Algebra II Semester 2 (Honors)

Required Material:

This course requires practice on GeoGebra and/or Desmos. These are both online free tools. In addition Graph paper may be needed for assignments.

Syllabus:

Section 1: Radical Functions

This section introduces radical functions and their relationship to rational exponents. Mathematics operations on radical expressions is discussed as well as composition of functions. Square root and cube root functions are presented as inverse functions of a quadratic and cubic function. Composing functions is introduced as a way to determine inverse functions. Radical equations are solved.

After this section the student will be able to:

• Perform mathematical operations on radical expressions.
• Simplify rational expressions with rational exponents.
• Compose functions.
• Graph a function and its inverse.
• Solve radical equations.
• Apply radical functions to real world situations.

Lessons:

• Radicals and Rational Exponents
• Inverse Functions
• Square Root Functions
• Cube Root Functions

Sections 2: Exponential Functions

This section extends the study of exponential functions introduced in Algebra 1. Parent exponential functions and their translations are graphed. Base e is introduced and application to compounding interest continuously presented. Complex exponential functions are solved by writing equations with like bases. Growth and decay models are used to represent real world situations. 

After this section the student will be able to:

• Graph parent exponential function and their transformations.
• Write exponential functions from given information.
• Recognize a geometric sequence as an exponential function.
• Understand that base e is a special exponential function.
• Solve compound continuously interest problems.
• Solve exponential functions.
• Model real world problems with growth and decay functions.

Lessons:

• Writing Exponential Functions
• Change of Base
• Solving Exponential Equations
• Modeling with Exponential Functions

Section 3: Logarithmic Functions

This section introduces the student to logarithmic functions as inverses to exponential functions. Log functions are graphed showing intercepts and end behavior. The properties of log functions are presented and used to simplify and evaluate log expressions. Exponential and logarithmic functions are solved using inverse operations.

After this section the student will be able to:

• Recognize log functions as inverse of exponential functions.
• Solve logarithmic and exponential equations.
• Graph parent log functions and their transformations.
• Know and use the properties of logs to simplify log expressions.
• Evaluate logarithmic expressions.

Lessons:

• Logarithm as Inverse Functions
• Transformations of Logarithms
• Solving Exponential and Logarithmic Functions
• Modeling with Logarithms

Section 4: Trigonometric Functions

This section extends the concepts of right triangle trigonometric learned in Geometry to all angles. The conversion from degree measure to radian measure is presented and the unit circle developed. Trigonometric functions are graphed showing period, midline and amplitude. Trig functions are used to model real world situations.

After this section the student will be able to:

• Graph Trig functions showing period, midline and amplitude.
• Explain the Pythagorean Identities.
• State the domain and range of trig functions.
• Graph translations of trig functions.
• Model real world situations with trig functions.

Lessons:

• Introduction to Trigonometry
• Unit Circle
• Graphing Trigonometric Functions
• Modeling Trigonometric Functions

Sections 5: Data Analysis

This section focuses on data analysis. The different methods of gathering data are presented. Data is analyzed for flaws and biases. Building on prior knowledge of central tendency and standard deviation, normal distribution is discussed. Finding the best fit curve to represent a data set is also presented.

After this section the student will be able to:

• Discern between the different methods of data collection.
• Recognize bias in data collection.
• Discuss randomization in collecting data.
• Find the area under the normal curve using tables or technology.
• Estimate population percentages. 
• Find the confidence interval and margin of error.
• Draw conclusions based on statistical analysis of data.
• Fit a function to a data set and use the function to make predications.

Lessons:

• Data Collection
• Dispersion
• Drawing Conclusions
• Curve Fitting