1. Fundamental operations with numbers -- Four operations -- System of real numbers -- Graphical representation of real numbers -- Properties of addition and multiplication of real numbers -- Rules of signs -- Exponents and powers -- Operations with fractions -- 2. Fundamental operations with algebraic expressions -- Algebraic expressions -- Terms -- Degree -- Grouping -- Computation with algebraic expressions -- 3. Properties of numbers -- Sets of numbers -- Properties -- Additional properties -- 4. Special products -- Products yielding answers of the form a"+b" -- 5. Factoring -- Factorization procedures -- Greatest common factor -- Least common factor -- 6. Fractions -- Rational algebraic fractions -- Operations with algebraic fractions -- Complex fractions -- 7. Exponents -- Positive integral exponent -- Negative integral exponent -- Roots -- Rational exponents -- General laws of exponents -- Scientific notation -- 8. Radicals -- Radical expressions -- Laws for radicals -- Simplifying radicals -- Operations with radicals -- Rationalizing binomial denominators -- 9. Simple operations with complex numbers -- Complex numbers -- Graphical representation of complex numbers -- Algebraic operations with complex numbers -- 10. Equations in general -- Operations used in transforming equations -- Equivalent equations -- Formulas -- Polynomial equations -- 11. Ratio, proportion, and variation -- Unit price -- Best buy -- 12. Functions and graphs -- Variables -- Relations -- Functions -- Function notation -- Rectangular coordinate system -- Function of two variables -- Symmetry -- Shifts -- Scaling -- Using a graphing calculator -- 13. Linear equations in one variable -- Linear equations -- Literal equations -- Word problems -- 14. Equations of lines -- Slope of a line -- Parallel and perpendicular lines -- Slope : intercept form of equation of a line -- Slope : point form of equation of a line -- Two-point form equation of a line -- Intercept form of equation of a line -- 15. Simultaneous linear equations -- Systems of two linear equations -- Systems of three linear equations.

16. Quadratic equations in one variable -- Quadratic equations -- Methods of solving quadratic equations -- Sum and product of the roots -- Nature of the roots -- Radical equations -- Quadratic-type equations -- 17. Conic sections -- General quadratic equations -- Conic sections -- Circles -- Parabolas -- Ellipses -- Hyperbolas -- Graphing conic sections with a calculator -- 18. Systems of equations involving quadratics -- Graphical solution -- Algebraic solution -- 19. Inequalities -- Definitions -- Principles of inequalities -- Absolute value inequalities -- Higher degree inequalities -- Linear inequalities in two variables -- Systems of linear inequalities -- Linear programming -- 20. Polynomial functions -- Polynomial equations -- Zeros of polynomial equations -- Solving polynomial equations -- Approximating real zeros -- 21. Rational functions -- Vertical asymptotes -- Horizontal asymptotes -- Graphing rational functions -- Graphing rational functions using a graphing calculator -- 22. Sequences and series -- Sequences -- Arithmetic sequences -- Geometric sequences -- Infinite geometric series -- Harmonic sequences -- Means -- 23. Logarithms -- Definition of a logarithm -- Laws of logarithms -- Common logarithms -- Using a common logarithm table -- Using a natural logarithms table -- Finding logarithms using a calculator -- 24. Applications of logarithms and exponents -- Simple interest -- Compound interest -- Applications of logarithms -- Applications of exponents -- 25. Permutations and combinations -- Fundamental counting principle -- Permutations -- Combinations -- Using a calculator -- 26. The binomial theorem -- Combinatorial notation -- Expansion of (a+x)n -- 27. Probability -- Simple probability -- Compound probability -- Mathematical expectation -- Binomial probability -- Conditional probability -- 28. Determinants -- Determinants of second order -- Cramer's Rule -- Determinants of third order -- Determinants of order n -- Properties of determinants -- Minors -- Value of a determinant of order n -- Cramer's Rule for determinants of order n -- Homogeneous linear equations -- 29. Matrices -- Operations with matrices -- Elementary row operations -- Inverse of a matrix -- Matrix equations -- Matrix solution of a system of equations -- 30. Mathematical induction -- Principle of mathematical induction -- Proof by mathematical induction -- 31. Partial fractions -- Rational fractions -- Proper fractions -- Partial fractions -- Identically equal polynomials -- Fundamental theorem -- Finding the partial fraction decomposition -- 32. Solving higher degree equations -- The iteration method -- The bisection method -- The approximation method -- 33. Algebra for calculus -- Introduction -- Limit of a sequence -- Limit of a series -- Convergence and divergence -- Limit of a function -- Appendix A. Table of common logarithms -- Appendix B. Table of natural logarithms.