Integers
In which of these situations would the answer to the question be 0?
A) Teddy jumped into a pool from a diving board 8 feet above the water. He sank 8 feet and then swam straight up to the surface of the water. How many feet did Teddy swim?
B) Jerry left his house and walked 1.5 miles directly west. Then he walked 1.5 miles directly east. At this point, how many miles was Jerry from his house?
C) A trail begins at an elevation of -50 feet. The trail ends at an elevation of 50 feet. By how many feet does the elevation of the trail change from beginning to end?
D) The low temperature one day was -3 degrees Celsius. The high temperature that day was 3 degrees Celsius. What is the difference between the low temperature and the high temperature that day?
B
Which expressions are equivalent to 3.25 - (-5/8)? Select all that apply.
A) 3.25 - (5/8)
B) 3.25 + (5/8)
C) 3.25 + (-5/8)
D) 3.25 + (+5/8)
E) -3.25 + (-5/8)
F) -3.25 + (+5/8)
B, D
What does the graph of a proportional relationship look like?
It is a straight line that touches the origin (0, 0).
At the start of the month, the value of an investment was $48.45. By the end of the month, the value of the investment changed by a loss of $13.80. What was the value, in dollars, of the investment at the end of the month?
$34.65
In which situation could the quotient of -24 / 3 be used to answer the question?
A) The temperature of a substance decreased by 24°C per minute for 3 minutes. What was the overall change of the temperature of the substance?
B) A football team lost 24 yards on one play, then gained 3 yards on the next play. How many total yards did the team gain on the two plays?
C) Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day?
D) A cookie jar contains 24 cookies. Each child receives 3 cookies. How many children are there?
C
Which expression is equivalent to 1/4(8 - 6x + 12)?
A) 7/2x
B) -13/2x
C) -6x + 14
D) -3/2x + 5
D
Which equation has a constant of proportionality equal to 4?
A) 4y = 4x
B) 4y = 12x
C) 3y = 4x
D) 3y = 12x
D
Jessica rented 1 video game and 3 movies for a total of $11.50. The video game cost $4.75 to rent. The movies cost the same amount each to rent. What amount, in dollars, did Jessica pay to rent each movie?
$2.25
A store owner paid $15 for a book. She marked up the price of the book by 40% to determine its selling price. What is the selling price, in dollars, of the book?
$21
Which expressions have products that are positive? Select all that apply.
A) (-5)(0.2)(-9)
B) (2/3)(3/2)(-1/2)
C) (6)(-3)(8)(-7)
D) (-4.3)(-1/4)(-5.5)(-7/9)
E) (5/6)(-10)(3.75)(2)
F) (-1.2)(-3.5)(2.7)(-0.8)
A, C, D
A garden is 15 feet long by 5 feet wide. The length and width of the garden will each be increased by the same number of feet. This expression represents the perimeter of the larger garden:
(x + 15) + (x + 5) + (x + 15) + (x + 5)
Which expression is equivalent to the expression for the perimeter of the larger garden? Select all that apply.
A) 4x + 40
B) 2(2x + 20)
C) 2(x + 15)(x + 5)
D) 4(x + 15)(x + 5)
E) 2(x + 15) + 2(x + 5)
A, B, E
Hayden mixed 6 cups of blue paint with 8 cups of yellow paint to make green paint. To represent the relationship between the number of cups of blue paint, b, and the number of cups of yellow paint, y, needed to make the same shade of green paint, Hayden wrote the equation b = ___y. What number should be placed in the blank?
0.75
Two equations are shown.
• Equation 1: -0.5x - 4 = 1.5
• Equation 2: -0.5(x - 4) = 1.5
Select each statement that must be true.
A) x represents a negative value in both equations.
B) x represents a positive value in both equations.
C) x represents a positive value in one equation and a negative value in the other equation.
D) The value x represents in Equation 1 is less than the value x represents in Equation 2.
E) The value x represents in Equation 1 is greater than the value x represents in Equation 2.
C, D
Sal exercised by stretching and jogging 5 days last week.
• He stretched for a total of 25 minutes during the week.
• He jogged for an equal number of minutes each of the 5 days.
• He exercised for a total of 240 minutes.
Determine the number of minutes Sal jogged each day last week. Show your work or explanation.
5x + 25 = 240
5x = 215
x = 43
Sal jogged for 43 minutes each day.
Elena exercised by stretching and jogging 5 days last week.
• She stretched for 15 minutes each day.
• She jogged for an equal number of minutes each of the 5 days.
• She exercised for a total of 300 minutes.
Determine the number of minutes Elena jogged each day last week. Show your work or explanation.
5(x + 15) = 300
x + 15 = 60
x = 45
Elena jogged for 45 minutes each day.
A customer buys a book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book. What is the total amount, in dollars, the customer pays for the discounted book?
$30.21