Arithmetic Series
\$u_n = a + (n – 1)d\$
\$S_n = 1/2n(a + l) = 1/2n[2a + (n – 1)d]\$

Geometric Series
\$u_n = ar^{(n – 1)}\$
\$S_n = {a{(1-r^n)}}/{1-r}\$
\$S_∞ = a/{1-r}\$ for |r| < 1

Trigonometric identities
\$sin(A±B) ≡ sin A cos B ± cos A sin B\$
\$cos(A±B) ≡ cos A cos B ∓ sin A sin B\$
\$tan(A±B) ≡ {tan A + tan B}/{1 ∓ tanA tanB}\$
\$sin A + sin B ≡ 2 sin {A + B}/2 cos{A - B}/2\$
\$sin A - sin B ≡ 2 cos {A + B}/2 sin{A - B}/2\$
\$cos A + cos B ≡ 2 cos {A + B}/2 cos{A - B}/2\$
\$cos A - cos B ≡ -2 sin {A + B}/2 sin{A - B}/2\$

Statistics - Probability
\$P(A∪B) = P(A) + P(B) − P(A∩B)\$
\$P(A∩B) = P(A) P(B|A)\$
\$P(A|B) = {P(B|A) P(A)}/P(B|A)P(A) + P(B|A')P(A')\$

\$ax^2 + bx +c = 0\$ has either one or two solutions
\$\$x = {-b±√{(b^2 − 4ac)}/{2a} \$\$
Points and lines
Given two points in a plane P = \$(x_1, y_1), Q = (x_2, y_2)\$, you can find the following information
1. Distance between the two points \$\$d(P,Q) = √{{(x_2-x_1)}^2 + {(y_2-y_1)}^2}\$\$
2. The coordinates of the midpoint between them,\$\$ M =({x_1+x_2}/2, {y_1+y_2}/2)\$\$
3. The slope of the line through them, \$\$m = {(y_2 - y_1)}/{(x_2 - x_1)} = {rise}/{run} \$\$
Lines can be represented in three different ways,
1. Standard form = \$ax + by = c\$, where a, b and c are real numbers
2. Slope-intercept form = \$y = mx + b\$, where m is the slope and b is the y-intercept
3. Point-Slope form = \$y-y_1= m (x-x_1)\$, where (x_1, y_1) is any fixed point on the line
Area
Parallelogram = bh where b = base and h = height
Trapezoid = \${h/2}(b_1 + b_2)\$
Ellipse = \$πr_1r_2\$
Triangle = \$1/2bh\$
Equilateral Triangle = \${√3/4}a^2\$
Triangle given a,b,c = \$√{s(s-a)(s-b)(s-c)}\$ when s = \$(a+b+c)/2\$ (Heron's formula)

Volume
Cylinder = \$πr^2h\$
Cone = \$1/3πr^2h\$
Sphere = \$4/3πr^3\$
Ellipsoid = \$4/3πr_1r_2r_3\$

Surface Area
Surface area of sphere = \$4πr^2\$
Area of curved surface of cone = \$πr x \$ slant height

Algebraic Identities
\${(x + y)}^2 = x^2 + 2xy + y^2\$, Square of a sum
\${(x - y)}^2 = x^2 - 2xy + y^2\$, Square of a difference
\${(x + y)}^3 = x^3 + 3x^2y + 3xy^2 + y^3\$, Cube of a sum
\${(x - y)}^3 = x^3 - 3x^2y + 3xy^2 - y^3\$, Cube of a difference
\${(x + y)}^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4\$, To the power four of a sum
\${(x - y)}^4 = x^4 - 4x^3y + 6x^2y^2 - 4xy^3 + y^4\$, To the power four of a difference

Factoring Formulas
\$x^2 - y^2 = (x + y)(x - y)\$, Difference of squares
\$x^3 - y^3 = (x - y)(x^2 + xy + y^2)\$, Difference of cubes
\$x^3 + y^3 = (x + y)(x^2 - xy + y^2)\$, Sum of cubes

Exponentiation rules
For any real numbers a and b, and any rational numbers \$p/q\$ and \$r/s\$, \$a^{p/q}a^{r/s} = a^{{p/q}+{r/s}} = a ^{ps+qr}/{qs}\$, Product rule
\$a^{p/q} / a^{r/s} = a^{{p/q}-{r/s}} = a ^{ps-qr}/{qs}\$, Quotient rule
\${(a^{p/q})}^{r/s} = a^{{pr}/{qs}}\$, Power of power rule
\${(ab)}^{p/q} = a^{p/q}b^{p/q}\$, Power of product rule
\${(a/b)}^{p/q} = a^{p/q}/b^{p/q}\$, Power of quotient rule
\${a^0} = 1\$, Zero exponent
\${a^{−{(p/q)}}} = 1/{a^{(p/q)}}\$, Negative exponents
\${1/{a^{−{(p/q)}}}} = {a^{(p/q)}}\$, Negative exponents
\$√^q{a} = a^{1/q}\$
\$√^q{a^p} = a^{p/q} = {(a^{1/q})}^p\$