Heart of Algebra
Linear equations, systems, inequalities, absolute value. Foundation of all SAT Math.
ax + b = c → x = (c − b) / a
System: elimination or substitution
Quick Check: 3x − 7 = 14 → x = 7 (add 7, divide by 3)
Advanced Math
Quadratics, polynomials, rational expressions, function notation & transformations.
Quadratic: x = (−b ± √(b²−4ac)) / 2a
Vertex form: a(x−h)² + k
Quick Check: x²−5x+6=0 → (x−2)(x−3)=0 → x=2 or 3
Problem Solving & Data
Ratios, percents, unit conversion, probability, and data interpretation.
% change = (new−old)/old × 100
P(A) = favorable outcomes / total
Quick Check: $200 increased by 30% → 200 × 1.30 = $260
Geometry & Trig
Area, volume, circles, Pythagorean theorem, SOH-CAH-TOA, special triangles.
sin=opp/hyp · cos=adj/hyp · tan=opp/adj
30-60-90: x, x√3, 2x
Quick Check: Circle x²+y²=r² has center (0,0), radius r
Statistics & Inference
Mean, median, range, standard deviation, correlation, best-fit lines.
Mean = Σx / n
Median = middle value (sorted list)
Quick Check: {2,4,6,8,10} → mean=6, median=6, range=8
Exponential & Complex
Exponential growth/decay, complex numbers (i²=−1), scientific notation.
Growth: P·aⁿ where n=# periods
i²=−1, i³=−i, i⁴=1
Quick Check: (2+3i)(2−3i) = 4+9 = 13 (real!)