GA Milestones Math Grade 8 cheat sheet

Grade 8 Mathematics Content Standards

• Rational vs. irrational: a rational number can be written as a fraction of two integers (terminating or repeating decimal); irrational numbers (√2, π, 0.101001000...) have non-terminating, non-repeating decimals.

• Perfect squares 1–144 and perfect cubes 1–125 should be memorized: √121 = 11, ∛64 = 4, ∛125 = 5; use these to estimate irrational roots between consecutive integers.

• Laws of exponents: a^m · a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(mn); a^0 = 1 for a ≠ 0; a^(−n) = 1/a^n.

• Square root of a product: √(ab) = √a · √b, so √50 = √25 · √2 = 5√2; similarly ∛(ab) = ∛a · ∛b.

• Scientific notation: a × 10^n with 1 ≤ |a| < 10; multiply coefficients and add exponents; 0.00042 = 4.2 × 10^(−4).

• Solve linear equations: distribute, combine like terms, then undo operations in reverse order; equations with variables on both sides need variable terms collected on one side.

• Slope formula m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form y = mx + b; a line through (0, b) with slope m rises m units per 1 unit right.

• Proportional relationships graph as straight lines through the origin with equation y = kx; the constant of proportionality k equals the unit rate (y/x).

• Systems of two linear equations: solution is the intersection point; solve by substitution or elimination, and classify as one solution, no solution (parallel), or infinitely many (same line).