Common Core Algebra 2 H– 3310
Grades 10 or 11
Prerequisite: Completion of Common Core Geometry R/H
Full year - 1 credit
The New York State Common Core Algebra 2, together with selected enrichment topics, constitutes the course
content for this honors class. Instructional units include: polynomials, rational expressions, quadratics and their
applications, factoring polynomial expressions, geometric and arithmetic sequences, infinite geometric series,
transformational properties, trigonometry, logarithmic applications, statistical measures of dispersions,
characteristics of normal distributions, and theoretical probabilities. Within this honors course, topics will be
studied in greater depth and detail. A graphing calculator (TI84+) will be used extensively in this course. This
class will prepare students to take the Common Core Algebra 2 Regents examination.
General Department Philosophy
The Garden City Mathematics Department presents courses that align with either the New York State Common
Core curriculum or the College Board’s Advanced Placement curriculum. In either case, the course material
prepared by the Department (Grades 6 – 12) is fully consistent with these standards. In particular, our
Advanced Placement syllabi have been approved by the College Board. Our Regents courses address the five
NYS common core content strands as well as the five process strands. Our instructional activities are created to
promote written and verbal mathematical communication and critical thinking skills that employ accurate
mathematical ideas. The Department develops student assessments that are also consistent with the New York
State and/or College Board assessment in both style and content. The scoring rubrics employed by the
Department are modeled after the particular associated scoring guides. Additional information about the NYS
Common Core Mathematics program can be found at https://www.engageny.org/resource/high-school-algebraii and Advanced Placement program at http://apcentral.collegeboard.com.
Members of the Department encourage their students to explore, discover and question the many fundamental
concepts developed within each courses. The primary objective is to engage our students in lessons that are
meaningful, inspiring and enjoyable and promote a greater interest in mathematics – at the post secondary level
and beyond. Technology applications, such as calculator usage, are incorporated as developmentally
appropriate and as specified by the NYS and/or College Board curriculum. The Department wants each student
to realize that they can make a contribution to their class and that others can benefit from their input. The
Department wants all students to maximize their mathematical potential as we move through the challenging
curriculum and prepare to master all course requirements.
General Skills
Polynomials
Factoring
Operations with Polynomials
Long Division
The Remainder Theorem
Greatest Common Factor (GCF)
Difference of Two Squares (DOTS)
Trinomial factoring
Factoring by Grouping
Factoring Sum/Difference of Two Perfect Cubes
Proving Polynomial Identities
Rational
Expressions
Simplify Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Complex Fractions
Solving Rational Equations
Solving Rational Inequalities
Word Problems with Rational Equations
Functions
Determine when a Relation is a Function
Determine if a Function is 1-1 and/or ONTO
Determine the Domain and Range of a Function
Transformations with Functions
Composition of Functions
Operations with Functions
Odd and Even Functions
Determine the Inverse of a function and Proving two Functions are Inverses
Using Direct & Inverse Variation Principles to Solve Problems
Key Features of Functions (zeros, relative max/min, end behavior, …)
Quadratics
Solving Quadratics by Factoring
Solving Quadratics by Completing the Square
Solving Quadratics using the Quadratic Formula
Solving Quadratic Inequalities
Vertex Form of a Quadratic
Quadratic Applications
Equation of a Circle
Focus and Directrix of a Parabola
Imaginary Numbers
Complex Numbers
Solving Quadratic Equations with Complex Roots
The Discriminant and Nature of the Roots
Sum and Product of the Roots
Writing an Equation given the Roots
Exponents
Laws of Exponents
Rational Exponents
Finding Equations of Exponential Functions
Exponential Modeling
Equations with Fractional Exponents
Solving Exponential Equations
Radicals
Using the operations of addition, subtraction, multiplication and division
within the context of radicals.
Solving equations involving radicals.
Logarithms
Graph of a Logarithm
Log form -- exponential form and vice-versa
Laws of logarithms
Common logs
Anti-logarithms
Undefined logarithms
Natural logarithms -- using e and ln
Solving Exponential Equations using Logs
Solving log equations using log rules
Simple and compound interest applications with logs
Sequences and Arithmetic and Geometric Sequences/Series
Summation Notation
Series
Derive the formula for the sum of a finite geometric series.
Find the sum of an infinite geometric series.
Trigonometric Understanding the components of the unit circle.
Angles as Rotations
Functions
Using reference angles to determine trigonometric values.
Converting angles into radian measure and vice-versa.
Finding remaining trigonometric function values when only one is given.
Trigonometry of a right triangle
Unit circle applications and demonstrations
Reciprocal trigonometric functions
Reference angles
Trigonometric values of special angles (0, 30, 45, 60, 90, 180, 270, 360
degrees)
Radian measure
Co-function relationships
Trigonometric Graphs of sine, cosine and tangent functions
Graphs of reciprocal trigonometric functions (secant, cosecant and
Graphs
cotangent).
Graphs of inverse trigonometric functions -- restricted domain considered.
Transformations of Trig Graphs
Graph Properties of Trig Graphs – Amplitude, Frequency, Period
Sinusoidal Modeling
Probability
Theoretical and Experimental Probability
Sets and Probability
Conditional Probability
Independent and Dependent Events
Binomial Probability
Statistics
Variability and Sampling
Population Parameters
The Normal Distribution and Z Scores
Sample Means
Sample Proportions
Regression and Correlation
Measures of central tendencies
Terms: mean, range, variance, standard deviation, etc.