# High School Algebra II Course

Time4Learning offers an online, interactive high school curriculum that correlates to state standards. It can be used as a primary homeschool curriculum, a supplement to your current curriculum and as an afterschool or summer skill building program. At the high school level, Time4Learning is organized by courses rather than grade levels, so parents have the option of choosing any four as part of membership.

The Algebra II curriculum is one of five Math courses offered at the high school level. Algebra II is taught using a combination of multimedia lessons, instructional videos, worksheets, quizzes, tests and both online and offline projects. The Algebra II course is designed to prepare students for college level mathematics.

### Chapter 1 – Functions I

The materials in this chapter introduce and cover the basics of functions. It is organized into sections that teach, reinforce and test students on the concepts of notation and computations with functions and functions and equations.

Lessons in this chapter are organized into the following sections:

• Notation and computations with functions – Students will be able to identify functions from symbols, graphs, tables, diagrams, or words. The lesson continues by teaching students how to use function notation and how to evaluate and compute with functions. Students will also use graphs, equations, and tables to find the domain and range of a function.
• Functions and equations – Students will learn the relationship between the roots of a function and the solutions of an equation, as well as the relationship between dependent and independent equations.

### Chapter 2 – Linear Functions

The materials in this chapter introduce and cover linear functions. It is organized into sections that teach, reinforce and test students on the concepts of solving linear equations and inequalities, linear functions and piecewise linear functions.

Lessons in this chapter are organized into the following sections:

• Solving linear equations and inequalities – Students are required to solve and graph linear equations and inequalities with one variable.
• Linear functions – Students must write the rules for linear functions and then graph them.
• Piecewise linear functions – Students are taught how to analyze, solve, and graph absolute value equations and step functions.

### Chapter 3 – Functions II

The materials in this chapter introduce and cover the second part of functions. It is organized into sections that teach, reinforce and test students on the concepts of parent functions and transformations, and composition and inverse functions.

Lessons in this chapter are organized into the following sections:

• Parent functions and transformations – Students must graph and transform parent functions using vertical and horizontal reflections, translations, stretches, and compressions. Students will also examine how changes in parameters stretch or compress functions.
• Composition and inverse functions – Students will learn how to perform the composition of functions and how to find the inverse of a function from a table, graph, or equation.

### Chapter 4 – Quadratic Functions

The materials in this chapter introduce and cover quadratic functions. It is organized into sections that teach, reinforce and test students on the concepts of complex numbers, solving quadratic equations and inequalities and graphing quadratic functions.

Lessons in this chapter are organized into the following sections:

• Complex numbers – Students are taught how to define complex numbers and compute them in order to plot complex numbers as points.
• Solving quadratic equations and inequalities – Students are required to solve quadratic equations and inequalities using graphic and algebraic methods.
• Graphing quadratic functions – Students learn how to analyze, graph, transform the graphs, and study the applications of quadratic functions.

### Chapter 5 – Polynomial Functions

The materials in this chapter introduce and cover polynomial functions. It is organized into sections that teach, reinforce and test students on the concepts of adding and subtracting polynomials, multiplying polynomials, dividing polynomials and polynomial functions.

Lessons in this chapter are organized into the following sections:

• Adding and subtracting polynomials – Students must add and subtract polynomials.
• Multiplying polynomials – Students must multiply polynomials and use the Binomial Theorem to expand powers of binomials.
• Dividing polynomials – Students must divide polynomials using both long division and synthetic division. Students will also have to use the Remainder Theorem and the Factor Theorem to factor polynomials.
• Polynomial functions – Students must find the roots of a polynomial with the Rational Roots Theorem. Students will also graph polynomial functions and learn how to use the Fundamental Theorem of Algebra.

### Chapter 6 – Rational Functions

The materials in this chapter introduce and cover rational functions. It is organized into sections that teach, reinforce and test students on the concepts of rational expressions, rational equations and inequalities and rational functions.

Lessons in this chapter are organized into the following sections:

• Rational expressions– Students are taught how to simplify rational expressions that contain negative exponents, perform operations on rational functions, and simplify complex fractions.
• Rational equations and inequalities – Students are required to solve rational equations and inequalities and use direct, indirect, and joint variation.
• Rational functions – Students will learn how to graph rational functions by using the following graph features: vertical and horizontal asymptotes, holes, and roots.

### Chapter 7 – Radical Functions

The materials in this chapter introduce and cover radical functions. It is organized into sections that teach, reinforce and test students on the concepts of radical expressions and radical equations and inequalities.

Lessons in this chapter are organized into the following sections:

• Radical expressions – Students are taught how to simplify and calculate radical expressions and how to simplify expressions with rational exponents.
• Radical equations and inequalities – Students will work on solving radical equations and inequalities by using graphical and algebraic methods. Graphing radical functions is also a part of the lesson.

### Chapter 8 – Exponential and Logarithmic Functions

The materials in this chapter introduce and cover exponential and logarithmic functions. It is organized into sections that teach, reinforce and test students on the concepts of exponential and logarithmic functions and exponential and logarithmic equations and inequalities.

Lessons in this chapter are organized into the following sections:

• Exponential and logarithmic functions – Students learn how to graph logarithmic functions and exponential functions, which include models of growth and decay.
• Exponential and logarithmic equations and inequalities – Students must solve exponential and logarithmic equations and inequalities by using properties of logarithms.

### Chapter 9 – Probability and Statistics

The materials in this chapter introduce and cover probability and statistics. It is organized into sections that teach, reinforce and test students on the concepts of describing data sets, fitting graphs to data and computing probabilities.

Lessons in this chapter are organized into the following sections:

• Describing data sets – Students learn how to calculate mean, median, mode, variance, standard deviation, range of data sets, quartiles, interquartile range, and percentile distribution of data sets.
• Fitting graphs to data – Students are taught how to make scatter plots, determine lines of best fit, and determine curves of best fit.
• Computing probabilities – Students must use experimental and theoretical probability, as well as permutations and combinations to calculate probabilities.

### Chapter 10 – Systems of Equality and Inequality

The materials in this chapter introduce and cover the systems of equality and inequality. It is organized into sections that teach, reinforce and test students on the concepts of solving systems of equations and solving systems of inequalities.

Lessons in this chapter are organized into the following sections:

• Solving systems of equations – Students must solve systems of linear and nonlinear equations. Students must also graph the linear equations.
• Solving systems of inequalities – Students will learn how to solve systems of linear equations and inequalities in two variables by graphing. In addition, students will learn how to solve linear programming problems by testing the corner points of the feasible regions.

### Chapter 11 – Matrices

The materials in this chapter introduce and cover matrices. It is organized into sections that teach, reinforce and test students on the concepts of operations with matrices and solving systems of equations using matrices.

Lessons in this chapter are organized into the following sections:

• Operations with matrices – Students must add, subtract, and perform scalar and matrix multiplication on matrices.
• Solving systems of equations using matrices – Students students are taught how to solve systems of equations using matrix row operations and Cramer’s Rule.

### Chapter 12 – Conic Sections

The materials in this chapter introduce and cover conic sections. It is organized into sections that teach, reinforce and test students on the concept of parabolas, circles, ellipses, and hyperbolas.

Lessons in this chapter are organized into the following sections:

• Parabolas, circles, ellipses, and hyperbolas – Students are responsible for graphing parabolas circles, ellipses, and hyperbolas as conic sections. Students must then analyze the graph to identify its features and then create an equation for the graph.

### Chapter 13 – Sequences and Series

The materials in this chapter introduce and cover sequences and series. It is organized into sections that teach, reinforce and test students on the concepts of sequences and series.

Lessons in this chapter are organized into the following sections:

• Sequences – Students are taught how to identify arithmetic and geometric sequences, and how to use recursive and iterative formulas on them. Students must also be able to point out patterns in sequences, including the Fibonacci sequence.
• Series – Students finish the chapter with this lesson on defining series as partial sums of a sequence, and using summation notation. Students must also find sums of arithmetic and geometric series, and use them in applied situations.

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