Algebra II – 12 (hrs)
Nov 06, 2020 20201124 12:42Algebra II – 12 (hrs)
Algebra II – 12 (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 Copy
 The Division of Polynomials Copy
 Dividing by 𝑥−𝑎 and by 𝑥+𝑎 Copy
 The Power of Algebra—Finding Primes Copy
 Radicals and Conjugates Copy
 The Power of Algebra—Finding Pythagorean Triples Copy
 The Special Role of Zero in Factoring Copy
 Overcoming Obstacles in Factoring Copy
 Mastering Factoring Copy
 Graphing Factored Polynomials Copy
 Structure in Graphs of Polynomial Functions Copy
 Modeling with Polynomials—An Introduction Copy
 The Remainder Theorem Copy

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

Exponential and Logarithmic Functions
 Integer Exponents Copy
 Base 10 and Scientific Notation Copy
 Rational Exponents Copy
 Irrational Exponents Copy
 Properties of Exponents and Radicals Copy
 Building Logarithmic Tables Copy
 Properties of Logarithms Copy
 Changing the Base Copy
 Solving Logarithmic Equations Copy
 Rational and Irrational Numbers Copy
 Graphing the Logarithm Function Copy

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