Algebra 2 A and B

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