ISEE Mathematics Achievement
The ISEE Mathematics Achievement domain tests direct computation and concept recall across arithmetic, algebra, geometry, measurement, and data analysis. Unlike Quantitative Reasoning, which favors multi-step logic puzzles, these questions ask you to recognize a procedure and execute it accurately without a calculator. Accuracy and formula recall matter more than clever shortcuts.
Core rules and concepts
- Convert freely among fractions, decimals, and percents; distinguish percent of, percent increase, and percent decrease.
- Apply order of operations, exponent rules, and inverse operations when solving equations and inequalities. Reverse the inequality symbol when multiplying or dividing by a negative number.
- Memorize geometry formulas: triangle angle sum, Pythagorean theorem, area and perimeter of polygons, circumference and area of circles, and volume of rectangular prisms and cylinders.
- Know vocabulary such as sum, product, quotient, consecutive integers, complementary (90°), and supplementary (180°) angles. For coordinate geometry, use slope = rise/run and y = mx + b.
- For data, compute mean, median, mode, and range, and use probability = favorable outcomes / total outcomes.
- Set up ratios and proportions carefully, labeling units so conversions cancel.
Worked example
After a 20% discount, a jacket costs $80. What was the original price? Let P be the original price. A 20% discount means you pay 80% of P, so 0.80P = 80. Divide both sides by 0.80: P = 100. Check: 20% of $100 is $20, and $100 − $20 = $80. The common wrong move is 80 × 1.20 = 96; that adds 20% to the sale price instead of reversing a discount taken from the original.
Traps that cost marks
- Reversing percent changes by adding the same percent to the result.
- Using a diameter as a radius in circle formulas.
- Forgetting that inequalities flip when you multiply or divide by a negative.
- Giving area when the question asks for perimeter, or leaving units mismatched.
- Choosing a distractor produced by one arithmetic slip; estimate first to eliminate impossible sizes.