Quiz & test questions Grade 10 Math

Northgate Operator Math: A Water Plant Unit Test

A grade 10, 30-point unit test on operator math: pressure, flow conversions, the pounds formula, tank volume, and detention time at a fictional water plant.

Grade: Grade 10
Subject: Math
Material: Quiz & test questions
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

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: Items 3, 4, 5, and 7 carry feet, psi, MGD, gpm, and mg/L through multi-step operator formulas, holding units consistent as this standard requires.

All materials for HSN-Q.A.1 →

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Items 6 and 10 model a rectangular basin and a cylindrical tank as geometric solids to find volume, the shape-based modeling this standard describes.

All materials for HSG-MG.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 operator formulas for pressure, flow, dose, and volume.
Students will convert units and report answers with appropriate accuracy.

Vocabulary

Detention time: Detention time is how long water stays inside a tank or basin before flowing out. Water must stay long enough for each treatment step, like settling or disinfecting, to finish its job.

Also: pounds formula, head, removal efficiency

Teacher overview

This unit test checks whether students can apply the core operator-math formulas taught in the treatment unit, using the fictional town of Northgate and its water plant. It is worth 30 points across ten items: two multiple-choice, one short-answer, and seven computation items. The mix spans conversions, pressure and head, the pounds formula, tank volume, detention time, and removal efficiency.

Northgate Operator Math: A Water Plant Unit Test — Grade 10 Math

Name: ____________________________ Date: ______________

Assessment

All items use the fictional town of Northgate. Standard constants: 1 cubic foot = 7.48 gallons; 1 psi = 2.31 feet of head; 1 foot of head = 0.433 psi; 1 MGD = 694 gpm; 8.34 pounds per gallon.

(2 points) One cubic foot of water holds how many gallons?
- A) 5.5
- B) 7.48
- C) 8.34
- D) 62.4
(2 points) One psi of pressure equals how many feet of head?
- A) 0.433
- B) 1.0
- C) 2.31
- D) 8.34
(3 points) A tank holds water 90 feet above a tap. Find the pressure at the tap in psi.
(3 points) Convert a flow of 2.0 MGD to gpm.
(3 points) Find the chlorine feed in pounds per day at a dose of 2.0 mg/L and a flow of 2.0 MGD.
(3 points) A rectangular basin measures 30 feet by 12 feet by 10 feet. Find its volume in gallons.
(3 points) Find the detention time in hours for the item 6 basin at a flow of 0.5 MGD.
(3 points) An influent turbidity of 10 NTU drops to 0.2 NTU after treatment. Find the removal efficiency as a percent.
(3 points) A distribution point reads 15 psi. State whether it meets the common 20 psi minimum, and why that minimum matters.
(5 points) A cylindrical tank is 40 feet across with water 20 feet deep. Find its volume in gallons. Use volume (cu ft) = 0.785 x diameter squared x depth.

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: B, 7.48 gallons.
One cubic foot of water holds 7.48 gallons, a standard operator constant.
Answer: C, 2.31 feet.
One psi equals 2.31 feet of head; its inverse, 0.433 psi per foot, is used in item 3.
Answer: 39 psi.
90 feet x 0.433 psi per foot = 38.97, which rounds to 39 psi.
Answer: 1,388 gpm.
2.0 MGD x 694 gpm per MGD = 1,388 gpm.
Answer: 33.4 lbs/day.
2.0 mg/L x 2.0 MGD x 8.34 = 4 x 8.34 = 33.36, which rounds to 33.4 pounds per day.
Answer: 26,928 gal.
Volume = 30 x 12 x 10 = 3,600 cubic feet. Then 3,600 x 7.48 = 26,928 gallons.
Answer: 1.3 hours.
Detention time = volume / flow = 26,928 gallons / 500,000 gallons per day = 0.0539 day. Then 0.0539 x 24 = 1.29, about 1.3 hours.
Answer: 98 percent.
(10 - 0.2) / 10 x 100 = 9.8 / 10 x 100 = 98 percent.
Answer: No, it is below the 20 psi minimum.
At 15 psi the point is under the common 20 psi minimum. Low pressure lets outside water be drawn in through cracks, which risks contamination from backflow.
Answer: 187,898 gal.
Volume = 0.785 x 40 squared x 20 = 0.785 x 1,600 x 20 = 25,120 cubic feet. Then 25,120 x 7.48 = 187,897.6, about 187,898 gallons.

Differentiation

Support

Provide a constants reference strip and let students use it during the test. Offer a version that gives the first step of items 6 and 10 already set up, so the geometry does not block the conversion practice.

Extension

Add a challenge item: ask students to find how many hours it takes to fill the item 10 tank at 300 gpm, and to state one reason a real fill would take longer than the math predicts.

ELL supports

Provide a labeled diagram bank for "head," "basin," and "detention time," and allow item 9 to be answered with a sentence frame: "It does not meet the minimum because ___."