Students judge the validity of an argument based on whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. Students know the laws of exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. Students use the definition of logarithms and the product formula for logs to translate between logarithms in any bases. Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and identify their approximate values. Students determine if a specific algebraic statement involving rational expressions, radical expressions, logarithmic or exponential functions, is sometimes true, always true, or never true.
Students can then graph the equation.
Students use fundamental counting principles to compute combinations and permutations. Students use combinations and permutations to compute probabilities. Students know the Binomial Theorem and use it to expand binomial expressions which are raised to positive integer powers. Students apply the method of mathematical induction to prove general statements about the positive integers. Students find the general term and the sums of arithmetic series and both finite and infinite geometric series.