Mathematics
Mathematics on the trooper exam covers arithmetic, fractions and decimals, ratios and proportions, percentages, averages, unit conversion, and single-variable word problems. The goal is accurate calculation under time pressure, so translate the words into an equation before computing.
Core rules
- Percent means per hundred. 'Increase by 6%' means multiply by 1.06; '6% of' means multiply by 0.06.
- Average = sum divided by count. To find a missing value, use sum = average times count.
- Keep units consistent; convert before calculating.
- Use order of operations: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.
- Check whether the question asks for the amount of change or the new total.
Worked example
A department fuel budget is $240,000. It increases by 6%. How much is the increase? 0.06 times 240,000 = 14,400. The increase is $14,400; the new budget is $254,400. If the item asks for the new budget, do not stop at $14,400.
Traps
- Reporting the new total when the question asks for the increase.
- Treating a percentage-point change as a percent change.
- Averaging two averages without weighting by group size.
- Rounding intermediate steps and changing the final answer.
- Mixing units such as minutes and hours before calculating a rate.