Topics covered include, but are not limited, to the following list.
Prerequisite Skills Review - working with Algebraic Expressions
Rules of Exponents, including all types and all operations with Like Bases
Polynomials - Multiplication, Proving Identities, Monomial Division
Long Division of Polynomials and Synthetic Division
Factor and Remainder Theorems
Factoring - all types as review from Algebra(GCF, Difference of Squares, Trinomials)
Factoring by Grouping and Sum and Difference of Two Cubes
Review of Algebraic Fractions - Add/Subtract/Multiply/Divide(A/S/M/D), Solving Equations
Rational Expressions - reducing, A/S/M/D, Solving Equations
Complex Fractions
Recap Quadratic Formula for Solving Equations
Completing the square for Solving Equations
Radical Equations
Recap working with Radicals
Rationalizing the Denominator
Complex Numbers and Working with “i” - including A/S/M/D, Multiplicative Inverse and Division
Use of the Discriminant of a Quadratic Equation
Applications Problems - including Work Problems and Distance Problems
Graphing Calculator Questions for Quadratic Applications - Interpret Vertex and Roots
Completing the Square for Center Radius Form of a Circle
Parent Graphs: f(x) = x, f(x) = x2, f(x) = |x|, f(x) = x3, f(x) = x, f(x) = 1/x, f(x) = 2x
Transformations of Parent Graphs - Translations, Reflections, Vertical and Horizontal Stretches and compressions, mixed transformations, writing equations from graphs
Even and Odd Functions
Vertex Form of a Quadratic including deriving by Completing the Square
Focus and Directrix Derivation of a Parabola
Quadratic/Linear Systems
3x3 Linear Systems, including Deriving Expressions for Quadratics
Polynomials - properties of Graphs, including End Behavior, Real Zeros with Multiplicities, and Complex Zeros
Given a polynomial P(x), factor completely using zeros and, given the zeros, sketch P(x) in an appropriate window to include all intercepts and relative maximum and minimum points
Real-World context problems as applications of Polynomial Function Models
Operations with Functions - A/S/M/D, Composition of Functions
Inverse Functions - all properties and routine for finding f -1(x)
Define Rational Exponents
Apply Rules of Exponents to Rational Exponents, including Solving Equations
Define and describe Exponential Functions
Writing Exponential Functions
Solving Exponential Equations
Converting between Exponential and Logarithmic Forms of an Expression
Properties of Logarithms
Solving Equations Containing Logarithms
Define and Describe Base e and and the Natural Logarithm Function lnx
Exponential and Logarithmic Applications - Modeling Problems
Sequences and Series (Including Summation and Sigma Notation)
Analyzing Arithmetic Sequences and Series
Analyzing Geometric Sequences and Series
Finding Sums of Infinite Geometric Series
Using Recursive Rules with Sequences
Sample Spaces and Probability - Review basic rules including Complements
Conditional Probability - Independent/dependent events, two-way tables and probability
Probability of Disjoint and Overlapping Events
Center, Shape, and Spread of Data
Normal Model - Normal Distribution, using normalcdf on Calculator to determine probabilities
z-scores
Margin of Error and Confidence Intervals
Sampling Variability With Means
Statistically Significant Differences
Hypothesis Testing
Review of Right Triangle Trigonometry and Introduction to Trigonometry in the Coordinate Plane