ALEKS Math cheat sheet

Slope between two points: m = (y2 - y1)/(x2 - x1); horizontal line m = 0, vertical line m is undefined.

Point-slope form: y - y1 = m(x - x1); slope-intercept form: y = mx + b; standard form: Ax + By = C.

Quadratic formula: x = (-b ± sqrt(b^2 - 4ac))/(2a); discriminant b^2 - 4ac > 0 gives two real roots, = 0 gives one, < 0 gives none.

Laws of exponents: a^m * a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn); a^(-n) = 1/a^n; a^0 = 1 for a != 0.

Log rules: log(ab) = log a + log b; log(a/b) = log a - log b; log(a^n) = n log a; log_b(x) = ln x / ln b.

Percent change = (new - old)/old * 100; percent increase of p multiplies by (1 + p/100), decrease by (1 - p/100).

Distance and midpoint: d = sqrt((x2-x1)^2 + (y2-y1)^2); midpoint = ((x1+x2)/2, (y1+y2)/2).

Circle: area = pir^2, circumference = 2pi*r; triangle area = (1/2)bh; Pythagorean theorem a^2 + b^2 = c^2 for right triangles.

Order of operations: parentheses, exponents, multiplication/division left to right, then addition/subtraction left to right.

Mole conversions: moles = mass (g) / molar mass (g/mol); particles = moles * 6.022 x 10^23.

Molarity M = moles of solute / liters of solution; dilution: M1V1 = M2V2.

Ideal gas law PV = nRT with R = 0.08206 Latm/(molK); temperature must be in kelvin (K = °C + 273.15).

pH = -log[H+]; pOH = -log[OH-]; pH + pOH = 14 at 25 °C; [H+][OH-] = 1.0 x 10^-14.

Percent yield = (actual yield / theoretical yield) * 100; limiting reactant is the one producing the least product.

Balancing requires equal atoms of each element on both sides; coefficients give mole ratios for stoichiometry.

Significant figures: nonzero digits count; zeros between nonzero digits count; leading zeros never count; trailing zeros count only with a decimal point.

Density = mass / volume; Avogadro's number of any gas occupies 22.4 L at STP (0 °C, 1 atm).

Oxidation is loss of electrons, reduction is gain; in a redox reaction the oxidizing agent is itself reduced.