Mathematics and Numerical Reasoning
What this domain measures
The mathematics items test practical arithmetic rather than abstract algebra: fractions, decimals, percentages, ratios and proportions, unit conversion, rate problems, averages, and multi-step word problems framed around apparatus, hose, water supply, staffing, and supply costs. A basic on-screen or supplied calculator may be available, but most marks turn on setting the problem up correctly.
Core rules
- Order of operations: parentheses, exponents, multiplication and division left to right, then addition and subtraction.
- Fractions: convert to a common denominator before adding or subtracting; multiply straight across; divide by multiplying by the reciprocal.
- Percent change uses the original value as the base. A rise from 40 to 50 is 10 divided by 40, or 25 percent, not 20 percent.
- Rate problems: quantity equals rate times time. Rearrange before you compute so the units you want are the ones left over.
- Unit conversion: write the conversion as a fraction and cancel units. Gallons per minute times minutes gives gallons.
- Averages: total divided by count. To find a missing value, multiply the average by the count and subtract the known values.
- Ratios and proportions: set two equal fractions with matching units in matching positions, then cross-multiply.
Worked example
A 750-gallon booster tank is three-fifths full. A line flowing 90 gallons per minute is opened. How long until the tank is empty?
Step 1 - find the water on board: three-fifths of 750 equals 750 divided by 5, then times 3, which is 450 gallons. Step 2 - apply the rate: time equals quantity divided by rate, so 450 divided by 90 equals 5 minutes. Step 3 - sanity check: 90 gallons per minute for 5 minutes is 450 gallons, which matches. The empty answer of 8.3 minutes comes from dividing the full 750 gallons and forgetting the tank was partly empty.
Traps that cost marks
- Answering the wrong quantity: the amount used instead of the amount remaining.
- Mixing minutes and hours inside one calculation without converting.
- Rounding mid-problem and then rounding again at the end.
- Forgetting that percent decrease and percent increase use different bases.