Algebra 2 Syllabus
High School for Enterprise, Business and Technology
850 Grand Street, Brooklyn, NY 11211 Tel 7183872800
Principal: Mr. Carrillo Asst. Principal: Mrs. Eboras
Mathematics Department  Common Core Algebra 2 Curriculum 202223
Course Philosophy/Description
Common Core Algebra 2 is the capstone course of the three units of credit required for a Regents diploma. This course is a continuation and extension of the two courses that preceded it. Algebra 2 continues the students’ study of advanced algebraic concepts including functions, polynomials, rational expressions, systems of functions and inequalities. While developing the algebraic techniques that will be required of those students that continue their study of mathematics, this course is also intended to continue developing alternative solution strategies and algorithms.
Within this course, the number system will be extended to include imaginary and complex numbers. The families of functions to be studied will include polynomials, absolute value, radical, trigonometric, exponential, and logarithmic functions. Students will be expected to describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relations and use those representations to solve problems. Emphasis will be placed on practical applications and modeling. Students extend their knowledge and understanding by solving open ended realworld problems and thinking critically through the use of high level tasks.
Students will be expected to demonstrate their knowledge in: utilizing essential algebraic concepts to perform calculations on polynomial expression; performing operations with complex numbers and graphing complex numbers; solving and graphing linear equations/inequalities and systems of linear equations/inequalities; solving, graphing, and interpreting the solutions of quadratic functions; solving, graphing, and analyzing solutions of polynomial functions, including complex solutions; manipulating rational expressions, solving rational equations, and graphing rational functions; solving logarithmic and exponential equations; and solving equations.
Standards Key
Common Core  Algebra II Curriculum Map 202223
TOPIC 
Skills, Strategies & Concept 
Linked Common Core Standards 
Students will be able to: 
Unit 1 

Review Lessons Equations and Inequalities (5 Days) 
Variables, Like Terms, and Expressions  Solving Linear Equations Common Algebraic Expressions Basic Exponent Manipulation  Multiplying Polynomials  Exponents 
ACED.1 NRN.2 ASSE.2 

Unit 2 

Intro to Functions (10 Days) 
 Intro to functions
Function Notation Function Composition Domain and Range One to One Functions
Inverse Functions Key Features of Functions

FIF.7c FIF.3 FBF.1b  Embedded in NQ.2 everything FBF.4a FIF.9 FIF.4 FBF.3 

Linear Functions, Equations, and their Algebra (7 Days) 
 Direct Variation Average Rate of Change Forms of a line
Linear Modeling Inverses of Linear Functions 
FIF.6 FLE.2 FLE.5 FBF.4 AREI.11 AREI.6 

Unit 3 

Quadratic Functions (16 Days) 
 Features of Quadratic Functions Factoring
Factoring Trinomials ( a=1, a>1) Complete factoring
Factoring by Grouping The Zero Product Law Quadratic Inequalities in One Variable
Completing the Square and Shifting Parabolas  Modeling with Quadratic Functions Equations of Circles
The Locus definition of a Parabola

FIF.4 A.SSE.2 A.SSE.2 A.SSE.2 A.SSE.2 A.APR.3 AREI.4b ACED.1 FBF.3 ACED.1 AREI.7 GGPE.2 

Unit 4 

Complex Numbers (10 Days) ***Potential to be shorter*** 
Define and use the imaginary unit i. Add, subtract, and multiply complex numbers. Find complex solutions and zeros. Imaginary Numbers Complex Numbers Solving Quadratic Equations with Complex Solutions The Discriminant of a Quadratic SPED Strategies: Relate the idea of adding, subtracting and multiplying complex numbers to whole numbers. Explain the background of complex numbers and connect to real life by explaining how they are used in electrical circuits. Use the example of the cyclical nature of the ones digit in the powers of 3 and connect it to the cyclical nature of the powers of i. Develop a reference document with students with verbal and pictorial descriptions. ELL Strategies: Discuss how to determine whether two complex numbers are equal. Explain that you want to add two complex numbers. “What would make sense for (6 + 3i) + (2 − 5i)? Describe and explain orally and in writing how to use properties of operations to add, subtract, and multiply complex numbers in the student’s native language and/or use selected technical vocabulary in phrases and short sentences with equations to explain the solution. Encourage students to highlight like terms  use one color for the real parts and another color for the imaginary parts. Make a table with the words: Imaginary Unit, Complex Number and Imaginary Number, then write an example for each word in the column. 
NCN.1 NCN.1,2 AREI.4 NCN.7 AREI.2 AREI.4 
What are the subsets of the set of complex numbers? What are the subsets of the set of complex numbers? Give an example of a number in each subset. Is it possible for a number to be both whole and natural? natural and rational? rational and irrational? real and imaginary? Explain your reasoning. What does the graph of f(x) = 4x2 + 20 look like?” 
Unit 5 

Radicals and the Quadratic Formula (13 Days) 
 Square Root Functions Solving Square Root Equations The Basic Exponent Properties Fractional Exponents Revisited More Exponent Practice The Quadratic Formula More work with the Quadratic Formula 
FIF.4 AREI.2 NRN.2 NRN.1,2 NRN.2 AREI.4b AREI.4b 

Unit 6 

Exponential Functions (10 days) 

IF.B.5, LE.A.1, A.1.C, LE.A.3, LE.B.5 

Unit 7 

Polynomials (14 Days) 
 Power Functions Graphs and Zeroes of a Polynomial Creating Polynomial Equations Polynomial Identities Intro to Rational Functions Simplifying Rational Expressions Mult./Div. Rational Expressions Add./Sub. Rational Expressions Complex Fractions 
FIF.4 FBF.3 AAPR.3 FIF.4 FIF.7 FIF.7 AAPR.4 FIF.4 AAPR.6 AAPR.6 AAPR.6 AAPR.6 

Unit 8 

Rational Functions (9 Days) 
Polynomial Long Division The Remainder Theorem  Synthetic Division *** ADDITIONAL Solving Rational (Fractional) Equations Solving Rational Inequalities Reasoning about Radical and Rational Equations 
AAPR.6 AAPR.2 AAPR.6 AREI.2 ACED.1 AREI.1 

Unit 9 

Logarithmic Functions 
Intro to logarithms Graphs of logarithms  Logarithm Laws
Solving Exponential Equations with Logarithms The number e and natural logarithms Compound Interest  Realworld Applications 
FIF.4 FIF.7e FLE.4 FLE.4 FIF.8 FBF.1a ASSE.3 FBF.1b 

Unit 10 

Trigonometry (15 Days) 
Rotations and Angle Terminology Radian Angle Measurement
Unit Circle
Def. of Sine and Cosine Functions
More Sine and Cosine Functions Basic Graphs of Sine and Cosine Vertical Shifting of Sine Graphs
Frequency and Period of Sine Graphs
Sine Modeling
Tangent Function
Reciprocal Functions

FTF.1 FTF.2 FTF.2 FTF.8 FTF.2 FTF.8 FTF.5 FIF.7e FTF.5 FIF.7e FTF.5 FIF.7e FTF.5 FIF.7e FTF.8 FTF.8 

Unit 11 

Sequence and Series (7 Days) 
 Sequences Arithmetic and Geometric Sequences Summation Notation Arithmetic Series Geometric Series  RealWorld Applications 
FIF.3 FBF.2 FBF.2 FLE.2 ASSE.4 ASSE.4 ASSE.4 

Unit 11 

Probability (8 Days) 
 Intro to Probability Sets and Probability
Adding Probabilities Conditional Probabilities Independent and dependent probabilities
Multiplying Probabilities 
SCP.1 SCP.7 SCP.3, SCP.4, SCP.5, SCP.6 SCP.2, SCP.4, SCP.5, SCP.2, SCP.4 

Statistics (10 Days) 
 Variability and Sampling
Population parameters The Normal Distributions (Calculator) The Normal Distribution and ZScores Sample Means Sample Proportions The Difference in Sample Means
Linear Regression and Lines of Best Fit
 Other Types of Regression
Margin of Error 
SIC.3 SID.4 SID.4 SIC.1, SIC.2 SIC.5 SIC.1 SIC.4 SIC.5 SID.6a SID.6a 
