Quiz & test questions Grade 9 Math

Varmoor Utility Operations Math: A Grade 9 Unit Test

A grade 9 unit test on the fictional Varmoor utility, mixing multiple-choice, short-answer, and computation items on the pounds formula, flow conversions, and pressure.

Grade: Grade 9
Subject: Math
Material: Quiz & test questions
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Students use the one-variable equation 0 = 500,000 - 20,000t in item 8 to solve for the hour the Varmoor tank runs empty.

All materials for HSA-CED.A.1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Students choose and carry consistent units through the pounds formula and the MGD-to-gpm conversion in items 3 and 6 of the test.

All materials for HSN-Q.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will apply the pounds formula and flow conversions to utility quantities.
Students will find pressure from water height using the standard constant.
Students will interpret and solve a linear tank-drain model.

Vocabulary

Key words: pounds formula, flow conversion, pressure, linear model, slope

Teacher overview

This 40-minute unit test, worth 30 points total, checks grade 9 skills on the fictional Varmoor utility. It mixes multiple-choice, short-answer, and computation items. Students apply the pounds formula, convert flow units, find pressure from water height, and interpret a linear tank-drain model.

Varmoor Utility Operations Math: A Grade 9 Unit Test — Grade 9 Math

Name: ____________________________ Date: ______________

Assessment

Varmoor (a fictional utility) serves a small city. Use this fact: pressure (psi) = height (ft) x 0.433.

(2 points) One MGD equals how many gpm?
- A) 694 gpm
- B) 448.8 gpm
- C) 8.34 gpm
- D) 2.31 gpm
(2 points) Which expression gives chemical loading in pounds per day?
- A) mg/L x MGD x 8.34
- B) mg/L divided by MGD
- C) MGD x 2.31
- D) mg/L x 0.433
(4 points) Varmoor doses chlorine at 2.5 mg/L into a 4 MGD flow. Find the chlorine feed in pounds per day.
(4 points) Varmoor's tower holds water 130 feet above Main Street. Find the pressure at Main Street, using pressure = height x 0.433. Round to the nearest psi.
(3 points) States generally require at least what water pressure at every connection?
- A) 20 psi
- B) 5 psi
- C) 80 psi
- D) 200 psi
(4 points) Convert a 3 MGD flow to gallons per minute, using 1 MGD equal to 694 gpm.
(4 points) A Varmoor tank drains on the model V = 500,000 - 20,000t, where V is gallons remaining and t is hours. How many gallons remain after 6 hours?
(3 points) Using the same model V = 500,000 - 20,000t, after how many hours is the tank empty?
(2 points) Interpret the slope -20,000 in the tank-drain model in one sentence.
(2 points) Finished drinking water turbidity must stay at or below what value in 95 percent of samples?
- A) 0.3 NTU
- B) 5 NTU
- C) 15 NTU
- D) 30 NTU

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

Answer Key

Answer: A) 694 gpm. One MGD equals 694 gallons per minute.
Answer: A) mg/L x MGD x 8.34. This is the pounds formula for daily chemical loading.
Answer: 83.4 lb/day. 2.5 mg/L x 4 MGD x 8.34 = 83.4 pounds per day. (2.5 x 4 = 10; 10 x 8.34 = 83.4.)
Answer: 56 psi. 130 ft x 0.433 = 56.29, about 56 psi.
Answer: A) 20 psi. Most states require at least 20 psi at every connection to prevent backflow.
Answer: 2,082 gpm. 3 MGD x 694 gpm per MGD = 2,082 gpm.
Answer: 380,000 gal. V = 500,000 - 20,000(6) = 500,000 - 120,000 = 380,000 gallons.
Answer: 25 hours. 0 = 500,000 - 20,000t, so 20,000t = 500,000 and t = 25 hours.
Answer: The tank loses 20,000 gallons for each hour that passes.
Answer: A) 0.3 NTU. Finished water must stay at or below 0.3 NTU in 95 percent of samples.

Differentiation

Support

Provide a formula strip listing the pounds formula, "1 MGD equals 694 gallons per minute," and "pressure equals height times 0.433," with one worked example of each that is not on the test. Allow a calculator on all computation items.

Extension

Ask students to find at what hour the Varmoor tank in items 7 and 8 is exactly half full, and to explain how they used the drain model to get there.

ELL supports

Provide the formula strip with a small labeled diagram for each formula, such as a tower for pressure and a pipe for flow. Let students answer item 9 with a sentence frame: "The slope means the tank ___ each hour."