Mathematics
Mathematics is the third domain of the NES Essential Academic Skills exam. It covers number and operations, algebraic thinking, geometry and measurement, and data analysis and probability. Items test procedural fluency and the ability to choose an appropriate strategy, often in multistep word problems.
Core rules
- Order of operations: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.
- Fractions: find common denominators for addition and subtraction; multiply straight across; divide by multiplying by the reciprocal.
- Ratios and proportions: set up equivalent ratios and cross-multiply; label units.
- Percent change: change divided by original times 100%. Successive percent discounts multiply; they do not add.
- Linear equations: isolate the variable by inverse operations; slope equals (y2 minus y1) divided by (x2 minus x1).
- Geometry: use area and perimeter formulas; volume of a rectangular prism is length times width times height; the Pythagorean theorem is a squared plus b squared equals c squared.
- Data: mean is sum divided by count; median is the middle value after ordering; mode is the most frequent value.
Worked example
A jacket costs $80. It is discounted 25%, then an additional 10% is taken off the sale price. What is the final price? Reasoning: After 25% off, pay 75%: 80 times 0.75 equals 60. The second discount applies to $60: 60 times 0.90 equals 54. The final price is $54. Trap: adding 25% and 10% to get 35% and computing 80 times 0.65 equals 52, which incorrectly applies both discounts to the original price.
Traps that cost marks
- Adding successive percents instead of multiplying discount factors.
- Misreading "percent of" versus "percent more than."
- Forgetting to convert units before calculating.
- Rounding too early in multistep problems.
- Confusing mean and median when data are skewed.