Topics covered by Infinite Precalculus in suggested order --------------------------------------------------------- Functions Continuity Extrema, intervals of increase and decrease Power functions Average rates of change Transformations of graphs Piecewise functions Operations Inverses Power, Polynomial, and Rational Functions Graphs, real zeros, and end behavior of polynomial functions Dividing polynomial functions The Remainder Theorem and bounds of real zeros Writing polynomial functions and conjugate roots Complex zeros and The Fundamental Theorem of Algebra Graphs of rational functions Rational equations Polynomial inequalities Rational inequalities Exponential and Logarithmic Expressions Graphing exponential functions Exponential equations not requiring logarithms Exponents and logarithms Evaluating logarithms Logarithms and exponents as inverses Properties of logarithms Writing logs in terms of others Exponential equations requiring logarithms Logarithmic equations, simple Logarithmic equations, hard Graphing logarithmic functions Compound interest Trigonometry Angles and angle measure Radians and degrees Right triangle trig: Finding ratios Right triangle trig: Finding angles and sides Trig functions of any angle Graphing trig functions Simple trig equations Inverse trig functions Fundamental identities Equations with factoring and fundamental identities Sum and Difference Identities Multiple-Angle Identities Product-to-Sum Identities Equations and Multiple-Angle Identities The Law of Sines The Law of Cosines Area and Laws of Sines and Cosines Parametric Equations Parametric equations Projectile motion Polar Coordinates Polar coordinates Graphs of polar equations Polar and rectangular forms of equations Polar forms of conic section Complex numbers in polar form Vectors Basics Diagrams Operations Dot products Three-Dimensional Vectors Points in three dimensions Basics Operations Cross products Matrices and Systems Operations Determinants Inverses Cramer's Rule Equations Multivariable linear systems and row operations Partial fraction decomposition Conic Sections Parabolas, graphing & properties Parabolas, writing equations Circles, graphing & properties Circles, writing equations Ellipses, graphing & properties Ellipses, writing equations Hyperbolas, graphing & properties Hyperbolas, writing equations Rotations of conic sections Discrete Mathematics Sample spaces and The Fundamental Counting Principle Permutations Combinations Permutations vs combinations The Binomial Theorem Mathematical induction Probability Probability of independent and dependent events, word problems Probability of independent and dependent events Probability of mutually exclusive events, word problems Probability of mutually exclusive events Probability with permutations and combinations Sequences and Series General sequences Arithmetic sequences Geometric sequences Arithmetic and geometric mean General series Arithmetic series Geometric series Power series Introduction to Calculus Limits by direct evaluation Limits at kinks and jumps Limits at removable discontinuities Limits at essential discontinuities Limits at infinity Definition of the derivative Instantaneous rates of change Power rule for differentiation Motion along a line Approximating area under a curve Area under a curve by limit of sums Indefinite integrals