Algebra II (Credit Recovery)

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:

Semester 1:

Section 1 - Algebra Foundations

This section introduces the complex number system. The concept of closure of sets is discussed. This section also reviews the definition of functions and transformations of functions. Sequences and series are introduced as an extension of the study of functions.

After this section the student will be able to:

• Perform mathematical operations with complex numbers.
• Understand the meaning of closure of sets of numbers.
• Define a function and determine the domain and range.
• Use function notation to represent a situation.
• Construct linear and exponential functions from given information.
• Write arithmetic and geometric functions to represent problems. 
• Write geometric sequences in function form.

Lessons:

• Complex Number System
• Function Fundamentals
• Sequences and Series

Section 2 - Quadratic Functions

This section extends the study of quadratic functions introduced in Algebra 1. Writing quadratic functions from given information is reviewed. Graphing parent quadratic functions and their transformations are discussed. Many methods are used to find complex solutions to quadratic equations.

After this section the student will be able to:

• Graph a quadratic function from given information.
• Write the quadratic function that models given information.
• Use many methods to find all complex solutions to a quadratic equation.
• Rewrite a quadratic function in a variety of forms.

Lessons:

• Writing Quadratic Functions
• Graphing Quadratic Functions
• Solve Quadratic Equations
• The Quadratic Formula

Section 3 - Polynomial Functions

This section introduces the student to polynomial functions and identities. Factoring of polynomials is reviewed and extended to include cubic binomials. Pythagorean triples are introduced and generated by using identities. Zeros and end behavior are used to aid in graphing a function. The Remainder Theorem and Fundamental Theorem of Algebra are explored as ways to analyze the characteristics of a polynomial function. 

After this section the student will be able to:

• Find complex factors of a quadratic function
• Factor cubic binomials
• Recognize Pythagorean Triples.
• Discuss the end behavior of function.
• Recognize the characteristics of an even or odd function.
• Combine polynomial functions
• Find the zero of a polynomial function from a graph and by factoring.
• Know and apply the Factor and Remainder Theorem.
• Use long division and synthetic division to factor a polynomial.
• Know and use the Fundamental Theorem of Algebra.

Lessons:

• Operations with Polynomials
• Factoring Higher Order Polynomials
• Analyzing Polynomial Functions
• Factors and Zeros

Section 4 - Radical Functions

This section introduces radical functions and their relationship to rational exponents. Mathematics operations on radical expressions are discussed. Square root and cube root functions are presented as inverse functions of a quadratic and cubic function. 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.
• 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

Section 5 - Systems

This section focuses on systems of equations. A review of solving linear systems is discussed and extended to solving nonlinear systems. Applications of systems are introduced.

After this section the student will be able to:

• Solve linear systems of equations and inequalities using a variety of methods
• Solve nonlinear systems using a variety of methods.
• Solve real world problems using linear programming methods.

Lessons:

• Systems of Equations
• Systems of Inequalities
• Linear Programming
• Operations on Matrices
• Solving Systems Using Matrices

Semester 2:

Section 1: 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 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 continuous interest problems.
• Solve exponential functions.
• Model real world problems with growth and decay functions.

Lessons:

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

Sections 2: 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:

• Logs as Inverse Functions 
• Transformations of Log Functions 
• Solving Exponential and Logarithmic Equations 
• Modeling with Logarithms 

Section 3: 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 4: 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 predictions.

Lessons:

• Data Collection
• Dispersion
• Drawing Conclusions
• Curve Fitting