Mathematical Reasoning
What this domain tests
Mathematical reasoning items use fire-service contexts: hose and water calculations, ladder placement, elapsed time, distance and rate, ratios for foam mix, pressure changes, and unit conversions. The math is usually arithmetic with some basic algebra, but the wording creates the difficulty.
Concepts to master
- Rates and time: distance = rate x time; rearrange for the unknown.
- Ratios and proportions: foam concentrate to water, e.g., 3% mix means 3 parts concentrate per 100 parts solution.
- Unit conversions: feet to inches, minutes to hours, gallons to liters when given a factor.
- Percentages: increase, decrease, and 'what percent of' problems.
- Averages and totals: mean, sum, and working backward from a total.
- Geometry: area and volume of rectangles and cylinders (tank capacity), and the Pythagorean relationship for ladder reach.
Traps to expect
- Mixing units (minutes vs. hours, feet vs. inches) within one problem.
- Confusing 'parts concentrate per 100 parts solution' with 'per 100 parts water.'
- Answering the wrong quantity (asking for time but options include distance).
- Rounding too early and drifting from the correct option.
Worked example / rule of thumb
A hose delivers 150 gallons per minute. How long to move 2,400 gallons? Divide: 2,400 / 150 = 16 minutes. If an option says 0.16 hours, check units: 16 minutes is about 0.27 hours, so that option is a unit trap. Rule of thumb: write the units next to every number, convert to one system before computing, and estimate the answer first so you can reject options that are off by a factor of ten or sixty.