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 
MultipleAngle Identities 
ProducttoSum Identities 
Equations and MultipleAngle 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 
ThreeDimensional 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 
