Standard form: \( ax^2 + bx + c = 0 \)

Roots: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Discriminant: \( D = b^2 - 4ac \)

General term: \( T_{r+1} = \binom{n}{r} a^{n-r} b^r \)

Expansion: \( (a + b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r \)

Derivative: \( \frac{d}{dx} (x^n) = nx^{n-1} \)

Integration: \( \int x^n dx = \frac{x^{n+1}}{n+1} + C \)

Limit: \( \lim_{x \to 0} \frac{\sin x}{x} = 1 \)

Distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Circle: \( x^2 + y^2 + 2gx + 2fy + c = 0 \)

Parabola: \( y^2 = 4ax \)

Identity: \( \sin^2 \theta + \cos^2 \theta = 1 \)

Formula: \( \tan(\alpha \pm \beta) = \frac{\tan\alpha \pm \tan\beta}{1 \mp \tan\alpha\tan\beta} \)

Law of Sines: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)

Mean: \( \bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} \)

Variance: \( \sigma^2 = \frac{\Sigma (x_i - \bar{x})^2}{N} \)

Standard Deviation: \( \sigma = \sqrt{\frac{\Sigma (x_i - \bar{x})^2}{N}} \)

\( P(E) = \frac{n(E)}{n(S)} \)

Addition law: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)

Conditional Probability: \( P(A|B) = \frac{P(A \cap B)}{P(B)} \)

Surface area of sphere: \( 4 \pi r^2 \)

Volume of cone: \( \frac{1}{3} \pi r^2 h \)

Volume of cylinder: \( \pi r^2 h \)

Identity: \( (a+b)^2 = a^2 + 2ab + b^2 \)

Identity: \( (a-b)^2 = a^2 - 2ab + b^2 \)

Identity: \( a^2 - b^2 = (a+b)(a-b) \)

n-th term: \( a_n = a + (n-1)d \)

Sum of n terms: \( S_n = \frac{n}{2} [2a + (n-1)d] \)

Sum of n terms (alternate): \( S_n = \frac{n}{2} [a + l] \) where l is last term