Bittinger and Beecher's precalculus book, starting trigonometry with right triangles. Lots of graphing-calculator work and real-data modeling.
Review of foundational algebra: real-number system, integer and rational exponents, polynomial operations, factoring, basic equation solving, rational expressions, and radical notation.
Introduction to the rectangular coordinate system, the function concept, linear functions and slope, equations of lines and modeling, solving linear equations and applications, and linear inequalities.
Increasing/decreasing/piecewise functions, algebra and composition of functions, symmetry, transformations of graphs, and direct/inverse variation.
Complex numbers, quadratic equations and modeling, analyzing quadratic-function graphs, solving rational and radical equations, and absolute-value equations and inequalities.
Polynomial-function modeling and graphing, polynomial division and the remainder/factor theorems, theorems about zeros, rational functions, and polynomial/rational inequalities.
Inverse functions, exponential and logarithmic functions, properties of logarithms, solving exponential and logarithmic equations, and exponential growth/decay applications.
Right-triangle definitions of the trigonometric functions, applications of right-triangle trigonometry, trig functions of any angle, radian measure, circular functions, and sinusoidal graphs.
Pythagorean and sum/difference identities, double-angle and half-angle identities, proving identities, inverse trig functions, and solving trig equations.
Law of sines, law of cosines, complex numbers in trigonometric form, polar coordinates and graphs, vectors, and vector operations.
Systems of equations in two and three variables, matrix methods for solving systems, matrix operations, matrix inverses, and determinants/Cramer's rule.
Parabolas, circles, ellipses, hyperbolas, and nonlinear systems of equations and inequalities.
Sequences and series, arithmetic and geometric sequences, and the binomial theorem.