ISEE Middle Level: Mathematics Achievement: Core Skills and Accuracy

What Mathematics Achievement tests

The ISEE Middle Level Mathematics Achievement section has 47 questions in 40 minutes, with no calculator. Content includes fractions, decimals, percents, ratios, proportions, algebraic expressions and equations, geometry, the coordinate plane, statistics, and probability.

Core rules

• Order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.
• Percent change = (new − old) / old × 100. "Increased by 20%" means multiply by 1.20; "increased to 120" means the final value is 120.
• For proportions, set corresponding units in the same positions and cross-multiply.
• Geometry: area of a triangle = ½bh; circle area = πr²; circumference = 2πr; volume of a rectangular prism = lwh. Keep units consistent.
• Mean = sum ÷ count; median = middle value after ordering; mode = most frequent value.

Worked example

A jacket costs $80. Its price is reduced by 25%, and then the sale price is reduced by another 10%. What is the final price? After 25% off: 80 × 0.75 = 60. After another 10% off: 60 × 0.90 = 54. The final price is $54. The discounts are successive, not additive; a 35% single discount would give $52, which is wrong.

Traps

• Adding successive percent discounts.
• Confusing perimeter and area, or using diameter instead of radius.
• Solving for x but selecting the value of a different expression.
• Dropping negative signs when distributing.