Symbols and Expressions

• Polynomial expressions

• Rational expressions

• Arithmetic and finite geometric series

 Linear Equations

• Real numbers as points on the number line

• Linear equations and their graphs

• Solving problems with linear equations

• Linear inequalities and their graphs

• Graphing and solving systems of simultaneous linear equations

 Quadratic Equations

• Completing the square in quadratic expressions

• Factors and factoring of quadratic polynomials with integer coefficients

• Quadratic formula and factoring of general quadratic polynomials

• Using the quadratic formula to solve equations

 Functions

• Linear functions

• Quadratic functions—word problems involving quadratic functions

• Graphs of quadratic functions and completing the square

• Polynomial functions (including graphs of basic functions)

• Simple nonlinear functions (e.g., square and cube root functions; absolute value; rational functions; step functions)

• Rational exponents, radical expressions, and exponential functions

• Logarithmic functions

• Trigonometric functions

• Fitting simple mathematical models to data

 Algebra of Polynomials

• Roots and factorization of polynomials

• Complex numbers and operations

• Fundamental theorem of algebra

• Binomial coefficients (and Pascal’s Triangle)

• Mathematical induction and the binomial theorem

 Combinatorics and Finite Probability

• Combinations and permutations, as applications of the binomial theorem and Pascal’s Triangle