Preliminaries -- Polynomials -- Exponents -- Rational and radical expressions -- Linear and nonlinear equations -- Linear and nonlinear inequalities -- Absolute value in equations and inequalities -- Analytic geometry -- Functions -- Linear functions -- Transformations and graphs -- Quadratic functions -- Algebra of functions; inverse functions -- Polynomial functions -- Rational functions -- Algebraic functions; variation -- Exponential functions -- Logarithmic functions -- Exponential and logarithmic equations -- Trigonometric functions -- Graphs of trigonometric functions -- Angles -- Trigonometric identities and equations -- Sum, difference, multiple, and half-angle formulas -- Inverse trigonometric functions -- Triangles -- Vectors -- Polar coordinates; parametric equations -- Trigonometric form of complex numbers -- Systems of linear equations -- Gaussian and Gauss-Jordan elimination -- Partial fraction decomposition -- Non-linear systems of equations -- Introduction to matrix algebra -- Matrix multiplication and inverses -- Determinants and Cramer's rule -- Loci; parabolas -- Ellipses and hyperbolas -- Rotation of axes -- Conic sections -- Sequences and series -- The principle of mathematical induction -- Special sequences and series -- Binomial theorem -- Limits, continuity, derivatives.