Mathematics and Quantitative Reasoning
What this domain tests
Mathematics and Quantitative Reasoning tests arithmetic, percentages, ratios, averages, unit conversion, distance/rate/time, basic algebra, and data interpretation in law-enforcement contexts such as pursuit distances, staffing, budgets, and crash data.
Core rules
- Carry units through every step; convert minutes to hours before using miles per hour.
- Follow order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.
- Percent change uses the original amount as the base: change divided by original, times 100.
- An average is a total divided by the number of items; it is not the same as a median or a total.
- For ratios, keep the same order on both sides and label the parts.
Worked example
A suspect vehicle travels at 48 mph for 15 minutes. How far does it travel? Reasoning: 15 minutes is 15/60 = 0.25 hour. Distance = rate × time = 48 × 0.25 = 12 miles. A common wrong answer is 48 × 15 = 720, which mixes minutes with miles per hour. Another wrong answer is 48 ÷ 15, which has no valid unit.
Traps that cost marks
- Forgetting to convert minutes to hours.
- Using the new amount as the base for a percent decrease.
- Averaging two averages without weighting by group size.
- Rounding too early and losing precision.
- Selecting an answer with the right number but the wrong unit.