Quiz & test questions Grade 12 Math

Kelverton Well 3 PFAS Compliance: Averages and Precision

A grade 12 quiz on PFAS compliance math: the running annual average, comparison to the 4.0 ppt limit, blending, reporting precision, and the rule's compliance timeline.

Grade: Grade 12
Subject: Math
Material: Quiz & test questions
Time: 30 min
Prep: No prep
Materials: Calculator

Standards

HSS-IC.A.1 Common Core Math

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

How this material aligns: Items 3, 8, and 10 treat quarterly samples as a process for inferring the well's true annual PFAS level rather than trusting any single grab sample.

All materials for HSS-IC.A.1 →

HSN-Q.A.3 Common Core Math

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

How this material aligns: Item 6 asks students to report a lab result to the precision the method allows, matching reported accuracy to the tenths-of-a-ppt limit of the measurement.

All materials for HSN-Q.A.3 →

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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 calculate a running annual average and compare it to the PFAS maximum contaminant level.
Students will report a result to appropriate precision and explain why PFAS compliance uses repeated sampling.

Vocabulary

PFAS: A large family of human-made chemicals used in things like nonstick pans, waterproof fabric, and firefighting foam. They are called forever chemicals because they take a very long time to break down.
Maximum contaminant level (MCL): A maximum contaminant level, or MCL, is the highest amount of a certain substance that federal rules allow in drinking water. Water systems test regularly to prove their water stays under each limit.

Also: running annual average, significant figures, compliance

Teacher overview

This 30-minute quiz is worth 30 points and checks whether students can run the compliance math behind a PFAS result at the fictional Kelverton Well 3. It mixes two multiple-choice items, four short-answer or reasoning items, and four computation items, together covering the running annual average, blending, reporting precision, carbon treatment, and the rule's compliance timeline, including a proposed deadline exemption. Students may use a calculator.

Kelverton Well 3 PFAS Compliance: Averages and Precision — Grade 12 Math

Name: ____________________________ Date: ______________

Assessment

Kelverton Well 3 is a fictional well. Its four quarterly PFOA results for the year are 3.2, 4.6, 5.1, and 3.9 ppt.

(2 points) Under the April 2024 federal rule, what is the maximum contaminant level for PFOA?
- A) 40 ppt
- B) 4.0 ppt
- C) 0.4 ppt
- D) 400 ppt
(2 points) In one or two sentences, explain what a running annual average is in PFAS compliance monitoring.
(4 points) Calculate the running annual average of Well 3's four quarterly PFOA results (3.2, 4.6, 5.1, and 3.9 ppt). Round to the nearest tenth.
(3 points) Compare the running annual average from item 3 to the 4.0 ppt limit. Is Well 3 in compliance? Explain in one sentence.
(4 points) The utility blends Well 3 water (running annual average 4.2 ppt) with an equal flow of a clean source at 0.0 ppt. Calculate the blended PFOA concentration, and state whether it meets the 4.0 ppt limit.
(3 points) A lab instrument reports a PFOA result as 4.28571 ppt, but the method reports only to the nearest tenth of a ppt. How should the result be reported?
(2 points) Which statement about the PFAS rule's timeline is correct?
- A) The rule was finalized in 2024 and its deadline cannot change.
- B) In 2026, EPA proposed letting eligible systems apply for a two-year exemption, moving their deadline from April 2029 to April 2031.
- C) The rule sets no compliance deadline at all.
- D) The rule was withdrawn entirely in 2026.
(4 points) Well 3's four results range from 3.2 to 5.1 ppt. Explain why a single quarterly sample below 4.0 ppt does not prove compliance, while the running annual average can still show a violation.
(3 points) The utility installs granular activated carbon that removes 85 percent of PFOA. Starting from the 4.2 ppt running annual average, calculate the treated concentration and state whether it meets the 4.0 ppt limit.
(3 points) Explain why the rule requires sampling at several times across the year rather than trusting one grab sample to judge PFAS compliance.

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) 4.0 ppt. The April 2024 federal rule sets the maximum contaminant level for PFOA at 4.0 parts per trillion.
Answer: The running annual average is the average of a site's most recent results across the required sampling period, used to judge compliance rather than any single result.
Answer: 4.2 ppt. The sum of 3.2, 4.6, 5.1, and 3.9 is 16.8; divided by 4 quarters that is 4.2 ppt.
Answer: No. The running annual average of 4.2 ppt is above the 4.0 ppt limit, so Well 3 is out of compliance.
Answer: 2.1 ppt. An equal-flow blend averages the two sources: (4.2 plus 0.0) divided by 2 is 2.1 ppt, which is below the 4.0 ppt limit, so the blend meets the standard.
Answer: 4.3 ppt. Rounded to the nearest tenth, the method's precision, 4.28571 becomes 4.3 ppt; reporting more digits would claim accuracy the method does not have.
Answer: B) In 2026, EPA proposed letting eligible systems apply for a two-year exemption, moving their deadline from April 2029 to April 2031. The rule is still in motion: the proposal was not yet final as of September 2026, it would not extend the deadline automatically for every system, and it would not change the 4.0 ppt limits.
Answer: One low quarter is only part of the picture. Compliance is judged on the running annual average, so a single result below 4.0 ppt can be offset by higher quarters; here the 5.1 and 4.6 ppt results pull the average above the limit even though two quarters were below it.
Answer: 0.63 ppt. Removing 85 percent leaves 15 percent: 4.2 times 0.15 is 0.63 ppt, which is below the 4.0 ppt limit, so the treated water meets the standard.
Answer: PFAS levels vary from quarter to quarter with source and demand conditions, so repeated sampling across the year estimates the well's true average more reliably than one grab sample, which could land unusually high or low by chance.

Differentiation

Support

Provide the running-annual-average setup for item 3 already written as a sum over four quarters, and give a number line marked at 4.0 ppt so students can see whether each computed value is in or out of compliance.

Extension

Ask students to find the highest a fifth quarterly result could be while still bringing the fictional well back into compliance once the oldest quarter (3.2 ppt) drops out of the running average, and to explain their reasoning.

ELL supports

Pre-teach "average," "limit," "compliance," and "precision" with a labeled example. Provide sentence frames for items 4 and 8: "The well is in / out of compliance because ___."

Extensions

Have students look up whether their state has begun PFAS compliance monitoring and compare the reporting rules with the fictional Kelverton example, noting how the proposed two-year exemption from the April 2029 federal deadline could affect a real utility's plans.