Basic Mathematics
Skills tested
Arithmetic with fractions, decimals, and percents; ratios and proportions; averages; rate, time, and distance; unit conversions; perimeter and area; and multi-step word problems drawn from scheduling, patrol coverage, staffing, and budget. Assume no calculator - practice estimating so you can eliminate answers quickly.
Concepts and formulas
Percent: part ÷ whole = percent ÷ 100. Percent change = (new − old) ÷ old × 100. Average = sum ÷ count, and a weighted average when groups differ in size. Distance = rate × time, so rate = distance ÷ time. Proportions: cross-multiply. Perimeter adds lengths; area of a rectangle is length × width. Convert before you compute: 1 hour = 60 minutes, 1 mile = 5,280 feet, 1 foot = 12 inches.
Traps
- Mixed units - minutes in one place, hours in another.
- "Percent of" versus "percent change."
- Averaging two averages of unequal groups.
- "How many more" (subtract) versus "how many times as many" (divide).
- Rounding too early, or rounding down when a question says "at least."
Rule of thumb
Write units next to every number and cancel them like fractions; the units tell you whether to multiply or divide. Then estimate to check the size of your answer.
Worked example: A unit covers 84 miles in 1 hour 45 minutes. What is the average speed? Convert: 1 h 45 min = 1.75 h. Rate = 84 ÷ 1.75 = 48 mph. The distractor 84 ÷ 1.45 ≈ 57.9 mph shows what happens if you treat 45 minutes as 0.45 hours.