Mathematics
What This Section Tests
Mathematics covers arithmetic, fractions and decimals, percents, basic algebra, geometry, and measurement. Most problems are multi-step, so setup matters as much as calculation.
Concepts to Know
- Fractions and decimals: find a common denominator to add or subtract; multiply straight across; invert and multiply to divide.
- Percents: part = percent × whole; percent change = (change ÷ original) × 100.
- Algebra: isolate the variable by doing the same operation to both sides. Distribute before combining like terms.
- Geometry: area of a rectangle = length × width; triangle = ½ × base × height; circle = πr². Perimeter is distance around; area is space inside.
- Order of operations: parentheses, exponents, multiply/divide, add/subtract.
Traps to Watch
- Mixing perimeter and area. They use different units and different formulas.
- Forgetting to distribute. 3(x + 4) = 3x + 12, not 3x + 4.
- Percent-of vs. percent-change. Read which one is asked.
- Sign errors when subtracting negatives or moving terms across the equals sign.
Rule of Thumb
Write down what you are solving for before computing. Label units at every step; mismatched units usually reveal a setup error early.
Worked example: Solve 2(x − 3) = 10. Distribute: 2x − 6 = 10. Add 6 to both sides: 2x = 16. Divide by 2: x = 8. Check by substituting: 2(8 − 3) = 2(5) = 10. ✓
For geometry word problems, sketch the figure and mark the given values - it prevents using the wrong dimension. Estimate the answer first so a calculation slip stands out.