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Education/Training + Get AlertsThe words "wastewater math" can create an undercurrent of fear for operators about to take a state exam.

Many students encounter a mental block when it comes to process control math. I even had a student who vowed not to do math and just ace the other portions of the 100-question wastewater exam. For the record, avoiding math questions is not a good strategy for passing an exam. Also, if you do get your license using this tactic, it will limit your professional career.

Instead, use these five tips to ace your math questions and pass your operator exam.

**1. Read questions thoroughly before looking at data**

Each math question will include a data set, which you should not look at until you’ve completely read the question. If you look at data first, you might answer what you think is being asked. After carefully reading the question, analyze the data to make sure you understand what is given and what is needed.

For example, solve the following question:

What is the volume in million gallons per day of the aeration basin? (cubic feet = length x width x depth) To convert to gallons, multiply cubic feet by 7.48.

By looking at the question and the data chart you’ll see the answer without having to use the given formula. The plant data already gives the capacity as 523,345 gallons per day. This means the dimensions listed in the data set are not the operating capacity of the tank. Therefore, you would just need to convert:

523,345 gallons per day/1,000,000 gallons = .523345 mgd.

**2. Use Davidson pie diagrams**

What happens if the known information is pounds and flow, but not concentration? Or pounds and concentration, but not flow? According to the principles of algebra, you can determine the missing element of a formula if you have two known elements. Operators frequently use a visual tool called the Davidson pie chart to show the relationship between each part of the formula.

The pie chart can be used for other application including but not limited to:

- Electromotive force
- Power equation
- Pump rates
- Chemical dosage

**3. Don’t mix units for detention time formulas**

Operators commonly make the mistake of using mgd for detention time questions when the answer should be in gallons. The basic formula for detention time is volume/flow, but the operator exam would have a formula similar to DT, hr = (tank volume, gal x 24 hr/day)/ flow, gal/day

When reading the problem, first determine which unit the answer needs to be in, then convert information given to that unit of measurement and setup the equation accordingly. Remember to keep apples with apples, so the formula is compatible.

Using the plant data, what is the detention time of the aeration basin in hours?

*First attempt using mgd and gallons:*

DT, hrs = (523,345 gal x 24 hrs/day)/13.5 mgd

DT, hrs = 12,560,280 gal /13.5 mgd

DT, hrs = 930,391 hours

Wrong answer! Time to check units and try again.

*Second attempt using gallons in both places:*

DT, hrs = (523,345 gal x 24 hrs/day)/13,500,000 gal [13.5 mgd x 1,000,000 gal]

DT, hrs = 12,560,280 gal /13,500,000 gal

DT, hrs = 0.93 hrs/day

To convert to minutes (0.93 hrs/day x 60 min/hr = 55.8 min)

*Third attempt using mgd in both places:*

DT, hrs = (.523345 x 24 hrs/day)/13.5 mgd

DT, hr = 12.56 mgd/13.5 mgd

DT, hr = 0.93 hrs/day

To convert to minutes (0.93 hrs/day x 60 min/hr = 55.8 min)

**4. Use units in the formula as clues**

Often the formula provides a blueprint to solving the question. The detention time formula in the previous section was DT, hr = (tank volume, gal x 24 hr/day)/Flow, gal/day. In the formula gallons are in the numerator and denominator. Therefore, an astute operator can ascertain the units right from the formula.

Another example is the calculation for finding the backwash rate required to backwash a filter.

Formula: backwash rate, gpm/sq ft = backwash flow, gpm/surface area, sq ft.

By dissecting the formula, you’ll see you’re looking for gallons and square feet. If an operator calculates length x width x depth of the filter, the answer is already wrong. Also, test writers like to give mgd for flow in this scenario to test whether you know to make the proper conversion.

**5. Breathe**

One of my greatest tips to students is to breathe. It sounds simple, but during a stressful event — such as taking an important test — shallow breathing comes naturally. Each deep, belly-filling breath will send more oxygen to your brain and help your body regulate stress. Harvard Medical notes that deep diaphragmatic breathing slows the heartbeat and lowers or stabilizes a person’s blood pressure. Breathing techniques are a valuable tool for reducing stress and eliminating mistakes.

Operator exams can be daunting, but math doesn’t have to be intimidating. Test writers design exams to verify operator knowledge and comprehension. By using these five tips, the math portion will be more manageable.

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