Exam: Math Final

When 2(3/5x + 2 3/4y - 1/4x - 1 1/2y + 3) is simplified, what is the resulting expression?

7/10x + 2 1/2y + 6

Laura determined the difference between 8 and -2 using the additive inverse. Her steps are shown below. 8 - (-2) = -8 + 2 = -6 Which best describes the error in Laura's work?

The 8 should have remained positive.

Four students were asked to write an expression which has terms that have a greatest common factor of 8c. The expressions provided by the students are shown below.TanyaWyattXavierYangWhich student wrote the correct expression?

Wyatt

A clothing shop is offering a 12 percent discount for senior citizens. Which equation represents the discount price?

discount price = (original price)(1 - 0.12)

Enrique says 0.4 repeating is a rational number. Which of the following best describes whether Enrique is correct and why?

Enrique is correct. Repeating decimals are rational numbers because they can be written as fractions. The number is actually equivalent to 4/9

Jakob simplified the expression as shown. What was Jakob's error in subtracting the expressions? (6.7x - 3) - (3.4x - 1) - (2x -2) 6.7x - 3 - 3.4x -1 - 2x - 2 (6.7x - 3.4x - 2x) + (-3 - 2 - 1) 1.3X - 6

He used the distributive property incorrectly.

Which question can be represented by the expression 120/y?

Judy plans to read a 120 - page book. If she reads y pages per day. how many days will it take her to finish the book?

Catron evaluates the expression (-9)(2 2/5) using the steps below. Step 1: (-9)(2 + 2/5) Step 2: (-9)(2) + (-9)(2/5) Step 3: -18 + (-9)(2/5) Step 4: (-27)(2/5) Solution: -54/5 = 10 4/5 Which describes Catron's error?

She did not follow order of operations

What is the unit rate depicted in the graph?

0.75 laps in one minute

What is the value of the expression below? -50 + 51

1

The perimeter of an equilateral triangle is 15x + 30 units. Which expression can be used to show the side length of one side of the equilateral triangle?

3(5x + 10): Each side length is 5x + 10 units

Which pair shows equivalent expressions?

3(x + 2) = 3x + 6

Louie made 8.1 liters of fruit punch using only grape juice and carbonated water. He used 4.2 liters of grape juice. The equation 4.2 + c = 8.1 can be used to represent this situation, where c is the number of liters of carbonated water used. How many liters of carbonated water did Louie use?

3.9 liters

What is the quotient? -4 1 3 -3 4

5 7 9

Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor?

Shannon paid $7 more per hour for labor.

What are the steps for using integer tiles to evaluate the expression ?

Start with 45 tiles and separate them into 15 same-sized groups.

Which expression is equivalent to 2w?

w + w

A bookstore bought a case of 10 books at a wholesale price of $84. The bookstore will sell the books at a 25 percent markup, and each book will be sold for the same amount. How much will they sell each book in the case for?

$10.50

What is the sale price of a phone that was originally $199 but that has been marked down by 15 percent?

$169.15

A 12-issue magazine subscription costs $36. What is the average cost per issue of the magazine?

$3

Mike paid $18.00 before taxes for 5 photo albums. His sister wants to buy two of the same type of album. What amount should she expect to pay before taxes?

$7.20

Nancy spent $44.59 on 5.25 quarts of olive oil. What is the cost of one quart of olive oil? Round to the nearest cent.

$8.49 per quart

What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. -3 + 1 4 2

-1 4

In the world's coldest freezer, sodium gas was cooled to a temperature of 78.5°C below zero and then cooled 194.65°C more. What was the new temperature of the sodium gas?

-273.15 C

What is the product of (9) (-9) (-1)?

81

Thirty cars pass through a certain toll booth each minute. At that rate, how many cars are expected to pass through the toll booth each half-hour?

900

Carmine mixes 2.8 pounds of cashews with almonds to make a trail mix. He divides the trail mix into 5 equal portions. Each portion weighs 1.5 pounds. Which equation and solution shows the total amount of almonds he used in the mixture?

1/5(2.8 + a) = 1.5; a = 4.7 per pounds of almonds

When Nancy started middle school, she was 60 inches tall. When she started high school, she was 66 inches tall. What was the percent change in her height?

10 percent increase

What is the difference of -96.43 - (-98.67)?

2.24

What is the value of the expression below? (8 + 1/8) divided by (2.5 + 3/4)

2.5

Lenore borrowed $400 to pay for car repairs. She needs to pay it back in 2 years with simple interest. Lenore wants to figure out the interest rate of her loan. What additional information does she need to find the interest rate?

interest she will owe

The price of a gallon of gasoline dropped by $0.08 on Wednesday and by 0.25 of that amount on Thursday. Which best represents how the price of a gallon of gasoline changed on Thursday?

-0.02

Sun estimated the quotient of -23.514 and -3.98 by rounding each to the nearest integer. Which equation shows the correct estimation? -23.514 divided by -3.98

-24 divided by -4 = 6

Julio predicted that the average high temperature for January would be . The actual average high temperature was 4 degrees higher than Julio's prediction. Which describes the actual average high temperature for January?

-3 C

Which equation best represents this statement? Negative five-sixths times the sum of a number and six and two tenths is seven and five-tenths.

-5(x + 6.2) = 7.5 6

What is the simplest form of the expression (-11.7y - 3.3x) + 1.2x + (5.2y + x)?

-6.5y - 1.1x

A student has $78 in his checking account. If the student spends $12 on lunch, which number could be combined with the amount left in the account to make zero?

-66

What is the value of x in the equation 3/5x = -45?

-75

Which expression is equivalent to 10k + 17 - 7j - 18 - 11k?

-7j - k - 1

Juan and Ari went to the farmers market to buy fruit. Juan's bag of apples that he bought weighed 31/7 pounds. Ari's bag of oranges that he bought weighed 19/3 pounds. Using compatible fractions, estimate how much heavier Ari's bag is compared to Juan's bag.

1 1 pounds 2

A customer buys a CD for $15 and a video game. The customer pays a total of $42.80 for the two items, which includes 7% sales tax. Which equation can be used to find x, the cost of the video game before tax?

1.07(15 + x) = 42.80

This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of proportionality?

1/15

Matthew plots an integer on a number line that has an absolute value of 119. Gabrielle plots a different integer on the same number line that also has an absolute value of 119. Which two integers could Matthew and Gabrielle have plotted?

119 and -119

Chris is standing on a cliff that is 3 feet above sea level. He dives into the water and descends to a depth 10 feet below the surface of the sea. On a number line, what is the distance between the two elevations?

13

Yuuma applied the steps below to find the product of (-10.2)(-16.4). Step 1: (-10.2)(-16.4) = (-16.4)(-10.2) Step 2: = (-16.4)(-10) + (-16.4)(-0.2) Step 3: = ____________ Step 4: = 167.28 Which expression correctly fills in the blank in Step 3?

164 + 3.28

The sum of three numbers is 180. If the first number is (2x - 11) , and the second is (x - 4) which expression represents the third number?

195 - 3x

Selina and three of her classmates each wrote out the steps for finding an approximate percent change. They all agreed on the first and fourth step:1. Find the positive difference between the original number and the new number.2. ________________________3. ________________________4. Round the answer if necessary.They did not agree on steps 2 and 3. Which instructions are correct for steps 2 and 3?

2. Divide the difference by the original number. 3. Multiply the quotient by 100 to change it from a decimal to a percent.

Kedwin has $150.00 and wants to buy a new pair of headphones that cost $175.00 plus 10% shipping. He decides to wait until the headphones go on sale. What is the smallest sale rate that he needs to be able to afford them?

25%

Tram left a tip of $9, which was 3/23 of the total cost of the food. Which shows the correct equation and value of x, the total cost of the food?

3/20x = 9; x = $60

For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day?

30 minutes

At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equations represents p, the number of seashells that Pierre collected.

3p + p = 52

Diego cut 7 smaller boards of equal length from a board that is 9 1/3 feet long. How long is each of the 7 smaller boards?

4/3

Kyoko is reading a book by her favorite author. She read the first 20 pages in 1/2 of an hour. Reading at the same pace, Kyoko wants to determine if she'll have enough time to finish the book before she has to go to bed.Reading TimeAccording to the graph, which statement must be true?

It will take her 3 hours to read 120 pages.

Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 5/8 inches thick. What was her error? 7(2 5/8) 7 (2 + 5/8) 14 + 5/8 14 5/8

Seven was not multiplied by 5/8

Allison is evaluating the expression -5 - (-2) using integer tiles. She begins with 5 negative tiles as shown. What should Allison do next to find the value of the expression?

remove 2 negative tiles

Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions and gives his assistant y dollars, which equation correctly models this situation?

y = 0.20x

A car travels 18 miles per gallon of gas used. Which equation best represents the proportional relationship between the y miles that the car has traveled and the x gallons of gasoline that it has used?

y = 18x