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Math 7R Final Review

REVIEW ALL TOPICS AND ROUNDS; REVIEW FINAL QUIZLETS; REVIEW FINAL TEST

STATISTICS

Round 1

Questions #1-5

The chart below shows the average grade for the final exam for six years.

|Year |Final |

|2012 |93 |

|2011 |63 |

|2010 |95 |

|2009 |97 |

|2008 |95 |

|2007 |94 |

1.) Determine the mean. Show your work. __________

2.) Determine the median. Show your work. __________

3.) What is the mode? __________

4) Which measure(s) of central tendency best represents the data? ______________

5.) The stem-and-leaf plot below shows the scores Alicia received on her math tests.

Find the range: ________

6.) Phil’s test scores are shown below. What is the range of this test score?

Show your work.

|98 |65 |

|2012 |105 |

|2011 |31 |

|2010 |28 |

|2009 |20 |

|2008 |30 |

|2007 |25 |

1.) Determine the mean. Round to the nearest tenth. _________

2.) Determine the median. Show your work. __________

3.) What is the mode? __________

4.) Which measure(s) of central tendency best represents the data? ______________

5.) Mark’s last 8 test scores are shown in the table below. What is the range?

Show your work.

TEST SCORES

|100 |91 |

|orange |8 |

|yellow |17 |

|blue |15 |

4.) What is the theoretical probability of Meg landing on orange? Answer: __________

5.) What is the experimental probability of Meg landing on orange? Answer: ______

6. ) A school menu lists two soups, three main dishes, three desserts, and four drinks. How many different meals consisting of one soup, one main dish, one dessert, and one drink are possible?

7) What is the probability of flipping tails on a coin and then rolling a 8 on a number cube?

A 0 B [pic] C 1 D None of the above

Questions #8-10

Sally goes to the Shake Shack to get a shake. She has a choice of the following:

Size: small, medium, large

Flavor: vanilla, chocolate

Topping: whipped cream, caramel

8.) Draw a tree diagram or list the sample space to show all the possible outcomes of one size, one flavor, and one topping. Show your work.

9.) What is the total number of possible outcomes for a shake? Answer: ________

10.) What is the probability Sally will select a small, vanilla shake with caramel?

11.) In a math class there are 20 girls and 40 boys. What is the probability that a

person chosen at random is a girl?

Round 2

1.) The probability of reaching into a box without looking and selecting a blue block is [pic].

If you reach into the box 56 times, how many blue blocks would you expect to get?

2.) The probability it will rain today is 80%. Which statement best describes the probability of this event?

1) It is unlikely it will rain today.

2) It is neither likely nor unlikely it will rain today.

3) It is likely it will rain today.

4) It is impossible for it to rain today.

3.) If you roll a die, what is the probability of getting an even number or a number

less than 3?

Questions #4-5

Joe conducted a math experiment and flipped a coin 80 times. The results are shown in the table below.

| |Number of Times |

|Heads |30 |

|Tails |50 |

4.) What is the theoretical probability of Joe flipping a coin and landing on heads?

5.) What is the experimental probability of Joe flipping a coin and landing on heads?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

Questions #6-9

The Rice-A-Maniacs can order team shirts. They have a choice of the following:

Size: small, medium, large

Color: green, yellow

Style: short-sleeve, long-sleeve

6.) Draw a tree diagram or list the sample space to show all the possible outcomes of one size, one color, and one style. Show your work.

7.) What is the total number of possible outcomes for a team shirt? Answer: ________

8.) What is the probability that Rice-A-Maniacs will select a large, green, short-sleeved shirt?

9.) What is the sample space for finding the probability that the number 6 will be rolled on a number cube?

A [pic] C {1, 2, 3, 4, 5, 6}

B {6} D {1, 3, 5}

Round 3

1.) The probability of reaching into a bag without looking and selecting an orange jellybean

is [pic]. If you reach into the bag 72 times, how many orange jellybeans would you expect to get?

2.) The probability of picking a broken crayon from a box of crayons is 8%. Which statement best describes the probability of this event?

1) It is unlikely you will pick a broken crayon.

2) It is neither likely nor unlikely you will pick a broken crayon

3) It is likely you will pick a broken crayon/

4) It is impossible for you to pick a broken crayon.

3.) If the probability that it will snow is [pic]what is the probability that it will not snow?

Questions #4-5

Lisa spins a game spinner 50 times and records the results in the table below. Use the spinner and the table below to answer the following questions.

|Letter |Number of Times |

|A |12 |

|B |30 |

|C |8 |

4.) What is the theoretical probability Lisa will land on the letter C?

5.) What is the experimental probability Lisa will land on the letter C?

Questions #6-8

Tony goes to Pizza Cove to get a pizza. He has a choice of the following:

Size: small, medium, large

Crust:: thin, deep

Topping: cheese, pepperoni

6.) Draw a tree diagram or list the sample space to show all the possible outcomes of one size, one crust, and one topping. Show your work.

7.) What is the total number of possible outcomes for a pizza?

8.) What is the probability Tony will choose a medium, thin crust, with pepperoni pizza?

9.) Describe the probability of picking a blue pencil from a bag containing 10 blue pencils,

2 white pencils and 8 red pencils:

A certain C as likely as not

B unlikely D likely

10). What is the probability of flipping heads on a coin and then rolling a 3 on a number cube?

A 0 B [pic] C 1 D None of the above

11) Pam wants to buy a suitcase. The order form she uses is shown below.

SUITCASE ORDER FORM

How many different combinations of color, size, and material are possible for Pam’s suitcase?

A) 10 B) 15 C) 24 D) 30

EXPRESSIONS:

1.) Choose the correct number and property that makes the following true:

(2 + 5) + 9 = 2 + (5 + ___)

1) 9, associative property 3) 9, distributive property

2) 9, commutative property 4) 5, associative property

2.) Simplify the following expression: 16n + 20 – 7n – 5

1) 9n + 15 3) 36n – 12

2) 9n – 15 4) 36n + 12

3.) Factor the following expression completely: 8x – 24

1) 4 (2x – 6) 3) 4 (2x + 6)

2) 8 (x – 3) 4) 8 (x + 3)

4.) Part A: Simplify the expression: 4x + 18 + 6x – 6

Part B: Evaluate your answer in Part A when x = –4. Show your work.

5.) Simplify the following expression: 5a + 7b – 6a + 4b

1) 11a + 11b 3) 12a – 2b

2) 10ab 4) −a + 11b

6.) Which expression is equivalent to –8 – 2 ?

1) 8 + 2 3) –8 + 2

2) 8 – 2 4) –8 + (–2)

7.) Part A:

Use the distributive property to write an equivalent expression for: 8 (2x – 5)

Part B:

Evaluate your answer in Part A when x = 7. Show your work.

8.) Part A:Express the perimeter of the triangle below in terms of x, in simplest form.

Part B:Find the perimeter of the above triangle when x = 4. Show your work.

9.) Which of the following is equivalent to (5d + 10) – (d – 8)?

1) 4d – 2 3) –8d

2) 4d + 18 4) 17d

Round 2

1.) Choose the correct number and property that makes the following true: 10 ( 2 ( 7 = 2 ( ___ ( 10

1) 7, commutative property 3) 7, distributive property

2) 7, associative property 4) 2, commutative property

2.) Simplify the following expression: 8x – 10x + x

1) -2x 3) x

2) -x 4) 2x

3.) Express the following as two factors: 9a + 15

1) 9 (a + 15) 3) 3 (3a – 5)

2) 3 (3a + 5) 4) 24a

4.) Part A:Simplify the expression: 5x + 10 – 3x - 7

Part B: Evaluate your answer in Part A when x = –5. Show your work.

5.) Which expression is equivalent to −12 – 6?

1) 12 + 6 3) −12 + 6

2) 12 – 6 4) −12 + (−6)

6.) Which of the following linear expressions cannot be factored?

1) 18x + 16 3) 25x − 10

2) 15x - 6 4) 27x + 4

7.) Part A:

Use the distributive property to write an equivalent expression for: 6 (3x + 2)

Part B:

Evaluate your answer in Part A when x = 8. Show your work.

8.) Part A:Express the perimeter of the rectangle to the right in terms of x, in simplest form.

Part B:Find the perimeter of the above rectangle when x = 2. Show your work.

9.) Which of the following is equivalent to (3s + 5) + (4s - 9)?

1) 7s – 4 3) 7s + 4

2) 7s − 14 4) 7s + 14

Round 3

1.) Choose the correct number and property that makes the following true: 3 (4 + 5) = 3 ( 4 + ___ ( 5

1) 4, distributive property 3) 3, commutative property

2) 3, distributive property 4) 3, associative property

2.) Simplify the following expression: 20n + 30 – 13n - 8

1) 7n + 22 3) 7n - 22

2) 50n - 21 4) 50n + 21

3.) Factor the following expression completely: 8n - 20

1) 2 (4n – 10) 3) 4 (2n – 5)

2) 8 (n – 12) 4) 4 (2n + 5)

4.) Part A:

Simplify the expression: 9x + 8 – 5x - 3

Part B: Evaluate your answer in Part A when x = 4. Show your work.

5.) Which of the following linear expressions cannot be factored?

1) 12x + 34 3) 28x – 15

2) 7x + 28 4) 42x – 35

6.) Which of the following is equivalent to (7g + 12) – (g – 4)? SHOW YOUR WORK!!!!!

1) 6g + 8 3) 16g

2) 6g + 16 4) 22g

7.) Part A: Use the distributive property to write an equivalent expression for: 3 (5x - 4)

Part B: Evaluate your answer in Part A when x = 3. Show your work.

8.) Part A:Express the perimeter of the triangle below in terms of x, in simplest form.

Part B:Find the perimeter of the above triangle when x = 5. Show your work.

9.) Tori’s savings account has $36.50. She withdraws $50 from her account. Which equation shows the new balance of Tori’s account?

1) 36.50 – 50.00 = 13.50 3) 36.50 – 50.00 = -13.50

2) 50 – 36.50 = -13.50 4) 50 – 36.50 = 13.50

ANGLES

Round 1

1.) Solve the following equation: 5x + 8 – 3x = 18

1) x = 3.25 3) x = 5

2) x = 1.25 4) x = 13

2.) Solve the following equation: + 1x = 1

3.) Solve the following equation: 2 (x – 4) = -16

4.) A cell phone company charges a monthly rate of $15.95 plus $0.20 a minute (m) per call. The total bill for last month was $39.95.

Part A:Write an equation to find the number of minutes used.

Part B:Solve the equation above and find the number of minutes used last month.

5.) Amy bought books at a book fair. She bought a hardcover book for $10 and some paperback books for $4 each. She spent $26 in all. Which of the following equations can be used to find the number of paperback books Amy bought?

1) 10 + 4 + x = 26 3) 4x + 10 = 26

2) 10x + 4 = 26 4) 14x = 26

6.) Simplify the following expression: 8x + 4 – 6x – 10

1) 2x – 14 3) 14x – 14

2) 2x – 6 4) 14x – 6

7.) Part A:

Express the perimeter of the rectangle below in terms of x, in simplest form.

Part B:

Find the perimeter of the above triangle when x = 5. Show your work.

8.) 3( (10 ( 5) = (3 ( 10) ( 5 is an example of which of the following properties?

1) identity property 3) commutative property

2) associative property 4) distributive property

Round 2

1.) Solve the following equation: 5x – 2 – 2x = 10

2.) Solve the following equation: -5 + 3x = 13

3.) Solve the following equation: 4 (x + 5) = 40

1) x = 5 3) x = 15

2) x = 10 4) x = 6

4.) Emily’s is 6 less than twice the age of her brother, Dave. Emily is 20 years old.

Part A:Write an equation that can be used to find Dave’s age.

Part B:Solve the equation above to find Dave’s age. Show your work.

5.) After a carpenter cut a 9.5 inch long piece of wood from a board, the remaining part of the board was 26.5 inches long. Which equation can be used to find the length of the board?

1) b – 9.5 = 26.5 3) 9.5b = 26.5

2) 26.5 – b = 9.5 4) b + 9.5 = 26.5

6.) Dan went to Smith’s Deli to get a sandwich. He has the choice of:

Bread: wrap, pita, roll

Meat: turkey, ham

Topping: pickles, mustard

Draw a tree diagram or list the sample space to show all possible sandwich choices including one bread, one meat and one topping.

7.) Lisa spins a game spinner 50 times and records the results in the table below. Use the spinner and the table below to answer the following questions.

|Letter |Number of Times |

|A |12 |

|B |30 |

|C |8 |

What is the theoretical probability Lisa will land on the letter A?

Round 3

1.) Solve the following equation for x: - x - = 1

2.) Solve the following equation: 9 – 3x = 27

3.) Solve the following equation: 2x + 12 + x = 42

4.) A cell phone company charges a monthly rate of $20.50 plus $0.15 per text message (t). The total bill for last month was $32.50.

Part A:Write an equation to find the number of minutes used.

Part B:Solve the equation above and find the number of tests sent last month.

5.) A moving company charges $250 to rent a truck and $0.40 for each additional mile driven. Matt paid a total of $314. Which equation can be used to find m, the number of miles, he drove the moving truck?

1) 0.40m + 250 = 314 3) 250m + 0.40 = 314

2) m + 0.40 (250) = 314 4) m(0.40 + 250) = 314

6.) What is the factored form of the following expression? 60n + 108

1) 6 (10n + 12) 3) 12 (5n + 9)

2) 6 (10n + 108) 4) 12 (5n + 108)

7.) Which expression has the same value as -24 – (-17) ?

1) 17 – 24 3) 24 – 17

2) -17 + 24 4) 24 + 17

8.) The stem-and-leaf plot shows the girls’ test scores on the last math test.

Find the mean, median, mode and range. Show your work.

mean: _______ median: _______

mode: _______

INEQUALITIES

Round 1

1.) Give the solution for the graph shown

1) x < -3 3) x > -3

2) x ≤ -3 4) x ≥ -3

2.) Which of the following is NOT a solution for x ≥ 3?

1) 2 3) 3

2) 5 4) 6

3.) Which of the following is the solution for the inequality 3x + 8 < 32?

1) x < 24 3) x < 40

2) x > 8 4) x < 8

4.) Which of the following is the solution for the following inequality? -2x + 8 ≥ 20

1) x ≤ -6 3) x ≥ -6

2) x ≤ 6 4) x ≥ 6

5.) Rachael has saved $216. She needs to save at least $550. Write an inequality to represent this situation, solve the inequality, and then graph the solution on the number line.

a) Write an inequality:

b) Solve the inequality:

c) Graph the solution on the number line below.

6.) Nick wants to join a gym. The membership is $350 for the year plus $12 for each class he attends. Nick wants to spend less than $650 for the year.

Part A:

Write an inequality that can be used to determine the number of classes Nick can take in one year.

Part B:

Solve the inequality from Part A. Show your work.

Part C:

Will Nick be able to take 20 classes and still spend less than $650 for the year? Explain.

Round 2

1.) Give the solution for the graph shown below.

1) x < -1 3) x > -1

2) x ≤ -1 4) x ≥ -1

2.) Which of the following is NOT a solution for x ≥ 0?

1) 0 3) 1

2) -1 4) 4

3.) Which of the following is a solution for the inequality 4x > 24 ?

1) 7 3) 6

2) 5 4) 4

4.) Which of the following is a solution for the following inequality? -3x + 1 ≤ 22

1) x ≤ -7 3) x ≥ -7

2) x ≤ 7 4) x ≥ 7

5.) Charlie bought 6 smoothies at Madison’s Smoothies. The bill was greater than $24.

Part A: Part B:

Write an inequality to represent the Solve the inequality from Part A.

cost of one smoothie. Show your work.

Part C:

Graph the solution on the number line below.

6.) Christine plans to join a book club. The membership is $25 for the year plus $3 for each book that she buys. She wants to spend less than $205.

Part A:

Write an inequality that can be used to determine the number of books Christine can buy for the year.

Part B: Solve the inequality from Part A. Show your work.

Part C: Will Christine be able to buy 50 books and still spend less than $205? Explain.

7.) Part A: Rewrite the following expression using the commutative property.

5m + 8 – 2m – 3 + 3m

Part B: Simplify your answer from Part A.

Round 3

1.) Give the solution for the graph shown below.

1) x < 2 3) x > 2

2) x ≤ 2 4) x ≥ 2

2.) Which of the following is NOT a solution for x ≤ 5?

1) 1 3) 3

2) 5 4) 6

3.) Which of the following is a solution for the inequality 5x < 45 ?

3) 9 3) 5

4) 10 4) 11

4.) Which of the following is a solution for the following inequality? -4x + 5 ≤ 21

1) x ≤ -4 3) x ≥ -4

2) x ≤ 4 4) x ≥ 4

5.) John bought 5 ice-cream cones. The bill was greater than $10

Part A: Part B:

Write an inequality to represent the Solve the inequality from Part A.

cost of one cone. Show your work.

Part C:

Graph the solution on the number line below.

6.) Sean wants to join a bowling league. The membership is $60 for the year plus $9 for each game he plays. Sean wants to spend less than $240 for the year.

Part A:Write an inequality that can be used to determine the number of games Sean can play for the year.

Part B:Solve the inequality from Part A. Show your work.

Part C: Will Sean be able to play 18 games and still spend less than $240? Explain.

7.) Derek conducts a probability experiment for his mathematics class. He uses the ten

cards shown below. Derek randomly picks one of the ten cards from the container, looks at the color, and replaces the card. He repeats this 100 times. How many times would you expect Derek to pick a gray card? Show your work.

PERCENTS

Round 1

1.) A sweater usually sells for $75 is on sale for $60. What is the percent of decrease, to the nearest tenth of a percent?

1) 20% 3) 25%

2) 80% 4) 1.25%

2.) This year’s enrolments in the 7th grade increased by 5%. Which expression represents this year’s enrollment?

1) 0.05x 2) 0.95x 3) 1.05x 4) 1.5x

3.) Megan left $4 as a tip on a breakfast bill of $17. Which proportion can be used to find the percent tip Megan left?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

4.) Huey and five friends went out to dinner. They paid a 18% tip on a $90 bill.

Part A: What was the amount of tip they paid? Show your work.

Part B: What was the total amount that they paid for dinner? Show your work.

Part C: How much did each person pay? Show your work.

5.) Ariana received $5,500 in Bat Mitzvah gifts in April.

Part A: How much simple interest will she earn in 7 years from investing her money in a savings account at 4% simple interest? Show your work.

Part B: How will she have in her account at the end of 7 years? Show your work.

6.) Tom bought movie tickets for himself and three of his friends. He paid $9.50 for each ticket. If Tom has $16.50 left, how much did he have before he bought the movie tickets?

7.) A $300 surfboard is marked up by 10% and then marked down by 10%. What is the final price?

8.) 30% of 600 8th graders surveyed said they prefer Fridays over Saturdays for their favorite day of the weekend. How many students prefer Saturdays?

9.) There are 300 7th graders and 700 8th graders in Reagan Middle School. What percent of the school is made up of 7th graders?

Round 2

1.) A jacket usually sells for $175 is on sale for $140. What is the percent of discount for the sale price, to the nearest tenth of a percent?

1) 80% 2) 20% 3) 1.25% 4) 2%

2.) A new Ipad costs $320 and the sales tax is 6.25%. What is the total cost of the Ipad?

1) $20 2) $200 3) $300 4) $340

3.) A wetsuit is on sale for $140. If this price represents a 20% discount from the original price, what was the original price of the wetsuit?

4.) In New York State, sales tax rates vary by county. In Suffolk County, the sales tax rate is [pic]%.

Part A: A shirt costs $12.75 and a baseball hat costs $8.25. Rounded to the nearest cent, how much more is the tax on the shirt than the tax on the baseball cap? Show your work.

Part B: Using b to represent the cost of an item before tax and t to represent the amount of sales tax for that item, write an equation to show the relationship between b and t.

Part C: Is this relationship proportional? Justify.

5) Use the distributive property to write an equivalent expression for: 4 (x – 3)

1) 4x – 3 3) 4x – 12

2) x – 12 4) 4x + 12

6.) Chris bought 6 movie tickets at $14 each. He had a coupon for 20% off. The sales tax was 9%. Find the following:

Part A: Find the cost of 6 movie tickets. Show your work.

Part B: Find the sale price of the 6 movie tickets after the 20% coupon. Show your work.

Part C: If he pays 9% sales tax, find the amount of the sales tax. Show your work.

Part D: Find the total price he paid for the movie tickets. Show your work.

7.) A $150 fishing pole is marked up by 10% and then marked down by 10%. What is the final price?

8.) 40% of 500 women surveyed said they prefer Spinning Class as compared to Zumba Class for their favorite exercise. How many women prefer Zumba Class?

1) 200 2) 300 3) 400 4) 460

9.) Solve the following equation: 7x + 9 – 3x = 33

Round 3

1.) A pair of sneakers which usually sell for $125 are on sale for $115. What is the percent of decrease, to the nearest tenth of a percent?

1) 25% 2) 8% 3) 80% 4) 92%

2.) Grace bought carnival admission tickets for herself and two of her friends. She paid $7.50 for each ticket. If Grace has $13.50 left, how much did she have before she bought the admission tickets?

3.) Mark left $16 as a tip on a dinner bill of $120. Which proportion can be used to find the percent tip Mark left?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

4.) Julia invests $496 into a savings account that earns 4.7% simple interest. If she plans on leaving the money in the account for 7 years, what will be the final balance of the savings account after 7 years?

5.) Simplify the following expression: (8n – 12) – (3n – 5)

1) 11n + 7 2) 11n – 17 3) 5n – 17 4) 5n – 7

6.) Gertrude and six friends went out to brunch. They paid a 15% tip on a $120 bill.

Part A: What was the amount of tip they paid? Show your work.

Part B: What was the total amount that they paid for brunch? Show your work.

Part C: How much did each person pay? Show your work.

7.) In New York State, sales tax rates vary by county. In Yonkers County, the sales tax rate is [pic]%.

Part A: A CD costs $15.75 and a poster costs $11.25. Rounded to the nearest cent, how much more is the tax on the CD than the tax on the poster? Show your work.

Part B: Using b to represent the cost of an item before tax and t to represent the amount of sales tax for that item, write an equation to show the relationship between b and t.

Part C: Is this relationship proportional? Justify.

8.) Which of the following measures of central tendency does an outlier affect the most?

1) mean 2) median 3) mode 4) range

9.) Carl and his three friends went out to lunch to celebrate Carl’s graduation from middle school. They decided to leave a 15% tip, which is based on the cost of the food plus tax (tax in San Diego is 8.5%). The receipt shown below lists the lunch total before tax and tip.

Part A: Use mental math to estimate the approximate total cost of the bill including tax and tip to the nearest dollar.

Part B: Find the actual total of the bill including tax and tip. If Carl and his three friends split the bill equally, how much will each person pay including tax and tip?

RATES & RATIOS PART 1

Round 1

1. Express the unit price of a notebook that costs $40.00 for a case of 16

2. A survey was taken at a local deli to determine whether students prefer coffee or tea. There were 178 people that were surveyed and 56 of them said that they prefer tea. What is the ratio of people who prefer coffee to the total number of people surveyed?

3. You can do 90 sit-ups in 2 minutes. Write and solve a proportion to find out how many sit-ups you can do in 3 minutes. Show work below!

4. This year’s enrollment in the SADD club increased from last year by 8%. Which expression represents this year’s enrollment?

1) 1.92x 2) 1.08x 3) .08x 4) .8x

5. Nolan is jogging from his house to Mark’s house. The distance he covers is 2 miles in 27 minutes. Express this relationship as a rate.

6. A billboard is 20 feet in height. The designer used a scale of 0.25 inch on his paper sketch represents 5 feet of actual distance. Which of the following proportions can be used to find x, the height of the billboard on the sketch?

1) = 2) = 3) = 4) =

7. Solve for x:

=

Round 2

1. Express the unit price of a calculator that costs $99.00 for a dozen. Show work below!

2. An escalator travels directly up 24 floors in 80 seconds. How many floors can this escalator travel directly up in 120 seconds?

3. A chili recipe calls for 9 ounces of tomato sauce for every 2 pounds of chop meat. How many ounces of tomato sauce would be needed if you used 4 pounds of meat?

4. Maria’s last 8 test scores are shown in the table below. What is the range?

TEST SCORES

|98 |91 |78 |32 |

|# of Words |45 |75 |105 |

Gus types 45 words in 1½ minutes. The table below shows this relationship.

What is the value of the constant for this proportional relationship?

Graphing an Equation from a table

|x |3x |y |(x,y) |

|0 | | | |

|1 | | | |

|2 | | | |

|3 | | | |

Part A:

Complete the table for the equation y = 3x.

Part B:

Graph the equation y = 3x on a coordinate plane. Connect the points with a line.

Part C:

Identify the constant of proportionality from the graph. Answer: ____________

Practice

|x |2x |y |(x,y) |

|0 | | | |

|1 | | | |

|2 | | | |

|3 | | | |

8. Complete the table for the equation y = 2x.

Part A:

Part B:

Graph the equation y = 2x on a coordinate plane. Connect the points with a line.

Part C:

Identify the constant of proportionality from the graph.

Answer: ____________

9. Using the table below, what is the value of the constant for this proportional relationship? Show work below!

|Gallons of Gasoline |3 |4 |5 |9 |

|Miles Driven |18 |24 |30 |54 |

10. Abigail’s hourly wages is proportional to the number of hours Abigail works The table below show this relationship

|Hours worked |12.5 |13.5 |14.5 |

|Amt. of $ earned |100 |108 |116 |

What is the constant of proportionality for the relationship shown in the table above?

1) 8 3) [pic]

2) 12.5 4) [pic]

Practice:

1. 30% of 400 people surveyed said they prefer mac & cheese over salad for lunch.

How many students prefer salad?

2. The additive inverse of 8 is

3. Erica is taking a train from New York City to Washington, D.C. The train travels 324 miles in [pic] hours. Express this relationship as a rate.

4. Show work for each part:

Convert .9 into a fraction in its simplest form

Convert [pic] into a decimal

Tell whether the fraction, [pic] will be terminating or non-terminating

AREA

Round 1

1. Find the perimeter of a regular octagon that has one side equal to 7y.

1) 56y[pic] 2) 56y 3) 7y[pic] 4) 8y

2. The area of a circle is 100[pic] cm[pic]. Find the measure of diameter of the circle. Show your work.

3. The perimeter of a square poster is 36 inches. What is the area of the poster in square inches? Show your work.

4. Martha has a circular pool that has a circumference of 20( feet.

Part A: Find the measure of the radius of Martha’s pool. Show your work.

Part B: What is the area of the Martha’s pool? Round your answer to the nearest tenth.

5. Part A:

Express the perimeter of the triangle below in terms of x, in simplest form.

Part B:

Find the perimeter of the above triangle when x = 4. Show your work.

6. Mary needs to paint a floor that measures 12 ½ feet by 10[pic]feet. One bucket of paint covers 14 square feet.

a) What is the area of the wall? Show all work

b) About how many buckets of paint will she need to completely cover the entire wall?

Round 2

1. The circumference of a circle is 50[pic]in. Find the measure of diameter of the circle.

2. What is the formula for the area of a square? ___________________, if the area of a square picture is 9 square inches. Find the length of one side.

3. Part A: The parallelogram below has a base of 13½ cm and a height of 11[pic]cm, find the area rounded to the nearest tenth.

Part B: One jar of paint can cover 4 square cm. What is the least number of jars of paint needed to cover the entire parallelogram?

4. This year’s enrollment in the Reading club increased from last year by 4%. Which expression represents this year’s enrollment?

1) 1.40x 2) .4x 3) .04x 4) 1.04x

5. Part A:

Express the perimeter of the rectangle below in terms of x, in simplest form.

Part B:

Find the perimeter of the above triangle when x = 2. Show your work.

6. Choose the correct number and property that makes the following true:

(2 + 5) + 9 = 2 + (5 + ___)

1) 9, associative property 3) 9, distributive property

2) 9, commutative property 4) 5, associative property

7. Subtract (3x + 8) – ( x – 4 ) ( Once again, if you don’t show work you WILL get it wrong!

Round 3

1. The area of a square is 144 square feet. Find the length of one side.

2. Find the perimeter of a regular pentagon that has one side equal to 5p.

3. The perimeter of a square poster is 80 in. What is the area of the table in square inches? Show your work.

4. The area of a square is 169 square feet.

a. Find the length of one side

b. Find the perimeter

5. Factor the following expression completely: 8x – 80

1) 4 (2x – 20) 2) 4 (2x + 20) 3) 8 (x – 10) 4) 8 (x – 80)

6. Mike has a circular rug that has a circumference of 18( feet.

Part A: Find the measure of the radius of Mike’s rug. Show your work.

Answer: _______________ feet

Part B: What is the area of the Mike’s rug? Round your answer to the nearest tenth.

7. Part A:

Express the perimeter of the triangle below in terms of x, in simplest form.

Part B:

Find the perimeter of the above triangle when x = 5. Show your work.

8. Which of the following is equivalent to (7g + 12) – (g – 4)? SHOW YOUR WORK!!!!!

1) 6g + 8 3) 16g

2) 6g + 16 4) 22g

VOLUME, SURFACE AREA, ANGLE RELATIONSHIPS

Round 1

1. What is the value of the larger angle?

3x° 2x°

2. Find the supplement of a 148.13 degree angle.

3. In the figure to the right, find the measure of [pic]2

4. Find the surface area of the prism shown

5. Two supplementary angles are in the ratio [pic].

What is the measure of the larger angle?

6. In the figure shown, line x is parallel to line y.

What type of angles are ∠1 and ∠3?

a. vertical angles c. complementary angles

b. supplementary angles d. regular angles

Round 2

1. In the diagram below, (1 and (4 and are an example of ____ angles and ___ angles

1) complementary 3) supplementary

2) adjacent 4) vertical

2. Find the volume of a cube that has one side that measures 6 cm.

3. Find the missing angles

a. b.

4. A box of chicken broth can hold 32 cubic ounces of stock.

Part A: If the width is 1 in and the height is 6 in, find the length of the box.

Part B: Using the info. from Part A, find the surface area of the present.

5. John would like to wrap a gift box. The box is a rectangular prism with edges measuring 12 inches, 7 inches, and 5 inches. What is the surface area of the gift box?

6. Line A intersects Line B. If [pic] and [pic] ,

find:

(a) the value of x __________________

(b) The measure of angle 1 __________________

(c) The measure of angle 2 __________________

Round 3

1. Find the complement of a 42.35 degree angle.

2. The two angles shown are supplementary. N

5x x

P U K

Part A: Write an equation to find the value of x.

Part B: Solve for the value of x.

Part C: Find the measure of (PUN.

3. The two lines below are intersecting. Find the values of angles x, y and z.

x = _____

y = ______

z = ______

4. (1 and (2 are an example of _____ angles.

1) complementary 3) supplementary

2) adjacent 4) vertical

5. Which of the following is a solution for the inequality 2x > 18 ?

3) 2 3) 18

4) 9 4) 10

6. A box of Lucky Charms can hold 135 cubic inches of water.

a. Find the height of the box. Show all work.

h

b. Find the surface area of the box. Show all work.

SCALE FACTORS AND INTEGERS

Round 1

1.) Ryan is making a model building. He measured the lengths of the pieces of wood. The measures are [pic] ft., 0.065 ft., [pic] ft., and 0.55 ft. List the length of the pieces of wood in order from least to greatest.

1) [pic], 0.065, 0.55, [pic] 3) [pic], 0.55, 0.065, [pic]

2) 0.065 [pic] 0.55 [pic] 4) [pic], [pic], 0.55, 0.65

2.) A scuba diver dove 90 feet below the water’s surface. Then he swam 52 feet toward the surface. Which integer represents where the scuba diver swam to?

1) 142 2) –142 3) –38 4) 38

3.) Which expression is equivalent to –9 – 3?

1) 9 + 3 2) –9 + 3 3) 9 – 3 4) –9 + (–3)

4.) The following table shows the admission prices for the Big Top Circus.

|Big Top Circus Admission |

|Adults |$8.00 |

|Children (under 10) |$5.25 |

If a group of people spent $45 on tickets, which combination of tickets could they have bought?

1) 4 adults, 3 children 3) 2 adults, 6 children

2) 3 adults, 4 children 4) 3 adults, 5 children

5.) A rectangle has a length of 24 inches and a width of 8 inches. What are the length and width after applying a scale factor of [pic]?

1) length= 24 inches, width = 8 inches

2) length = 48 inches, width = 16 inches

3) length = 12 inches, width = 4 inches

4) length = 6 inches, width = 3 inches

6.) Nick is making shelves for his living room. He needs to make two shelves.

Shelf #1 is [pic] feet long and shelf #2 is [pic] feet long.

Part A: What is the total length of the two shelves? Show your work.

Part B: Nick is using a 20 foot long board. If he already used [pic] feet of the board, what will be the total number of feet he has used after making these two shelves? Show your work.

Part C: Is there enough wood to make these shelves. Explain your reasoning in words.

7.) Which of the following problems has a result that is negative?

1) │7 + (–20)│ 3) │7 – (–20)│

2) │7│ – │–20│ 4) │–7 – (–20)│

Round 2

1.) Jane has 3[pic] yards of yarn. She uses [pic] yards to knit a scarf. How many scarves can she make?

1) 6 3) 9

2) 20 4) [pic]

2.) Kirsten’s savings account has $32.50. She withdraws $80 from the account. Which equation shows the new balance, in dollars, of Kirsten’s account?

1) 80 – 32.50 = 47.50 3) 80 – 32.50 = 52.50

2) 32.50 – 80 = –47.50 4) 32.50 – 60 = –52.50

3.) A rectangle has a length of 18 inches and a width of 9 inches. What are the length and width after applying a scale factor of [pic]?

1) length= 54 inches, width = 27 inches

2) length = 21 inches, width = 12 inches

3) length = 6 inches, width = 3 inches

4) length = 36 inches, width is 18 inches

4.) Joe bought 2 salads and a beverage. Each salad cost $7.25. The beverage cost $1.49. How much change should Joe get if he pays with a $20 bill?

1) $15.99 3) $5.50

2) $4.01 4) $11.26

5.) Which number forms a repeating decimal?

1) 1[pic] 2) 2[pic] 3) [pic] 4) [pic]

6.) Simplify the following expression: (8n – 14) – (2n – 7)

1) 6n – 21 2) 6n –7 3) 10n – 21 4) 10n – 7

7.) A number line is shown below.

Part A:

Plot the point [pic] on the number line below.

Part B:

What is the opposite of [pic]? _______________

Part C: Use the number line and the definition of additive inverse to explain why the number [pic] and its opposites are additive inverses.

8.) Choose the correct number and property that makes the mathematical sentence true.

(2 ( 4) ( 5 = 2 ( (4 ( _____ )

1) 5, associative 3) 5, commutative

2) 4, associative 4) 5, distributive

9.) A triangle is shown to the right.

Part A: Express the perimeter of the triangle below in terms of x, in simplest form.

Part B: Find the perimeter of the above triangle when x = 4. Show your work.

Rounds 3

1.) Pete has [pic] yards of rope. He uses [pic] yards of rope to connect his boat to the dock. How many connections can he make? Show your work.

2.) Dave’s checking account has $62.75. He withdraws $100 from the account. Which equation shows the new balance of Dave’s account?

1) 62.75 – 100 = –37.25 3) 62.75 – 100 = 48.75

2) 100 – 62.75 = –37.25 4) 100 – 62.75 = –48.75

3.) Which number is NOT a terminating decimal?

1) [pic] 2) [pic] 3) 2[pic] 4) [pic]

4.) This year’s enrollment on the football team increased by 12% from last year. Which expression represents the increase in this year’s enrollment?

1) 12x 2) 0.12x 3) 1.12x 4) 1.88x

5.) Part A:

Lucy deposits $450 in a savings account that earns 3% simple interest. How much interest will Lucy earn at the end of 5 years? Show your work.

Part B:

How much money will Lucy have in her account at the end of 5 years, including interest?

Show your work.

6.) Put the following numbers in order from least to greatest. [pic] 0.2 [pic] 0.045

7.) Which expression is equivalent to –15 – 9?

1) –15 + 9 3) 15 + 9

2) –15 +(–9) 4) 15 – 9

8.) Which of the following is a solution for the inequality –2x + 10 > –16?

1) x > 13 3) x < 13

2) x > –3 4) x < –3

9.) A fishing pole that usually sells for $145 is on sale for $116. What is the percent of discount for the sale price, to the nearest tenth of a percent?

10.) A scuba diver dove 70 feet below the water’s surface. Then he swam 48 feet toward the surface. Which integer represents where the scuba diver swam to?

1) 118 2) –118 3) 22 4) –22

-----------------------

Colors available (choose one): __Tan __Blue __Green __ Black __ Red

Sizes available: __ Small __Medium __Large

Material: __Leather __Nylon

TURN

OVER(

Peter’s Pork Palace

Pork Sandwich $10.75

Pork Platter $9.50

Pork Taco $7.99

Pork Salad $12.85

TOTAL: $41.09

A = ( r2

C = 2(r

A = (r2

C = 2 ( r

A = bh

C = 2(r

A = (r2

SA= 2lw + 2lh + 2wh

3

1

V = s3

2.5 in.

V = l w h

h

6 in.

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