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Create a 100 question multiple choice assessment with explanations and an answer key at the end.
Of course. Here is a 100-question multiple-choice assessment based on the instructional unit, complete with a detailed answer key and explanations.
Proportional Relationships Unit Assessment
Instructions: Choose the best answer for each of the following questions.
Part 1: Identifying Proportional Relationships
Which of the following tables shows a proportional relationship between x and y? A)
B)
C)
D)
For a graph to represent a proportional relationship, it must be a straight line that... A) passes through the y-axis. B) is horizontal. C) passes through the origin (0,0). D) has a positive slope.
A movie streaming service charges a $10 monthly fee plus $3 per movie rented. Is the relationship between the total monthly cost and the number of movies rented proportional? A) Yes, because the price per movie is constant. B) No, because the $10 monthly fee means the ratio of cost to movies is not constant. C) Yes, because the more movies you rent, the more you pay. D) No, because you can't rent a negative number of movies.
Which scenario describes a proportional relationship? A) A savings account is opened with $50, and $10 is added each week. B) A tree grows 3 inches every year. C) A taxi ride costs $2.50 plus $1.50 per mile. D) The temperature drops by 2 degrees every hour from an initial temperature of 50 degrees.
Examine the table below. Does it represent a proportional relationship?
A) Yes, the ratio y/x is always 0.4.
B) No, because x is greater than y.
C) Yes, the ratio y/x is always 2.5.
D) No, the ratio y/x is not constant.
Which graph represents a proportional relationship? A) A straight line that intersects the y-axis at (0, 4). B) A U-shaped curve that contains the point (0,0). C) A vertical line at x = 2. D) A straight line passing through (0,0) and (5, 10).
A recipe states that for every 4 cups of flour, you need 2 cups of sugar. Is the relationship between the amount of flour and the amount of sugar proportional? A) No, because the numbers are different. B) Yes, because the ratio of flour to sugar is constant (4:2 or 2:1). C) No, because you can't use half a cup. D) It is impossible to tell without more information.
Which set of points lies on the graph of a proportional relationship? A) (1, 3), (2, 4), (3, 5) B) (0, 1), (1, 2), (2, 3) C) (2, 5), (4, 10), (6, 15) D) (1, 1), (2, 4), (3, 9)
The cost to print photos is $0.25 per photo. Is the relationship between the total cost and the number of photos proportional? A) Yes, because the cost per photo is constant. B) No, because the total cost changes depending on the number of photos. C) Yes, but only if you print more than 10 photos. D) No, because there might be a service fee.
A map scale indicates that 1 inch represents 50 miles. Is the relationship between the map distance and the actual distance proportional? A) No, because the distances are very large. B) Yes, because the ratio of actual distance to map distance is constant. C) No, because a map is a flat object. D) Yes, but only for distances under 1,000 miles.
Which statement about the graph of a proportional relationship is FALSE? A) The graph is a straight line. B) The graph must pass through the origin. C) The graph can be a horizontal line where y > 0. D) The graph represents a constant rate of change.
A cell phone plan costs $40 per month for unlimited talk and text, but data costs an extra $5 per gigabyte. Is the total monthly cost proportional to the gigabytes of data used? A) Yes, because the cost per gigabyte is constant. B) No, because the base $40 fee makes the relationship non-proportional. C) Yes, because the cost increases with data usage. D) No, because the plan includes unlimited talk and text.
Which of the following is an example of a non-proportional relationship? A) The number of wheels on a group of bicycles. B) The cost of buying gasoline at $3.50 per gallon. C) The total distance a car travels at a constant 60 mph. D) The age of a person in relation to their height.
A table shows that 2 items cost $10, 4 items cost $20, and 6 items cost $30. Is this relationship proportional? A) No, because the cost is increasing. B) Yes, because the ratio of cost to items is always 5. C) No, because the table doesn't show the cost of 1 item. D) Yes, because the numbers are all even.
A graph passes through the points (1, 4), (2, 6), and (3, 8). Does this graph represent a proportional relationship? A) Yes, because the points form a pattern. B) No, because it is a straight line that does not pass through the origin. C) Yes, because the y-values are increasing. D) No, because the x-values are consecutive.
A machine produces 50 widgets every hour. Is the relationship between the number of widgets produced and the time in hours proportional? A) Yes, because the production rate is constant. B) No, because the machine might break down. C) No, because the total number of widgets is always changing. D) Yes, because 50 is a round number.
Which equation does NOT represent a proportional relationship? A) y = 10x B) y = x C) y = 0.5x D) y = 3x + 2
A plumber charges a $50 service fee plus $75 per hour of work. Is the total charge proportional to the number of hours worked? A) Yes, because the hourly rate is constant. B) No, because the service fee makes the ratio of total charge to hours not constant. C) Yes, because the total charge increases with more hours of work. D) No, because plumbing work is expensive.
Look at the table below. Is the relationship between x and y proportional?
A) No, because the numbers are not multiples of 2.
B) Yes, because the ratio y/x is always 3.
C) No, the ratio y/x is not constant.
D) Yes, because y is always greater than x.
The area of a square is given by the formula A = s², where s is the side length. Is the relationship between the side length and the area proportional? A) Yes, because as the side length increases, the area increases. B) No, because the relationship is not linear (the ratio A/s is not constant). C) Yes, because a square has four equal sides. D) No, because area is measured in square units.
A restaurant offers a buffet for $15 per person. Is the total cost for a group proportional to the number of people? A) Yes, the ratio of cost to people is constant. B) No, because the total cost changes. C) No, because drinks might cost extra. D) Yes, but only for groups smaller than 10 people.
Which of the following must be true for the ratio y/x in a proportional relationship? A) It must be a whole number. B) It must be greater than 1. C) It must be constant for all (x, y) pairs, where x ≠ 0. D) It must be equal to the x-value.
The circumference of a circle is given by C = 2πr. Is the relationship between the radius (r) and the circumference (C) proportional? A) No, because π is an irrational number. B) Yes, because the ratio C/r is always constant (2π). C) No, because the formula involves multiplication. D) Yes, because all circles are the same shape.
A student is paid $20 for mowing a lawn, regardless of how long it takes. Is the relationship between the hours worked and the payment proportional? A) Yes, because the payment is fixed. B) No, because the ratio of payment to hours will change depending on the time taken. C) Yes, because the student is earning money. D) No, because $20 is not enough money.
A graph of a relationship is a straight line passing through (3, 6) and (5, 10). For this to be a proportional relationship, it must also pass through which point? A) (1, 3) B) (0, 1) C) (0, 0) D) (2, 5)
Part 2: The Constant of Proportionality (Unit Rate)
In the equation y = 1.5x, what is the constant of proportionality? A) y B) x C) 1.5 D) 1
A train travels 240 miles in 4 hours. What is the constant of proportionality (in miles per hour)? A) 4 B) 240 C) 60 D) 1/60
The table shows the cost of apples. What is the constant of proportionality (cost per pound)?
A) $3.00
B) $2.00
C) $1.50
D) $0.67
A graph of a proportional relationship passes through the point (1, 9). What is the constant of proportionality? A) 1 B) 9 C) 1/9 D) The point itself
If y is proportional to x, and y = 45 when x = 5, what is the constant of proportionality, k? A) 45 B) 5 C) 9 D) 1/9
A factory produces 150 cars in 30 days. What is the unit rate in cars per day? A) 150 cars per day B) 30 cars per day C) 5 cars per day D) 1/5 cars per day
The equation d = 55t represents the distance (d) a car travels in time (t). What is the constant of proportionality? A) d B) t C) 55 D) 1
On a graph of a proportional relationship, the constant of proportionality is equal to the... A) x-intercept. B) y-intercept. C) slope of the line. D) length of the line.
A baker uses 12 cups of flour to make 4 batches of cookies. What is the unit rate in cups per batch? A) 12 cups per batch B) 4 cups per batch C) 3 cups per batch D) 1/3 cups per batch
In the relationship shown in the table, what is the constant of proportionality, k?
A) 2.5
B) 0.4
C) 6
D) 10
A cyclist travels 45 kilometers in 3 hours. What is her speed in kilometers per hour? A) 45 km/h B) 3 km/h C) 15 km/h D) 1/15 km/h
The total cost C is proportional to the number of tickets n. If 6 tickets cost $72, what is the constant of proportionality? A) 6 B) 72 C) 12 D) 1/12
A graph of a proportional relationship passes through the point (12, 3). What is the constant of proportionality (k = y/x)? A) 12 B) 3 C) 4 D) 0.25
If 5 US dollars can be exchanged for 600 Japanese Yen, what is the constant of proportionality in Yen per dollar? A) 5 B) 600 C) 120 D) 1/120
The equation W = 12.5h relates wages earned (W) to hours worked (h). What does the constant of proportionality, 12.5, represent? A) The total wages earned. B) The total hours worked. C) The hourly pay rate. D) The number of jobs.
A map scale is 1 inch : 25 miles. What is the constant of proportionality in miles per inch? A) 1 B) 25 C) 0.04 D) 26
If y = kx and y = 35 when x = 7, what is the value of k? A) 35 B) 7 C) 5 D) 1/5
A water pump moves 42 gallons of water in 6 minutes. What is the pump's unit rate? A) 42 gallons/min B) 6 gallons/min C) 7 gallons/min D) 252 gallons/min
The point (4, 24) is on the graph of a proportional relationship. What is the constant of proportionality? A) 4 B) 24 C) 6 D) 1/6
A 16-ounce box of cereal costs $4.00. What is the unit price per ounce? A) $0.16 per ounce B) $0.25 per ounce C) $4.00 per ounce D) $0.50 per ounce
In the equation y = (2/5)x, what is the constant of proportionality? A) 2 B) 5 C) 2/5 D) x
A computer downloads a 120-megabyte file in 40 seconds. What is the download speed in megabytes per second? A) 120 MB/s B) 40 MB/s C) 3 MB/s D) 1/3 MB/s
The table shows a proportional relationship. What is the constant of proportionality?
A) 1.67
B) 0.6
C) 4
D) 10
A plant grows 3/4 of an inch in 1/2 of a week. What is the growth rate in inches per week? A) 3/8 inches per week B) 1.5 inches per week C) 2 inches per week D) 3/4 inches per week
The constant ratio between two variables in a proportional relationship is called the... A) origin. B) variable. C) constant of proportionality. D) coordinate.
Part 3: Writing and Using Equations
A person types at a constant rate of 50 words per minute. Which equation represents the number of words w typed in m minutes? A) w = 50 + m B) m = 50w C) w = 50m D) w = m/50
The cost of gasoline is $3.25 per gallon. Which equation finds the total cost, C, for g gallons of gas? A) g = 3.25C B) C = 3.25g C) C = g + 3.25 D) C = g/3.25
A proportional relationship is represented by the equation y = 6x. If x = 8, what is the value of y? A) 14 B) 1.33 C) 48 D) 68
The table shows a proportional relationship. Which equation represents this relationship?
A) y = x + 10
B) y = 6x
C) x = 6y
D) y = x/6
The equation for a proportional relationship is y = 8x. If y = 96, what is the value of x? A) 96 B) 8 C) 12 D) 768
A factory produces 15 items per hour. Which equation shows the relationship between the number of items produced, p, and the time in hours, h? A) h = 15p B) p = h + 15 C) p = 15h D) p = h/15
A graph of a proportional relationship passes through the point (8, 2). Which equation represents this relationship? A) y = 4x B) y = 8x + 2 C) y = 0.25x D) x = 2y
Using the equation y = 3.2x, what is the value of y when x = 5? A) 8.2 B) 1.56 C) 16 D) 32
A recipe requires 0.5 cups of sugar for every cup of flour. Which equation relates the amount of sugar, s, to the amount of flour, f? A) s = 0.5f B) f = 0.5s C) s = f + 0.5 D) s = f - 0.5
The constant of proportionality in a relationship is 11. Which equation represents this relationship? A) y = x + 11 B) y = 11x C) y = x/11 D) x = 11y
The weight of an object in pounds (p) is proportional to its weight in kilograms (k). The relationship is p = 2.2k. A rock weighs 50 kilograms. What is its weight in pounds? A) 22.7 lbs B) 52.2 lbs C) 110 lbs D) 50 lbs
The equation y = 9x represents a proportional relationship. If the y-value is 108, what is the corresponding x-value? A) 9 B) 108 C) 12 D) 972
A streaming service costs $12 per month. Which equation represents the total cost, C, for m months of service? A) C = 12m B) m = 12C C) C = m + 12 D) C = 12/m
The table below shows the distance a snail travels over time. Which equation represents the relationship?
A) y = 5x
B) y = x + 8
C) x = 5y
D) y = 10x
Using the equation C = 4.5n, find the cost of 10 items. A) $14.50 B) $45.00 C) $4.50 D) $0.45
A cyclist travels at a constant speed. She goes 50 miles in 2.5 hours. Write an equation to represent the distance, d, she travels in t hours. A) d = 50t B) d = 2.5t C) d = 20t D) t = 20d
The constant of proportionality is 0.8. If x = 20, what is y? A) 16 B) 25 C) 20.8 D) 0.8
A graph of a proportional relationship contains the point (15, 5). What is the equation for this relationship? A) y = 3x B) y = 15x + 5 C) y = (1/3)x D) y = 5x
The amount of tip is proportional to a restaurant bill. If a $50 bill has a $9 tip, which equation calculates the tip, t, on a bill of price p? A) t = 0.18p B) p = 0.18t C) t = p - 41 D) t = 9p
Using the equation y = (5/2)x, what is the value of y when x = 8? A) 20 B) 3.2 C) 40 D) 10
Part 4: Interpreting Graphs and Points
On the graph of a proportional relationship showing cost vs. items, what does the point (0,0) represent? A) The maximum cost. B) The price of one item. C) That zero items cost zero dollars. D) That the items are free.
A graph shows the relationship between gallons of water used and time in minutes. If the point (1, 5) is on the graph, what does it mean? A) 1 gallon of water is used in 5 minutes. B) 5 gallons of water are used in 1 minute. C) A total of 6 gallons were used. D) The process takes 5 minutes.
A graph shows the distance traveled versus time. What does the point (1, k) on the graph represent, where k is the y-value? A) The total length of the trip. B) The time it takes to travel one mile. C) The speed (the unit rate). D) The starting point of the trip.
The graph of a proportional relationship shows the number of pages read over time. If the point (4, 120) is on the graph, what does this mean? A) The reader read 4 pages in 120 minutes. B) The reader read 120 pages in 4 minutes. C) The reader's speed is 4 pages per minute. D) The reader read 120 pages in 4 hours.
On a graph showing the earnings for hours worked, the point (5, 75) is plotted. What does the x-coordinate, 5, represent? A) The total earnings ($75). B) The number of hours worked (5 hours). C) The hourly wage ($15). D) The number of jobs completed.
Two proportional graphs are plotted on the same axes. Graph A is steeper than Graph B. What does this mean? A) Graph A has a smaller constant of proportionality. B) Graph A represents a faster rate or higher price. C) Graph B has a larger constant of proportionality. D) Graph B represents a faster rate or higher price.
A graph represents the cost of bulk nuts by weight. The line passes through (3, 18). What does the constant of proportionality represent in this context? A) The total weight of nuts purchased. B) The total cost of the nuts. C) The price per pound. D) The number of different types of nuts.
Any point (x, y) on the graph of a proportional relationship, other than the origin, has a ratio y/x that is... A) always changing. B) equal to the constant of proportionality. C) equal to the x-coordinate. D) equal to 1.
A graph shows the relationship between the number of cookies baked and the amount of flour used. The point (5, 10) is on the graph. What is the meaning of this point? A) 5 cups of flour make 10 cookies. B) 10 cups of flour make 5 cookies. C) The recipe requires 5 cups of flour. D) The recipe makes 10 cookies.
On a graph of distance vs. time, what does the point (1, 55) signify? A) It takes 55 hours to travel 1 mile. B) A distance of 55 miles is traveled in 1 hour. C) The total trip is 55 miles long. D) The graph starts at 55 on the y-axis.
A graph shows the conversion between Pounds (£) and US Dollars ($). The point (10, 12.5) is on the line, with Pounds on the x-axis. What does this mean? A) £10 is worth $12.50. B) $10 is worth £12.50. C) The exchange rate is £10 per dollar. D) The exchange rate is $12.50 per pound.
Why is the point (1, k) on the graph of a proportional relationship y = kx considered a key point? A) It is always the end of the line. B) It directly shows the unit rate, as its y-coordinate is the constant of proportionality. C) It is the only point with whole numbers. D) It shows the starting value of the relationship.
A graph shows the cost of renting a machine over time. The line is not very steep. This means... A) the rental cost per hour is high. B) the machine is very large. C) the rental cost per hour is low. D) the machine is old.
If a graph shows the relationship between the number of songs downloaded (x) and the total cost (y), what does the point (0,0) imply? A) The first song is free. B) There is a monthly subscription fee. C) Downloading zero songs costs zero dollars. D) The music service is having a sale.
A graph shows the amount of water in a tank as it drains over time. The point (3, 90) is on the graph, with time in minutes on the x-axis and gallons drained on the y-axis. What is the unit rate? A) 90 gallons are drained per minute. B) 30 gallons are drained per minute. C) 3 gallons are drained per minute. D) It takes 90 minutes to drain the tank.
Part 5: Application and Word Problems
A recipe for 3 dozen cookies requires 4 cups of flour. How many cups of flour are needed to make 9 dozen cookies? A) 6 cups B) 9 cups C) 12 cups D) 36 cups
A 12-ounce bottle of shampoo costs $3.60. A 20-ounce bottle of the same shampoo costs $5.00. Which is the better buy? A) The 12-ounce bottle B) The 20-ounce bottle C) They cost the same per ounce. D) Cannot be determined.
A train travels 195 miles in 3 hours. At this constant rate, how far will it travel in 5 hours? A) 65 miles B) 325 miles C) 390 miles D) 975 miles
If 5 pounds of potatoes cost $4.00, how much will 8 pounds of potatoes cost? A) $5.00 B) $6.40 C) $10.00 D) $32.00
A model car is built with a scale of 1 inch : 3 feet. If the actual car is 12 feet long, how long is the model? A) 3 inches B) 4 inches C) 12 inches D) 36 inches
It takes a printer 4 minutes to print 180 pages. How many pages can it print in 10 minutes? A) 45 pages B) 1800 pages C) 450 pages D) 720 pages
A soccer player scores 6 goals in 8 games. At this rate, how many goals can be expected in a 28-game season? A) 21 goals B) 24 goals C) 32 goals D) 37 goals
For every 5 tickets sold, a fundraiser earns $12. If the fundraiser earned $180, how many tickets were sold? A) 15 tickets B) 43 tickets C) 75 tickets D) 180 tickets
A landscaper can mow 4 lawns in 6 hours. How long will it take to mow 10 lawns? A) 15 hours B) 24 hours C) 10 hours D) 60 hours
The ratio of students to teachers at a school is 22:1. If there are 660 students, how many teachers are there? A) 22 B) 30 C) 1 D) 660
A car's gas tank holds 15 gallons and can travel 450 miles on a full tank. How far can the car travel on 6 gallons of gas? A) 30 miles B) 180 miles C) 200 miles D) 450 miles
A 3-pound bag of oranges costs $4.50. How many pounds of oranges can you buy for $12.00? A) 1.5 pounds B) 6 pounds C) 8 pounds D) 12 pounds
A map has a scale of 1 cm = 20 km. The distance between two towns is 150 km. How far apart are they on the map? A) 7.5 cm B) 15 cm C) 20 cm D) 150 cm
A phone battery uses 15% of its charge in 30 minutes of gaming. If it continues at this rate, how long will it take to use 100% of the charge? A) 150 minutes B) 200 minutes C) 300 minutes D) 450 minutes
A quality control check finds 2 defective items for every 1,000 produced. If the factory produces 25,000 items, how many are likely to be defective? A) 25 B) 50 C) 100 D) 200
Answer Key
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