Summary Math flash cards

12th Grade Math Flashcards

Algebra & Functions
 Quadratic Formula: x = [-b ± √(b²-4ac)] / 2a
 Factoring: a² - b² = (a-b)(a+b)
 Function Composition: (f∘g)(x) = f(g(x))
 Inverse Functions: f⁻¹(x) such that f(f⁻¹(x)) = x
Trigonometry
 SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
 Pythagorean Identity: sin²θ + cos²θ = 1
 Double Angle Formulas: sin2θ = 2sinθcosθ, cos2θ = cos²θ - sin²θ
Calculus
 Derivative Definition: f’(x) = lim(h→0) [f(x+h)-f(x)] / h
 Power Rule: d/dx [x^n] = nx^(n-1)
 Product Rule: (uv)’ = u’v + uv’
 Quotient Rule: (u/v)’ = (u’v - uv’) / v²
 Chain Rule: d/dx [f(g(x))] = f’(g(x))·g’(x)
 Integral Rules: ∫x^n dx = x^(n+1)/(n+1) + C (n≠-1)
Probability & Statistics
 Mean: sum of values / number of values
 Standard Deviation: σ = √(Σ(x-μ)² / N)
 Probability: P(E) = favorable outcomes / total outcomes
 Combinations: nCr = n! / [r!(n-r)!]
 Permutations: nPr = n! / (n-r)!
Additional Topics
 Logarithms: log_b(a) = c → b^c = a
 Exponential Functions: y = a·b^x
 Sequences & Series: Arithmetic: a_n = a_1 + (n-1)d, Sum =
n/2(a_1+a_n); Geometric: a_n = a_1·r^(n-1), Sum = a_1(1-r^n)/(1-r)