Quiz & test questions Grade 10 Math
Dunmarrow Treatment Wetland Quiz: Area, Loading, and Removal
A 30-point grade 10 quiz on a fictional constructed wetland covering area in acres, hydraulic loading rate, detention time, and pounds of BOD and nitrogen removed.
Objectives
- Students will calculate the area, volume, and detention time of a rectangular treatment wetland.
- Students will express plant flow as a hydraulic loading rate per square foot of surface.
- Students will use the pounds formula to report removal in pounds per day.
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: constructed wetland, hydraulic loading rate, removal efficiency, BOD
Teacher overview
This 30-point quiz covers the geometry and loading math behind a constructed treatment wetland, using the fictional Dunmarrow wetland as its single scenario. It mixes two multiple-choice items, eight computation items, and one short written explanation, and it is written for one 45-minute period with a calculator. The misconception it checks most directly is the belief that a longer detention time can be gained by raising flow, which items 5, 10, and 11 disprove. Full credit on computation items requires the work as well as the final value.
Assessment
The Dunmarrow constructed wetland is fictional, and every value below is set for this quiz. The wetland is a rectangular cell 420 feet long and 260 feet wide, holding water 1.5 feet deep. It receives 0.35 MGD, which is 350,000 gallons per day, of treated effluent before that water reaches Dunmarrow Creek. Incoming BOD is 26 mg/L and outgoing BOD is 8 mg/L. Incoming total nitrogen is 14 mg/L and outgoing total nitrogen is 5 mg/L. Use these formulas: 1 acre = 43,560 square feet; 1 cubic foot holds 7.48 gallons; loading in pounds per day = concentration (mg/L) × flow (MGD) × 8.34; removal efficiency (%) = (in − out) ÷ in × 100.
(2 points) Which quantity best describes how much flow each unit of wetland surface must handle?
A. total gallons per day entering the cell
B. gallons per day for each square foot of surface
C. days of detention in the cell
D. pounds of BOD removed each day(3 points) Find the wetland's area in acres. Round to the nearest hundredth.
(3 points) Find the hydraulic loading rate in gallons per day for each square foot of surface. Round to the nearest tenth.
(3 points) Find the volume of water in the cell, in gallons, at the 1.5-foot depth.
(3 points) Find the detention time in days at 0.35 MGD. Round to the nearest hundredth.
(3 points) Find the BOD removal efficiency as a percent. Round to the nearest tenth.
(3 points) Find the pounds of BOD removed per day.
(2 points) The secondary treatment standard is a monthly average of 30 mg/L or less. Which statement about the 8 mg/L outgoing BOD is correct?
A. It meets the standard, with 22 mg/L to spare.
B. It exceeds the standard by 22 mg/L.
C. It meets the standard only if the flow doubles.
D. There is not enough information to decide.(3 points) Find the pounds of total nitrogen removed per day.
(3 points) A new subdivision doubles the flow to 0.70 MGD. Find the new detention time in days. Round to the nearest hundredth.
(2 points) Explain in two or three sentences why the detention time changes the way it does when the flow doubles and the cell keeps the same volume.
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. A loading rate divides flow by surface area, so gallons per day for each square foot states how hard each part of the wetland is working. Choice A gives the total without regard to size, and choices C and D describe other quantities.
Answer: 2.51 acres. Area = 420 × 260 = 109,200 square feet, and 109,200 ÷ 43,560 = 2.5069, which rounds to 2.51 acres.
Answer: 3.2 gallons per day per square foot. 350,000 ÷ 109,200 = 3.205, which rounds to 3.2.
Answer: 1,225,224 gallons. Volume = 109,200 × 1.5 = 163,800 cubic feet, and 163,800 × 7.48 = 1,225,224 gallons.
Answer: 3.50 days. 1,225,224 ÷ 350,000 = 3.5006, which rounds to 3.50 days.
Answer: 69.2 percent. (26 − 8) ÷ 26 × 100 = 18 ÷ 26 × 100 = 69.23, which rounds to 69.2 percent.
Answer: 52.5 lb/day. The concentration removed is 26 − 8 = 18 mg/L, so 18 × 0.35 × 8.34 = 52.54, which rounds to 52.5 pounds per day.
Answer: A. The outgoing BOD of 8 mg/L is below the 30 mg/L monthly average standard, and 30 − 8 = 22 mg/L of margin. Choice B reverses the comparison, and choice C invents a condition the standard does not contain.
Answer: 26.3 lb/day. The concentration removed is 14 − 5 = 9 mg/L, so 9 × 0.35 × 8.34 = 26.27, which rounds to 26.3 pounds per day.
Answer: 1.75 days. 1,225,224 ÷ 700,000 = 1.7503, which rounds to 1.75 days.
Answer: Detention time is the cell's volume divided by the flow. The volume does not change when the subdivision comes online, so doubling the number in the denominator cuts the quotient in half, from 3.50 days to 1.75 days. Water spends less time in contact with the plants and sediment, which is why removal usually falls at higher flow.
Differentiation
Support
Provide a version with the wetland area from item 2 already calculated, so items 3 and 4 begin from a known figure. Give the pounds formula written with labeled blanks for concentration, flow, and the 8.34 constant, and allow the removal-efficiency formula to be used from a reference card.
Extension
Ask students to find the flow, in MGD, at which the fictional Dunmarrow cell would fall to exactly 2.00 days of detention, then state what that flow would be in gallons per day. A second challenge is to find the additional wetland area, in acres, that would hold the hydraulic loading rate at 3.2 gallons per day per square foot once the flow doubles.
ELL supports
Provide a labeled plan view of the rectangular cell showing length, width, and depth, along with an arrow for inflow and outflow marked with their concentrations. Supply a card pairing the words influent and effluent with the plain phrases water coming in and water going out, and allow item 11 to be answered with a labeled diagram plus one sentence.
Extensions
Have students find a public description of a constructed wetland or a lagoon system serving a small community, note its stated acreage and design flow, and compute its hydraulic loading rate for comparison with the fictional Dunmarrow value. A short paragraph explaining which system gives water more contact time makes a useful follow-up assignment.