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Quiz & test questions Grade 11 Math

Marden Water District Bills: A Rates and Water-Use Quiz

A grade 11 quiz mixing multiple-choice, short-answer, and computation items on a fictional district's per-capita use, affordability, and rate growth.

Objectives

  1. Students will compute per-capita water use and a household's water cost as a percent of income.
  2. Students will distinguish linear from exponential rate increases and project each over time.

Vocabulary

Key words: per-capita use, affordability, linear growth, exponential growth

Teacher overview

This 30-minute quiz is worth 24 points and checks whether students can reason about the numbers behind a water bill: how much water each person uses, whether a bill is affordable, and how a rate increase grows over time. It mixes two multiple-choice items, two short-answer items, and four computation items built around a fictional district's data. The affordability threshold used here is a widely used rule of thumb built from two EPA benchmarks; every other figure belongs to the invented scenario.

Marden Water District Bills: A Rates and Water-Use Quiz — Grade 11 Math
Name: ____________________________ Date: ______________

Assessment

The Marden Water District (a fictional district used for this quiz) serves 12,000 people and delivers 1.2 MGD of water. Answer each item and show your work where a calculation is required.

  1. (2 points) Using the district's totals, what is its water use per person per day?
    • A) 10 gallons per person per day
    • B) 100 gallons per person per day
    • C) 1,000 gallons per person per day
    • D) 1,200 gallons per person per day
  2. (4 points) A Marden household earns 40,000 dollars per year and pays 1,900 dollars per year for combined water and sewer service. What percent of its income is that? Round to the nearest hundredth of a percent.
  3. (2 points) A widely used rule of thumb, built from two EPA benchmarks, treats combined water and sewer costs above about 4.5 percent of household income as a high burden. Based on item 2, is this household above or below that threshold?
  4. (4 points) Plan A raises the monthly bill by a flat 3 dollars each year. Plan B raises the bill by 5 percent each year. Which plan is linear and which is exponential? Explain how you can tell.
  5. (4 points) A Marden bill is 60 dollars per month this year. Under Plan A (up 3 dollars per year), what is the monthly bill in 4 years?
  6. (4 points) Under Plan B (up 5 percent per year), what is the 60-dollar monthly bill after 2 years? Round to the nearest cent.
  7. (2 points) After many years, which plan produces the larger bill, assuming both keep their pattern?
    • A) Plan A, because adding a fixed amount each year outpaces multiplying.
    • B) Plan B, because an exponential pattern eventually outgrows a linear one.
    • C) They stay equal forever.
    • D) It cannot be determined.
  8. (2 points) Give one reason a district might need to raise rates even when customers object.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: B) 100 gallons per person per day. 1.2 MGD is 1,200,000 gallons per day; 1,200,000 / 12,000 people = 100 gallons per person per day.
  2. Answer: 4.75 percent. 1,900 / 40,000 = 0.0475, which is 4.75 percent of income.
  3. Answer: Above the threshold. 4.75 percent is greater than the 4.5 percent high-burden benchmark, so this household is above it.
  4. Answer: Plan A is linear; Plan B is exponential. Plan A adds the same 3 dollars every year, an equal difference each interval, which is linear. Plan B multiplies by 1.05 every year, an equal factor each interval, which is exponential.
  5. Answer: 72 dollars per month. 60 + 4 x 3 = 60 + 12 = 72 dollars per month.
  6. Answer: 66.15 dollars per month. 60 x 1.05 squared = 60 x 1.1025 = 66.15 dollars per month.
  7. Answer: B) Plan B, because an exponential pattern eventually outgrows a linear one. A fixed percent increase compounds, so after enough years it passes any fixed-dollar increase.
  8. Answer: Any reasonable reason, such as replacing aging pipes, repairing frequent main breaks, covering rising treatment or energy costs, or meeting a new drinking-water regulation. Each raises the district's costs regardless of customer preference.

Differentiation

Support

Provide item 2 with the division already set up (1,900 / 40,000) and give a filled example of a one-year Plan A and Plan B increase before students project further. Allow calculators on all computation items.

Extension

Ask students to find the first whole year in which the Plan B monthly bill passes the Plan A monthly bill, starting both at the 60-dollar figure, and to show the year-by-year values that justify their answer.

ELL supports

Provide a two-column table labeled "linear" and "exponential" with one worked row so students can sort Plans A and B by pattern. Offer a sentence frame for item 8: "A district might raise rates because ___."