Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. 12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. 13.0 Students use the definition of logarithms to translate between logarithms in any base. Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. 15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.
Students can then graph the equation.
18.0 Students use fundamental counting principles to compute combinations and permutations. 19.0 Students use combinations and permutations to compute probabilities. 20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. 21.0 Students apply the method of mathematical induction to prove general statements about the positive integers. 22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.