Quiz & test questions Grade 12 Math
Sourwood Plant Certification Exam: Multi-Step Operator Math Practice
A grade 12 certification-style practice exam covering chained unit conversions, the pounds formula, tank volume, and detention time for a fictional treatment plant.
Objectives
- Students will apply the pounds formula, cylinder-volume formula, and detention-time formula to a treatment-plant scenario.
- Students will convert a flow rate through a chain of units and convert pressure using the standard psi-to-feet relationship.
- Students will calculate a sample mean for water-quality data and evaluate it against a federal regulatory standard.
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.
- Clearwell
- A clearwell is a large storage tank at a treatment plant that holds finished water right after it comes out of the filters. It gives the disinfectant enough time to work before the water is pumped out to homes and businesses.
- Turbidity
- Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.
- Operator certification
- The official license a person earns to run a drinking water or wastewater plant. Operators study, gain work experience, and pass a state exam to become certified.
Teacher overview
This 50-minute exam (26 points total) is built in the style of a state operator-certification test, using the fictional Sourwood Water Treatment Plant as its running scenario. It mixes two multiple-choice recall items with computation items covering the pounds formula, cylinder-tank volume, detention time, chained flow conversions, pressure-to-head conversion, and a short data-mean item, so it exercises the same multi-step, unit-driven mathematics a licensed operator uses on the job.
Every operator-certification formula referenced here is standard across state licensing exams: the pounds formula (concentration in mg/L times flow in MGD times 8.34), the cylinder-volume formula (0.785 times diameter squared times depth, times 7.48 for gallons), detention time (volume divided by flow), and the standard flow and pressure conversions (1 MGD equals 694 gpm and 1.547 cfs; 1 psi equals 2.31 feet of head).
A common misconception to watch for: students sometimes plug numbers into the pounds formula in the wrong order, or forget to convert a volume in gallons into millions of gallons before dividing by a flow rate given in MGD. Reminding students to write out each unit at every step, rather than only the numbers, catches most of these errors before the final answer.
Assessment
The fictional Sourwood Water Treatment Plant is used for every item below.
(2 points) Which set of operations correctly calculates a chemical feed rate in pounds per day?
- A) Flow (MGD) × 7.48
- B) Concentration (mg/L) × Flow (MGD) × 8.34
- C) Concentration (mg/L) ÷ Flow (MGD) × 8.34
- D) Concentration (mg/L) × Flow (MGD) ÷ 8.34
(4 points) Sourwood's plant treats a flow of 2.4 MGD and needs a chlorine dose of 3.2 mg/L. Using the pounds formula, calculate the pounds of chlorine required per day. Round to the nearest tenth of a pound.
(4 points) Sourwood's cylindrical clearwell has a diameter of 40 feet and a water depth of 12 feet. Using the cylinder-volume formula, calculate the clearwell's volume in gallons. Round to the nearest hundred gallons.
(4 points) The clearwell from item 3 receives an inflow of 1.8 MGD. Using your volume from item 3 and the detention-time formula, calculate the clearwell's detention time in hours. Round to the nearest tenth of an hour.
(3 points) Sourwood's raw-water intake pump moves 1.2 MGD. Convert this flow first to gallons per minute (gpm), rounding to the nearest whole gpm, then to cubic feet per second (cfs), rounding to the nearest hundredth.
(3 points) A pressure gauge at a Sourwood fire hydrant reads 58 psi. Using the standard psi-to-feet conversion, calculate how many feet of elevation this pressure represents. Then, in one or two sentences, explain why this conversion matters when firefighters are drawing water from a hydrant.
(4 points) Over five days, Sourwood's finished-water turbidity readings (fictional practice data for this exam) were 0.18, 0.21, 0.15, 0.24, and 0.19 NTU. Calculate the mean turbidity for the five days, and state whether this sample mean, on its own, proves the plant is meeting the federal requirement that finished-water turbidity stay at or below 0.3 NTU in 95 percent of monthly samples.
(2 points) A 1 percent chemical solution is equivalent to how many mg/L?
- A) 100 mg/L
- B) 1,000 mg/L
- C) 10,000 mg/L
- D) 100,000 mg/L
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) Concentration (mg/L) × Flow (MGD) × 8.34. This is the standard pounds formula used for chlorine feed, BOD loading, and similar dosing calculations; option A uses the wrong constant and ignores concentration, and options C and D apply the correct terms with the wrong operation.
Answer: 64.1 lbs/day. 3.2 mg/L × 2.4 MGD × 8.34 = 64.0512, which rounds to 64.1 pounds per day.
Answer: 112,700 gallons. Volume (cu ft) = 0.785 × 40² × 12 = 0.785 × 1,600 × 12 = 15,072 cubic feet. Converting to gallons: 15,072 × 7.48 = 112,738.56 gallons, which rounds to 112,700 gallons to the nearest hundred.
Answer: 1.5 hours. Converting the item 3 volume to millions of gallons: 112,700 ÷ 1,000,000 = 0.1127 MG. Detention time in days = 0.1127 ÷ 1.8 = 0.06261 days. Converting to hours: 0.06261 × 24 = 1.503 hours, which rounds to 1.5 hours.
Answer: 833 gpm (about 1.86 cfs). 1.2 MGD × 694 gpm/MGD = 832.8 gpm, rounding to 833 gpm. 1.2 MGD × 1.547 cfs/MGD = 1.8564 cfs, rounding to 1.86 cfs.
Answer: 134.0 feet. 58 psi × 2.31 ft/psi = 133.98 feet, which rounds to 134.0 feet. Accept any explanation noting that converting pressure to feet of head tells firefighters how much elevation is behind the water in the system, which affects how much pressure and flow will actually reach the nozzle at a fire scene.
Answer: 0.194 NTU (rounds to about 0.19 NTU); this sample mean alone does not prove compliance. (0.18 + 0.21 + 0.15 + 0.24 + 0.19) ÷ 5 = 0.97 ÷ 5 = 0.194 NTU. All five fictional readings fall below the 0.3 NTU limit, which is a good sign, but the actual federal requirement is based on 95 percent of a full month of samples never exceeding 0.3 NTU, with no single sample ever exceeding 1 NTU, so five days of data cannot confirm monthly compliance on their own.
Answer: C) 10,000 mg/L. A 1 percent solution equals 10,000 mg/L by the standard percent-to-mg/L conversion used on certification exams.
Differentiation
Support (below grade level)
Provide the pounds formula, cylinder-volume formula, and detention-time formula on a printed reference card with each variable labeled in plain language, and allow students to complete items 3 and 4 with the arithmetic steps already broken into separate labeled boxes.
Extension (above grade level)
Ask students to recalculate item 3's clearwell volume for a tank with the same depth but a diameter of 50 feet instead of 40 feet, then explain in their own words why a 25 percent increase in diameter raises the volume by more than 25 percent.
ELL supports
Pre-teach "detention time," "clearwell," and "turbidity" with a simple labeled diagram of a treatment plant showing where the clearwell sits in the treatment train. Allow item 6's explanation to be answered as one short sentence using a provided sentence frame: "This conversion matters because ___."