ISEE Math Achievement cheat sheet

ISEE Mathematics Achievement - Core Facts and Formulas

• Order of operations: evaluate parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Example: 6 + 2 × 3² = 6 + 18 = 24.

• Percent change = (new − old) ÷ old × 100. A price rising from $40 to $50 is a 25% increase; falling from $50 to $40 is a 20% decrease, because the base changes.

• Percent of a number: convert to a decimal and multiply. 15% of 80 = 0.15 × 80 = 12. To find the whole when given a part, divide: 12 ÷ 0.15 = 80.

• Average (mean) = sum ÷ count. To find a missing value, multiply the mean by the count and subtract the known values: if 4 scores average 85, the total is 340.

• Distance, rate, time: d = rt. Convert units before computing; 45 minutes = 0.75 hour, so 60 mph for 45 minutes covers 45 miles.

• Area formulas: rectangle A = lw; triangle A = ½bh; circle A = πr²; parallelogram A = bh; trapezoid A = ½(b₁ + b₂)h.

• Volume formulas: rectangular solid V = lwh; cylinder V = πr²h. Surface area of a rectangular solid = 2(lw + lh + wh).

• Slope of a line through (x₁, y₁) and (x₂, y₂) is (y₂ − y₁) ÷ (x₂ − x₁). A horizontal line has slope 0; a vertical line has undefined slope.

• Exponent and radical rules: xᵃ · xᵇ = xᵃ⁺ᵇ; xᵃ ÷ xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1 for x ≠ 0; √(ab) = √a · √b.