Algebra II & Trigonometry - Regents

Course Topics

*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

Review for Regents Exam