Subtract 48 d. Add 3

6.18: One-step linear equations

Use the balance scale above to answer numbers 1 and 2.

1. What equation is being modeled above? _____________________________________

2. What is the solution to the above equation?___________________________________

Use the following to answer questions 3 - 5: 4𝑥2 + 10x + 8

3. Is this an equation or an expression? How do you know?__________________________

________________________________________________________________________

4. How many terms does it have? _____ Name them. ______________________________

5. Name the coefficient(s). ____________________________________________________

= x

= 1

Solve algebraically and check answer.

6. 15m = 105 7. 17 = k – 17 8. 𝑝

5 = 5

9. What operation would you do in order to solve the following equation:

12m = 30

a. Multiply both sides of the equation by 12

b. Subtract 12 from both sides of the equation

c. Divide both sides of the equation by 12.

d. Subtract 30 from both sides of the equation

6.19: Properties

Fill in each blank to make a true statement using your knowledge of properties; then identify each

property being illustrated.

3 + __ = 3 13 ∙ __ = 13 1

4 ∙ __ = 1 5 ∙ = 1

5 ∙ __ = 5 12 ∙ = 1 __ + 2 = 2 6 ∙ __ = 0

6.20: Graphing inequalities

1. Using the inequality 6n ≤ 30 circle all true statements about the value of n.

a. n = 10 b. n = 6 c. n = 4 d. n = 0

2. Write and graph the following inequality on the number line:

Sally is babysitting in order to earn enough money to buy a new $95 iPod. She makes $8 an hour. What

is the minimum amount of hours Sally must work to buy the new iPod?

Inequality:____________

3. Choose the correct inequality for the following statement. It never takes Jacob longer than 20 minutes to

walk home from school.

a. j > 20 b. j < 20 c. j ≤ 20 d. j ≥ 20