Middle School Math Quiz: Proportional Vs Non Proportional
5 questions · exam conditions
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Proportional Vs Non ProportionalQuestion 1 of 5

A phone plan charges a monthly fee plus an additional cost per gigabyte of data used. The total monthly cost CC (in dollars) for using dd gigabytes can be modeled by C=25+5dC = 25 + 5d. A competing plan offers a total cost that varies directly with data usage, charging 8d8d dollars for dd gigabytes with no monthly fee. For what range of data usage would a student be correct in choosing the proportional model over the non-proportional model to minimize cost?

When data usage is less than approximately 3.1 gigabytes per month
When data usage is greater than approximately 8.3 gigabytes per month
When data usage is less than approximately 8.3 gigabytes per month
When data usage is greater than approximately 3.1 gigabytes per month
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Middle School Math Quiz

Middle School Math Quiz: Proportional Vs Non Proportional

Practice Proportional Vs Non Proportional in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Proportional Vs Non Proportional, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A phone plan charges a monthly fee plus an additional cost per gigabyte of data used. The total monthly cost CC (in dollars) for using dd gigabytes can be modeled by C=25+5dC = 25 + 5d. A competing plan offers a total cost that varies directly with data usage, charging 8d8d dollars for dd gigabytes with no monthly fee. For what range of data usage would a student be correct in choosing the proportional model over the non-proportional model to minimize cost?

  1. When data usage is less than approximately 3.1 gigabytes per month
  2. When data usage is greater than approximately 8.3 gigabytes per month
  3. When data usage is less than approximately 8.3 gigabytes per month (correct answer)
  4. When data usage is greater than approximately 3.1 gigabytes per month
Explanation: The proportional model costs 8d8d dollars, while the non-proportional model costs 25+5d25 + 5d dollars. To find when the proportional model is cheaper, solve 8d<25+5d8d < 25 + 5d. Subtracting 5d5d from both sides gives 3d<253d < 25, so d<8.33...d < 8.33... gigabytes. The proportional model is cheaper when usage is less than approximately 8.3 gigabytes. Choice A uses an incorrect calculation. Choice B reverses the inequality direction. Choice D also reverses the inequality and uses the wrong breakeven point.

Question 2

A recipe calls for ingredients in the following amounts: 2 cups flour, 1 cup sugar, and 12\frac{1}{2} cup butter. Maria wants to determine if the relationship between the number of batches made and the total amount of flour needed is proportional. She also considers whether the relationship between cups of flour and cups of sugar within the recipe is proportional. Which analysis is correct?

  1. Both relationships are proportional since they involve constant ratios between quantities (correct answer)
  2. Neither relationship is proportional because recipes involve discrete quantities, not continuous functions
  3. The batches-to-flour relationship is proportional, but flour-to-sugar is not because different ingredients are involved
  4. The flour-to-sugar relationship is proportional, but the batches-to-flour relationship requires additional context to determine
Explanation: Both relationships are proportional. The number of batches to flour follows the pattern: 1 batch = 2 cups flour, 2 batches = 4 cups flour, etc., giving a constant ratio and passing through (0,0). The flour-to-sugar relationship also maintains a constant ratio of 2:1 and would pass through (0,0) when graphed. Choice B incorrectly suggests that discrete quantities cannot form proportional relationships. Choice C wrongly assumes different ingredients cannot be proportionally related. Choice D incorrectly suggests the batches-to-flour relationship needs more context when it clearly follows proportional patterns.

Question 3

Two swimming pools are being filled with water. Pool A starts empty and fills at 50 gallons per minute. Pool B already contains 200 gallons and fills at 30 gallons per minute. A student must choose between modeling Pool A's water amount as a proportional relationship and Pool B's as a non-proportional relationship, or vice versa. After 10 minutes of filling, what should guide the student's choice of which model to use for which pool?

  1. Both pools should use the same model type since they both fill at constant rates
  2. Pool B should use the proportional model because it has a slower rate of change
  3. Pool A should use the non-proportional model because its rate of filling is faster
  4. Pool A should use the proportional model because it starts at zero and increases at a constant rate (correct answer)
Explanation: When you encounter problems about relationships between variables, the key distinction is whether the relationship is proportional or non-proportional. A proportional relationship must pass through the origin (0,0) and have a constant rate of change, meaning you can write it as y=kxy = kx where k is the constant rate. Let's examine each pool. Pool A starts with 0 gallons and fills at 50 gallons per minute, so after t minutes it contains 50t50t gallons. This passes through (0,0) and has the form y=kxy = kx, making it proportional. Pool B starts with 200 gallons and fills at 30 gallons per minute, so after t minutes it contains 200+30t200 + 30t gallons. Because of the initial 200 gallons (the y-intercept), this relationship doesn't pass through the origin and has the form y=mx+by = mx + b, making it non-proportional. Choice A is incorrect because having constant rates doesn't automatically make relationships proportional—the starting point matters. Choice B misses the point entirely; the rate of change doesn't determine proportionality, and Pool B should actually use the non-proportional model. Choice C incorrectly suggests that a faster rate makes a relationship non-proportional, when it's actually the zero starting point that makes Pool A proportional. Choice D correctly identifies that Pool A should use the proportional model because it starts at zero and increases at a constant rate. Remember: proportional relationships must start at the origin. If there's an initial amount or y-intercept other than zero, the relationship is non-proportional, regardless of whether the rate of change is constant.

Question 4

A science experiment measures the relationship between the mass of a substance (in grams) and its volume (in cubic centimeters). The data shows: 10g corresponds to 4 cm³, 20g corresponds to 8 cm³, and 30g corresponds to 12 cm³. A student claims this relationship is proportional and can be used to find the density. However, when the experiment is repeated with a different starting temperature, the same masses correspond to volumes of 6 cm³, 10 cm³, and 14 cm³ respectively. What should guide the choice between proportional and non-proportional models?

  1. Use the proportional model since both datasets show constant ratios between consecutive measurements
  2. Use the non-proportional model since the second dataset doesn't pass through the origin when extended (correct answer)
  3. Use the proportional model for the first dataset only since it has the lower y-intercept value
  4. Use the non-proportional model since temperature changes indicate the relationship has additional variables
Explanation: The first dataset (10g→4cm³, 20g→8cm³, 30g→12cm³) is proportional because extending the pattern backward gives 0g→0cm³. The second dataset (10g→6cm³, 20g→8cm³, 30g→12cm³) is non-proportional because extending backward gives 0g→2cm³, indicating a y-intercept of 2. This suggests thermal expansion affects the base volume. Choice A incorrectly focuses on consecutive ratios rather than proportionality through the origin. Choice C misunderstands that y-intercept magnitude doesn't determine model choice - only whether it's zero or non-zero matters. Choice D incorrectly suggests additional variables automatically make relationships non-proportional.

Question 5

A student observes that when she increases her study time, her test scores improve. She records the following data: 2 hours of study yields a score of 75, 4 hours yields 85, and 6 hours yields 95. She concludes this represents a proportional relationship and predicts that 0 hours of study would yield a score of 0. What error has the student made in her reasoning?

  1. She failed to recognize that test scores have a practical minimum baseline regardless of study time (correct answer)
  2. She incorrectly calculated the rate of change between study time and test score improvement
  3. She assumed correlation implies causation when study time may not directly cause score changes
  4. She used too few data points to establish whether the relationship is truly proportional
Explanation: The student's error is assuming that zero study time would result in zero points, when in reality, students typically have some baseline knowledge that would yield a non-zero score even without studying. This baseline makes the relationship non-proportional because it doesn't pass through the origin. The relationship is linear (10-point increase per 2 hours), but the y-intercept would be around 55 points, not 0. Choice B is incorrect because the rate calculation appears correct. Choice C addresses a different issue about causation vs. correlation. Choice D is wrong because even with few points, the proportional assumption can be evaluated based on the origin requirement.