Mathematics
Mathematics
The Mathematics domain tests practical arithmetic: percentages, ratios and proportions, averages, unit conversions, time-rate-distance problems, perimeter and area, and interpretation of tables or graphs. A calculator may not be allowed, so careful setup and estimation matter more than complex computation.
Core rules
- Identify the quantity asked and label every unit before calculating.
- Percent: part = rate × whole. Percent change = (new − old) ÷ old × 100. A 20% discount multiplies by 0.80; a 20% increase multiplies by 1.20.
- Ratios: set up a proportion with matching units and cross-multiply.
- Average = sum ÷ count. For a weighted average, multiply each group value by its weight, add, then divide by total weight.
- Distance = rate × time. Convert minutes to hours before multiplying by miles per hour.
- Geometry: rectangle area = length × width; triangle area = ½ × base × height; circle area = πr²; circumference = 2πr.
- Follow order of operations and estimate to catch unit errors.
Worked example
A patrol car travels 45 mph for 40 minutes, then 60 mph for 20 minutes. What is the total distance?
Convert: 40 minutes = 2/3 hour; 20 minutes = 1/3 hour. First leg: 45 × 2/3 = 30 miles. Second leg: 60 × 1/3 = 20 miles. Total = 50 miles.
Reasoning check: the common error is treating 40 and 20 as hours, which gives 1,800 + 1,200 miles. Unit conversion prevents that mistake.
Traps that cost marks
Mixing minutes and hours; taking a percent of the wrong base after a discount; confusing “percent more than” with “percent of”; averaging averages without weighting; rounding too early; and misreading a graph's scale or units.