Algebra II – 5 (hrs)
Sep 24, 2020 20201124 13:02Algebra II – 5 (hrs)
Algebra II – 5 (hrs)
Students draw on their foundation of the analogies between polynomial arithmetic and base ten computation, focusing on properties of operations, particularly the distributive property. A starts by asking students to graph the height of a passenger car on a Ferris wheel as a function of how much rotation it has undergone and uses that study to help define the sine, cosine, and tangent functions as functions from all (or most) real numbers to the real numbers. A precise definition of sine and cosine (as well as tangent and the cofunctions) is developed using transformational geometry. This precision leads to a discussion of a mathematically natural unit of measurement for angle measures, a radian, and students begin to build fluency with values of sine, cosine, and tangent, etc. The topic concludes with students graphing the sine and cosine functions and noticing various aspects of the graph, which they write down as simple trigonometric identities.
They extend the domain of exponential functions to the entire real line and then extend their work with these functions to include solving exponential equations with logarithms. They use appropriate tools to explore the effects of transformations on graphs of exponential and logarithmic functions.
Students calculate probabilities based on twoway data tables and interpret them in context. Students are introduced to conditional probability, and the important concept of independence is developed.

Polynomial, Rational, and Radical Relationships
 The Multiplication of Polynomials
 The Division of Polynomials
 Dividing by 𝑥−𝑎 and by 𝑥+𝑎
 The Power of Algebra—Finding Primes
 Radicals and Conjugates
 The Power of Algebra—Finding Pythagorean Triples
 The Special Role of Zero in Factoring
 Overcoming Obstacles in Factoring
 Mastering Factoring
 Graphing Factored Polynomials
 Structure in Graphs of Polynomial Functions
 Modeling with Polynomials—An Introduction
 The Remainder Theorem

Trigonometric Functions
 The Height and CoHeight Functions of a Ferris Wheel
 The Motion of the Moon, Sun, and Stars—Motivating Mathematics
 From Circleometry to Trigonometry
 Extending the Domain of Sine and Cosine to All Real Numbers
 Secant and the CoFunctions
 Graphing the Sine and Cosine Functions
 Basic Trigonometric Identities from Graphs
 Transforming the Graph of the Sine Function
 Using Trigonometric Functions to Model Cyclical Behavior
 Tides, Sound Waves, and Stock Markets
 Graphing the Tangent Function
 Proving Trigonometric Identities
 Trigonometric Identity Proofs

Exponential and Logarithmic Functions

Inferences and Conclusions from Data
 Calculating Probabilities of Events Using TwoWay Tables
 Calculating Conditional Probabilities and Evaluating Independence Using TwoWay Tables
 Events and Venn Diagrams
 Probability Rules
 Distributions—Center, Shape, and Spread
 Using a Curve to Model a Data Distribution
 Normal Distributions
 Using Sample Data to Estimate a Population Characteristic
 Sampling Variability in the Sample Proportion
 Margin of Error When Estimating a Population Proportion
 Sampling Variability in the Sample Mean
 Margin of Error When Estimating a Population Mean
 Evaluating Reports Based on Data from a Sample
 Experiments and the Role of Random Assignment
 Differences Due to Random Assignment Alone