Nyack High School

Select topics from the following list will be presented throughout the year.

Unit 1 – Algebraic Essentials Review

1. Variables, Terms, Expressions
2. Solving Linear Equations
3. Common Algebraic Expressions
4. Basic Exponent Manipulation
5. Multiplying Polynomials
6. Using Tables on Your Calculator

 

Unit 2 – Functions as the Cornerstones of Algebra II

1. Introduction to Functions
2. Function Notation
3. Function Composition
4. Domain and Range
5. One-to-One Functions
6. Inverse Functions
7. Key Features of Functions

 

Unit 3 – Linear Functions, Equations, and Their Algebra

1. Direct Variation
2. Average Rate of Change
3. Forms of a Line
4. Linear Modeling
5. Inverses of Linear Functions
6. Piecewise Linear Functions
7. Systems of Linear Equations (3 by 3)

 

Unit 4 – Exponential and Logarithmic Functions

1. Integer Exponents
2. Rational Exponents
3. Exponential Function Basics
4. Finding Equations of Exponentials
5. The Method of Common Bases
6. Exponential Modeling with Percent Growth and Decay
7. Mindful Percent Manipulations
8. Introduction to Logarithms
9. Graphs of Logarithms
10. Logarithm Laws
11. Solving Exponential Equations Using Logarithms
12. The Number "e" and the Natural Logarithm
13. Compound Interest
14. Newton's Law of Cooling

 

 

Unit 5 – Sequences and Series

1. Sequences
2. Arithmetic and Geometric Sequences
3. Summation Notation
4. Arithmetic Series
5. Geometric Series
6. Mortgage Payments

 

Unit 6 – Quadratic Functions and Their Algebra

1. Quadratic Function Review
2. Factoring
3. Factoring Trinomials
4. Complete Factorization
5. Factoring by Grouping
6. The Zero Product Law
7. Quadratic Inequalities in One Variable
8. Completing the Square and Shifting Parabolas
9. Modeling with Quadratic Functions
10. Equations of Circles
11. The Locus Definition of a Parabola

 

Unit 7 – Transformations of Functions

1. Shifting Functions
2. Reflecting Parabolas
3. Vertically Stretching Functions
4. Horizontal Stretching Functions
5. Even and Odd Functions

 

Unit 8 – Radicals and the Quadratic Formula

1. Square Roots Functions
2. Solving Square Roots Equations
3. Basic Exponent Properties
4. More Work with Fractional Exponents
5. More Exponent Practice
6. The Quadratic Formula
7. More Work with the Quadratic Formula

 

Unit 9 – Complex Numbers

1. Imaginary Numbers
2. Complex Numbers
3. Solving Quadratic Equations with Complex Solutions
4. The Discriminant of a Quadratic

 

Unit 10 – Polynomial and Rational Functions

1. Power Functions
2. Graphs and Zeros of Polynomial Functions
3. Creating Polynomial Equations
4. Polynomial Identities
5. Introduction to Rational Functions
6. Simplifying Rational Expressions
7. Multiplying and Dividing Rational Expressions
8. Adding and Subtracting Rational Expressions
9. Complex Fractions
10. Polynomial Long Division
11. The Remainder Theorem
12. Solving Rational Equations
13. Solving Rational Inequalities
14. Reasoning About Radical and Rational Equations

 

Unit 11 – The Circular Functions

1. Rotations and Angle Terminology
2. Radian Angle Measurement
3. The Unit Circle
4. The Definition of the Sine and Cosine Functions
5. More Work with the Sine and Cosine Functions
6. Basic Graphs of Sine and Cosine
7. Vertical Shifting of Sinusoidal Graphs
8. The Frequency and Period of a Sinusoidal Graph
9. Sinusoidal Modeling
10. The Tangent Function
11. The Reciprocal Functions

 

Unit 12 – Probability

1. Introduction to Probability
2. Sets and Probability
3. Adding Probabilities
4. Conditional Probability
5. Independent Events
6. Multiplying Probabilities

 

 

 

 

 

 

 

Unit 13 – Statistics

1. Variability and Sampling
2. Population Parameters
3. The Normal Distribution
4. Normal Distribution Z-Scores
5. Sample Means
6. Sample Proportions
7. The Difference in Samples Means
8. The Distribution of Sample Means
9. The Distribution of Sample Proportions
10. Margin of Error
11. Linear Regression
12. Other Types of Regression