Mathematics
What this section tests
Mathematics questions cover arithmetic with fractions, decimals, and percents; ratios and proportions; basic algebra (solving equations, simplifying expressions); geometry (perimeter, area, angles); and interpreting word problems and simple data.
Concepts to master
- Order of operations: work parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Fractions and decimals: to add or subtract fractions, find a common denominator; to multiply, multiply across; to divide, multiply by the reciprocal.
- Percents: part = percent × whole. Convert percents to decimals by dividing by 100. Percent increase or decrease compares the change to the original amount.
- Ratios and proportions: set up equal fractions and cross-multiply; keep units consistent.
- Algebra: isolate the variable by doing the same operation to both sides; combine like terms first.
- Geometry: know area and perimeter formulas for rectangles, triangles, and circles, and that angles in a triangle sum to 180°.
Traps
- Unit mismatches: minutes versus hours, or centimeters versus meters, cause wrong answers.
- Percent-of-what: a 20% increase then a 20% decrease does not return to the original value.
- Sign errors: subtracting a negative, or distributing a negative across parentheses.
- Answering the wrong question: the problem may ask for the remainder, the total, or a single unit rather than the full amount.
Rule of thumb
Write down what is given and what is asked, convert all units to one system, then estimate the answer before computing. If your result is far from the estimate, recheck your setup.
Example: A shirt costs $40 and is discounted 25%. The discount is 0.25 × 40 = $10, so the sale price is $40 − $10 = $30.