Mathematics
What the section tests
Mathematics items cover arithmetic, fractions and decimals, ratios and proportions, percentages, unit conversions, averages, and basic algebra and geometry applied to practical situations. Expect word problems about hose flow, tank capacity, distances, times, and costs. The math itself is not advanced; the challenge is translating the words into the right operation and working accurately without a calculator.
Concepts to master
Be fluent converting between fractions, decimals, and percentages, and simplify fractions before multiplying to save effort. For proportions, set up two equal ratios and cross-multiply. Percentage change is the difference divided by the original amount. For rates, remember distance = rate × time, and rearrange to solve for the missing quantity. For averages, sum the values and divide by the count; to find a missing value from a known average, multiply the average by the count and subtract the known values. Know common area and volume formulas: rectangle area, circle area, and rectangular volume.
Traps to watch
Watch for unit mismatches (minutes versus hours, inches versus feet) and convert before computing. Distinguish percent of a number from percent increase. In rate problems, check whether you are solving for time, rate, or distance. Estimate first so an unreasonable answer stands out.
Worked example
A hose delivers 40 gallons per minute. How long to fill a 1,200-gallon tank? Time = 1,200 ÷ 40 = 30 minutes. Rule of thumb: write the units next to each number so mismatches are obvious, and sanity-check the answer against a rough estimate.