Mathematics
What this domain tests
The Mathematics section samples arithmetic, fractions and decimals, percentages, ratios and proportions, basic algebra, measurement, and geometry. Most items are short word problems, so translation from English to an equation matters as much as calculation.
Core rules
- Follow order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.
- Convert fractions, decimals, and percents to one form before comparing; 'of' usually means multiply and 'per' means divide.
- In a linear equation, distribute first, then collect variable terms on one side and constants on the other.
- Label units and check that the answer is reasonable. Area is square units; perimeter is linear units.
- For a rectangle, area = length × width and perimeter = 2(length + width).
Worked example
Solve 3(x − 2) = 2x + 7. Distribute: 3x − 6 = 2x + 7. Subtract 2x from both sides: x − 6 = 7. Add 6: x = 13. Check: 3(13 − 2) = 33; 2(13) + 7 = 33. Correct.
Traps
- Dropping the negative sign when distributing, as in −2(x − 5).
- Adding numerators and denominators separately for fractions.
- Multiplying by a percent without converting it to a decimal first.
- Mixing units, such as centimeters and meters, without converting.
- Solving for x but answering a different quantity the question asks for.