Mathematics: Arithmetic, Rates, and Practical Calculations
Core skills
The math section rewards clean fundamentals more than cleverness. Expect fractions and decimals, percents, ratios and proportions, unit conversions, averages, rate problems (including flow rates and distance/time), simple algebra for an unknown, and perimeter, area, and volume of rectangles, circles, and cylinders. Fire-service contexts - gallons per minute, hose lengths, tank capacity, pressure - are just scenery wrapped around ordinary arithmetic.
Traps to watch for
- Unit mismatch. Minutes mixed with hours, inches with feet, or pounds with gallons. Convert before you compute.
- "Percent of" versus "percent increase." A 20% increase means multiplying by 1.20, not adding 20.
- Premature rounding. Keep full precision until the final step, then round as the question asks.
- Operation order. Work parentheses, then exponents, then multiply/divide left to right, then add/subtract.
- Distractor arithmetic. Wrong answers are built from plausible mistakes (adding instead of multiplying, using the wrong denominator).
Rule of thumb
Label every number with its unit, write the relationship as an equation, and estimate the answer first so you can reject implausible choices instantly.
Worked example
A tank holds 1,500 gallons and a supply line delivers 250 gallons per minute. How long to fill the tank to three-quarters capacity?
- Three-quarters of 1,500 = 1,125 gallons.
- Time = volume ÷ rate = 1,125 ÷ 250 = 4.5 minutes. Notice that 6 minutes (a full tank) is almost certainly among the answer choices - that is the trap for skipping step one.