Algebra 1A is a prerequisite course for Algebra 1B. Before beginning this course, you should be able to do the following:

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1 Syllabus Algebra 1B Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. You already have experience with expressions containing monomials and binomials. In Algebra 1B, you ll extend these ideas to factor and perform operations on polynomials which are expressions with more than two terms. Until now, many of the equations that you ve solved have been linear, or proportional. In Algebra 1B, you ll begin to solve quadratic equations. These are equations where the highest power on any variable is two. You ll look closer at the parabola, a conic section defined by a quadratic equation. Additionally, you ll build your graphing skills by analyzing and plotting different types of functions: absolute value, piecewise, exponential, and logarithmic. Finally, you ll learn more about statistics as you interpret the shapes of data distributions and delve into correlation and causation. Course Goals By the end of this course, you will be able to do the following: Add, subtract, multiply, divide, and factor polynomials. Solve quadratic equations by factoring or using the quadratic formula. Determine the orientation of a parabola and find its x- and y-intercepts and its vertex. Analyze exponential and logarithmic functions. Graph absolute value and piecewise functions. Calculate the composite and inverse of a function. Solve real-world problems involving linear, quadratic, and exponential functions. Interpret the statistical similarities and differences between two or more data sets. Distinguish between correlation and causation. Math Skills Algebra 1A is a prerequisite course for Algebra 1B. Before beginning this course, you should be able to do the following: Add, subtract, multiply, and divide monomials and binomials. Solve and graph linear equations and inequalities in one or more variables. Understand patterns, sequences, series and functions. Solve problems involving linear functions. Apply rules for exponents and radicals. Interpret the features of a line from an equation written in point-slope or y-intercept form EDMENTUM, INC.

2 General Skills To participate in this course, you should be able to do the following: Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through and participate in discussion boards. For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course. Credit Value Algebra 1B is a 0.5-credit course. Course Materials Notebook Pencils Graphing calculator, recommend TI-83 or equivalent Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class. Unit 1: Expressions and Equations Summary This unit begins with operations involving polynomials expressions with more than two terms. You will learn how to factor polynomials and then use factoring to solve quadratic equations. You will also solve quadratic equations using the quadratic formula. You ll employ both methods to solve practical math problems in this unit. Day Activity / Objective Type 1 Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at 2 Course Orientation

3 2 4 the beginning of this course. Special Quadratic Equations, Part 1 Solve quadratic equations in which both sides are perfect squares. Special Quadratic Equations, Part 2 Solve certain types of quadratic equations by factoring. 15 days: 5 19 Using Quadratic Equations to Solve Problems Use quadratic equations in one variable to solve practical problems. Classifying Polynomials Classify polynomials. Polynomial Sum Find the sum of two polynomials. s Polynomial Difference Find the difference of two polynomials. Product of a Monomial and Polynomial Find the product of monomials and polynomials. Product of Polynomials Find the product of polynomials. Quotient of a Monomial and Polynomial Divide a polynomial by a monomial. Quotient of a Binomial and Polynomial Divide a polynomial by a binomial. Greatest Common Factors of Monomials Find the greatest common factor of two or more monomials. Monomial Factors of Polynomials Factor a polynomial that has monomial factors. 3

4 Binomial Factors of Polynomials, Part 1 Use the distributive property to write an expression as the product of two sums or differences. Binomial Factors of Polynomials, Part 2 Group terms to write an expression as the product of two sums or differences. Factoring the Difference of 2 Squares Factor a difference of squares. Factoring Perfect Square Trinomials Factor a perfect square trinomial. Factoring Trinomials, Part 1 Factor trinomials of the form x 2 + bx + c. 6 days: Factoring Trinomials, Part 2 Factor trinomials of the form x 2 + bx + c. Solving Simple Quadratic Equations Find the solution for quadratic equations of the form x 2 + bx + c = 0. s Solving Quadratic Equations by Factoring, Part 1 Find the solution set of quadratic equations that factor as the difference of two squares. Solving Quadratic Equations by Factoring, Part 2 Find the solution set of a quadratic equation that is the perfect square of a binomials Solving Quadratic Equations by Factoring, Part 3 Find the solution set of quadratic equations by factoring. Quadratic Formula Use the quadratic formula to find a solution set for a quadratic equation. Solving Problems With Quadratic Equations 4

5 Solve word problems that can be represented by quadratic equations. Solving Linear-Quadratic Systems of Equations Solve linear-quadratic equations algebraically and graphically. Rules for Exponents and Radicals Apply the rules for exponents when the exponents are rational numbers Applying Rules for Exponents and Radicals Simplify rational expressions with exponents and radicals. Unit Activity and Discussion Unit 1 Posttest Unit 1 Unit Activity Discussion Assessment Unit 2: Quadratic Functions and Modeling Summary This unit focuses on functions. You ll begin by identifying the features of a quadratic function called a parabola. You ll also check your graphing skills by plotting more complex functions: piecewise and absolute value. In addition to creating graphs, you ll be comparing and contrasting exponential and logarithmic functions in real-world contexts. Finally, you will transform functions by finding composite functions and computing the inverse of a function. Day Activity / Objective Type Parabola and Its Intercepts Find the x- and y-intercepts of a parabola. s Parabola and Its Vertex Find the vertex of a parabola Parabola and Its Coefficients Learn how changing the coefficients of a parabola affects its position and shape. Graphing Piecewise Functions Graph greatest integer and general piecewise functions. 5

6 Graphing Absolute Value Functions Graph absolute value functions. Functional Values Compute functional values by translating and transforming a function. Composite Functions Find composite functions, their values, and the simpler functions that make up composite functions. s Domain Values of Composite Functions Define the restrictions on the domain of a composite function and determine whether a value is in the domain of a composite function. Inverse of a Function Find the inverse of a function. s Determining if a Function Has an Inverse Determine whether a function has an inverse by looking at a mapping diagram or by inspecting a graph. Solving Problems with Linear Functions Describe real-world situations as linear functions. s 50 Solving Problems with Quadratic Functions Describe real-world situations as quadratic functions. Properties of Exponential Functions Study the properties of exponential functions. 6

7 51 52 Properties of Logarithmic Functions Study the properties of logarithmic functions. s Recognizing Graphs of Types of Functions Identify exponential and logarithmic functions by looking at graphs of these functions. Unit Activity and Discussion Unit 2 Posttest Unit 2 Unit Activity Discussion Assessment Unit 3: Descriptive Statistics Summary This unit focuses on displaying and interpreting data using statistics. In this unit, you ll graph data using dot plots, histograms, and box plots. You ll use statistics to compare the shape and characteristics of two or more data sets. You ll also see how you can use the equation of a line to draw conclusions from certain types of data, completing the unit with a study of correlation versus causation. Day Activity / Objective Type Data Plots Represent data with plots on the real number line using dot plots, histograms, and box plots. Showing Data Center and Spread Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. Interpreting the Shape of Data Distributions Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Relating Categorical Data Summarize data for two categories in two-way frequency tables and interpret their relative frequencies in the context of the data. 7 Interpreting Data as a Line

8 72 74 Interpret the slope and the intercept of a linear model in the context of the data Relating Quantitative Data Represent data of two quantitative variables using a scatter plot, describe and fit a function to the data, and solve problems in the context of the data. Making and Interpreting Correlations Use technology to compute and interpret the correlation coefficient of a linear fit. Correlation Versus Causation Distinguish between correlation and causation. Unit Activity and Discussion Unit 3 Posttest Unit 3 Semester Review End-of-Semester Exam Unit Activity Discussion Assessment Assessment 8

Algebra 1B. Syllabus. Course Overview. Course Goals

Algebra 1B. Syllabus. Course Overview. Course Goals Syllabus Algebra 1B Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. In Algebra 1A you worked with expressions containing