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8th Grade Math (all summer school answers)
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The table below shows the distance a car travels and the amount of gasoline left in the tank of the car. [insert table] How many gallons of gasoline does the car have left after it has traveled 330 miles?
B. 4
Hector hires a caterer who charges $12 per person plus a set up fee of $75. He uses the equation 12p + 75 = c to determine the total cost, c, where p is the number of persons. Hector wants to set up a table like the one below to help determine costs. [insert table] Which heading should Hector use in in column B to create the table?
C. Total Cost
Healthy Gym charges members a fee for each visit, while Fitness Gym charges members a one-time yearly charge plus a fee for each visit. The equations below represents the amounts members pay at each gym, where t represents the total yearly cost and n represents the number of visits.
Healthy Gym : 6n = t
Fitness Gym : 50 + 5n = t
Which statement about the total yearly cost of the memberships is true?
A. The total yearly cost is $300 at each gym for 50 visits
A school library charges a fine of 5 cents on the first day a book was overdue, then doubles the amount owed each day until payment is made. Jada and Juan each had a book that was overdue. Jada paid a fine that was $2.40 more than Juan's fine. Which statement about the overdue books is true?
NOT D. Jada's book was overdue by 48 more days than Juan's book.
An internet store charges a base fee plus $1.50 per pound to ship items. The table below shows samples of their shipping rates. [insert table] Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. How much more does Keisha pay for shipping than Derek?
NOT C. 9.50
Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours. [insert table] Which value completes the table to show the amount Carey earns for working 3 hours?
$29.25
The equation r = 3c + 5 represents the values shown in the table below. [insert table] What is the missing value in the table?
C. 41
Malik borrowed $105 from his brother and his plans to repay $12 per week. He creates a table to help him determine the number of weeks it will take to repay his brother. How many weeks will it take Malik to repay his brother?
B. 9
Which table can be created using the equation below?
-2 + 4x = y
A. [insert table]
Carlotta handpaints T-Shirts and sells them to her friends. She uses the equations below to determine her costs and the money she makes when she sells the shirts.
Production Cost: c = 8 + 3s, where c is the total cost and s is the number of shirts
Amount made: a = 10s, where a is the amount and s is the number of shirts
How many shirts must Carlotta sell to make a profit?
NOT B. 3
NOT C. 4
The equation c = 6.5h represents the cost, c, of renting a bicycle for h hours. The table below can be used to show the information. [insert table] If Franchesca rents a bicycle for 2 hours and Phil rents a bicycle for 6 hours, how much more does Phil pay?
B. 26
Jordan is saving for a new laptop that costs $325. He uses the equation and table below to show the number of months he has been saving, m, and the total amount he has saved so far, d.
d = 80 + 75m [insert table]
Which is the first month in which Jordan will have enough saved money to buy the laptop?
C. Month 4
A company has two warehouses that are 360 miles apart. A truck leaves Warehouse A and heads towards Warehouse B traveling at 45 miles per hour. At the same time, a truck leaves Warehouse B and heads towards Warehouse A traveling at 60 miles per hour. How long will the trucks be driving before they meet each other on the road?
C. Between 3 and 4 hours
Akeem fills the tank of his car with gasoline. He completes the table below to show the distance he travels and the amount of gasoline left in the tank. [insert table] Which problem can Akeem solve when he completes the table?
B. The distance the car can travel on a fill tank of gasoline
A scientist conducting an experiment creates a table to record the growth of two plants. The scientist uses the equation below to represent the growth of the plants, where w is the number of weeks of plant growth and h is the height of the plant in inches.
Plant 1: 1.75 + 1/2w = h
Plant 2: 1.75 + 3/4w = h
Which describes the difference in the heights of the two plants in week 5?
B. Plant 2 is 1.25 inches taller than Plant 1
The admission to a local carnival is 8.50 per person and 1.50 for each rise. How much more will it cost a group of 3 friends to ride 8 rides each than to ride 3 rides each?
NOT A. 7.50
William is in the middle of swimming a ten-mile race. He swims at a steady speed, and then slows down, stops to eat, swims faster to get back in the race, and returns to a steady speed. He later stops for water, and then swims faster to get back in the race. Which graph best represents this situation?
A. [insert graph]
The table represents the cost of flowers at the Tigerlily Flower Shop. [insert table] Which graph is the best interpretation of this table?
A. [insert graph]
A line graph in the coordinate plane that has no breaks in it is
B. A continuous graph
On the way to the mall Miguel rides his skateboard to get to the bus stop. He then waits a few minutes for the bus to come, then rides the bus to the mall. He gets off the bus when it stops at the mall and walks across the parking lot to the closest entrance. Which graph correctly models his travel time and distance?
C. [insert graph]
A graph that has a finite or limited number of data points is
A. A discrete graph
The table below shows the predicted number of words Janae can type, y, in x minutes. [insert table] Which describes the pattern in the table?
B. Janae types 30 words each minute
Micah sketches the graph below to represent a scenario his teacher gave him. [insert graph] Which scenario could Micah's graph represent?
B. Valerie has $2 and then earns $1 per week (where x is the number of weeks) in allowance, for a total of y dollars.
Kelly and Greta are asked to write an equation for the scenario below.
"One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees."
The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation "y = 1/4x," and Greta wrote the equation "y = 4x." Which person is correct, and why?
D. Greta is correct, 4 = 4 x 1 and 20 = 4 x 5
The chart below lists the original and sale prices of items at a clothing store. [insert chart] Which statement best describes why the sale price is a function of the original?
C. For every original price, there is exactly one sale price.
Which equation is a function of x?
NOT B. x = y2 + 9
Which statement describes how to determine if a relation given in a table is a function?
NOT A. If none of the output values are repeated, the relation is a function.
Which graph is a function of x?
NOT C. the sideways "u" one
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? [insert graph; "it's an oval"]
A. The graph is not a function of x because the line x = 0 intersects the graph at two points.
The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter.
h = -16t^2 + 105t + 3
Why is the height of the ball a function of time?
A. Each value of time is associated with exactly one height.
Removing which point from the coordinate plane would make the graph a function of x? [note: NO points can be intersecting. the graph cannot look like a hook.]
B. (-2, 1)
If the relationships below are given in the form of (input, output), which pairing always describes a function?
B. (height of a building in feet, height of the building in inches)
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
NOT B. It is a function because the oven temperature was the same at different times
Reza paid $4,500 as a down payment on a car. She then made equal monthly payments of $200. Reza paid a total of $10,500 for her car. How many months did she make down payments on the car and which function can be used to find the answer?
A. F(x) = 4500 + 250x; 24 months
A function is a relation in which each element in the input is mapped to how many elements in the output?
A. Exactly one
A function is defined by f(x) = 5(2 - x). What is f(-1)?
C. 15
A function is defined by f(x) = x/4. What is f(-8)?
A. -2
Which word best describes the domain of a function?
A. Input
Marisol attempted to determine the slope of a line based on the two points shown in the table below. [insert table]
Step one: (-1, 4) and (3, 10)
Step two: 10 - 3/4 - (-1)
step three: 7/5
Which statement best explains Marisol's error?
C. Marisol computed y2 - x2 / y1 - x1
Xavier is attempting to recreate a problem his teacher showed him in class. To do so, he creates the table below. [insert table]
He remembers that the slope of the line through the ordered pairs in the table was 4. What is the missing y-value in the table?
B. 7
Mia records the distance traveled in x minutes in the table below, while Alexa uses a graph to record her distance traveled over the same time period.
Based on the data on the graph and in the table, which statement gives an accurate comparison?
NOT C. Mia traveled at a faster rate because the slope of the line described by the data in her table in 1/2, which is greater than the slope of alexa's graph.
The ordered pairs in the table below represent a linear function. [table below]
X | Y
2 | 3
5 | 9
What is the slope of the function?
NOT B . 1/2
Michelle and Andrea are walking laps for charity. The amount of money, y, that each girl raises for a certain number of laps, x, is shown in the tables below. [insert tables]
Which statement explains who will raise $100 with the fewest number of laps?
A. Michelle will, because the slope of the line described by the data in her table is the greatest.
Four students drew graphs of a linear function. Which student drew a line with a slope of 3? (analise, benito, charlie, or dariya?)
NOT A. Analise
The graph below displays the wrist circumferences and heights of six students in Alyssa's classroom.
[insert graph]
Is the height of these students a function of their wrist circumference?
NOT C. No because the height of 151 cm is paired with two wrist circumferences
The table below lists some characteristics of the houses on Katrina's street.
[insert graph]
Which relationship describes a function?
NOT C. (sale price, bedrooms)
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation
F = 5/9c + 32
Which statement best describes the relation (c,f) ?
B. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.
Which statement is a correct interpretation of the vertical line test?
D. If any vertical line can intersect the graph at more than one point, the graph does not represent a function.
Asha found that a vertical line intersects the graph of X=|Y| at two points. What can Asha conclude about X=|Y|?
B. It is a relation but not a function of x.
The graph below models the value of a $20,000 car t years after it was purchased.
[insert graph]
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
B. Each time, t, is associated with exactly one car value, y.
Which equation is a function of x?
NOT B. X = Y2 + 9
If the relationships below are given in the form (input, output) which pairing always describes a function?
NOT D. (Distance from home during a trip, time elapsed during the trip.)
A botanist uses the representations below to show the heights in inches, h, of different plants over a period of time, t. [insert table, equation, graph]
If the growth patterns continue, how much taller is the tallest plant than the shortest plant at 120 weeks of growth?
NOT C. 270 inches
NOT A. 180 inches
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
A. S = 3/10m
A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of paint varies directly with the area of each wall. [insert table] How much paint should the painter expect to use to paint a wall with an area of 256 square feet?
A. 16 pints
The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight, w, and the dosage, d?
NOT C. d = 18w
NOT B. d = 3/5w
A person weighs a different amount on other surfaces in space than they do on Earth because the gravitational pull of each surface is different than that of Earth. The table and graph show the weights of objects on Earth, Mars, and the Moon. [insert table, graph]
If a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the moon (based on the table and graph)?
A. The person weighs 56 pounds more on Mars than on the moon
Which explains whether or not the graph represents a direct variation? [insert graph]
A. The graph has a constant variation of 3, so it represents a direct variation
The table below shows the number of color pages a printer prints out over a period of time. [insert table] What is the constant of variation?
NOT D. 3
Corrine wrote temperatures in degrees Celsius and the equivalent temperatures in degrees Fahrenheit. [insert table] Which explains how Corrine could determine if the temperatures very directly?
NOT D. Look for a pattern in the table; if the pattern is consistent, then the temperatures vary directly.
Which statement correctly compares the constants of variation for the graph and the equation below? [insert graph and equation]
NOT A. The graph has a greater constant of variation
The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. [insert table] If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation?
NOT B. Y = 20x
A veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine, and that the number of milligrams varies directly with the weight of the dog, w. The vet uses these steps to find the amount of medicine to give a 10-pound dog. [insert steps here] In which step did the veterinarian make the first error?
NOT B. Step 2
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