ISEE Mathematics Achievement: Content and Computation
What the section tests
Mathematics Achievement (Upper Level: 47 questions in 40 minutes) is the content section: arithmetic, fractions/decimals/percents, ratios and proportions, exponents and roots, algebra (linear equations, inequalities, factoring, functions), geometry (angles, triangles, circles, area, volume, Pythagorean theorem, coordinates), measurement and unit conversion, and data and probability (mean, median, mode, range, simple probability, graph reading). No calculator; no penalty for guessing.
Core rules
- Estimate first: answer choices are usually far enough apart that rounding eliminates three of them.
- Back-solve from the choices when an equation looks messy; plug a choice in and check it.
- Keep units attached to every number and convert before combining quantities.
- Answer the quantity asked for. If the question says “what is 3x?”, finding x is a step, not the answer.
Worked example
A jacket priced at $80 is marked down 30%, and the register takes another 10% off the reduced price. What is the final price before tax? Successive percents do not add. The first markdown leaves 70% of $80: 0.70 × 80 = $56. The second discount applies to $56, not to $80: 0.90 × 56 = $50.40. The tempting wrong answer, $48, comes from treating the total discount as 40%.
Traps that cost marks
- Adding percents that apply in sequence (30% then 10% is not 40%).
- Confusing “percent of” with “percent off,” or “increased by 25%” with “is 25% of.”
- Sign errors when distributing a negative: −3(x − 4) = −3x + 12.
- Mixing up area and perimeter, or radius and diameter.
- Long division by habit when estimation would resolve the choice faster.