ESCONDIDO UNION HIGH SCHOOL DISTRICT COURSE OF STUDY OUTLINE AND INSTRUCTIONAL OBJECTIVES

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1 ESCONDIDO UNION HIGH SCHOOL DISTRICT COURSE OF STUDY OUTLINE AND INSTRUCTIONAL OBJECTIVES COURSE TITLE: Algebra II A/B COURSE NUMBERS: (P) 7241 / 2381 (H) 3902 / 3903 (Basic) 0336 / 0337 (SE) 5685/5686 DEPARTMENT: PREREQUISITE: LENGTH OF COURSE: SEMESTER PERIOD OF CREDITS: GRADE LEVEL(S): Mathematics Recommend C or better in Algebra I and Geometry Two Semesters Five per semester 9-12 or teacher recommendation DATE ADOPTED: April 17, 2001 Revision: June 12, 2001 Meets EUHSD Mathematics Requirement MEETS UC c ADMISSION REQUIREMENTS TEXTBOOK: Algebra 2, 2008 by Holt McDougal, ISBN COURSE DESCRIPTION: Algebra II expands on the mathematical content of Algebra I A/B. Emphasis is given to understanding the nature of a function, its domain and range and specific function families: Linear, Exponential, Power, Inverse and Periodic. Techniques, such as graphing, symbolic manipulation, and matrices, for solving a variety of equations and inequalities will be covered. Other topics introduced are probability and statistics, trigonometry, conic sections, sequences and series, logarithms and complex numbers with attention to real world applications. Technology will be used to aid student understanding and solve problems. 5/18/12 1

2 COURSE UNITS/TOPICS AND ALLOCATED INSTRUCTIONAL TIME Algebra II Chapter Analysis Instruction in the use of a graphing calculator is strongly recommended. Use your discretionary days to allow for extra time in almost every chapter. Sections skipped in this outline are not required, but may be covered at the teacher s discretion. Time PLACEMENT AND DIAGNOSTIC TESTING Instructional 2 DAYS CHAPTER ONE - DATA & LINEAR REPRESENTATIONS 11 DAYS 1.1 Tables & Graphs of Linear Equations 1.2 Slopes & Intercepts 1.3 Linear Equations in Two Variables 1.6 Introduction to Solving Equations 1.7 Introduction to Solving Inequalities 1.8 Solving Absolute Value Equations & Inequalities [Std 1.0] CHAPTER TWO - NUMBERS & FUNCTIONS 13 DAYS 2.1 Operations w/numbers [Std 25] 2.2 Exponents [Std 12] 2.3 Intro to Functions [Std 24] 2.4 Operations with Functions [Std 24] 2.5 Inverses of Functions [Std 24] 2.6 Special Functions [Std 24] 2.7 Transformations CHAPTER THREE - SYSTEMS OF LINEAR EQUATIONS & INEQUALITIES 14 DAYS 3.1 Solving Systems by Graphing or Substitution [Std 2.0] 3.2 Solving Systems by Elimination [Std 2.0] 4.4 Solving System with Matrix Equations (Linear Algebra Std 2.0)* OR 4.5 Using Matrix Row Operations (Linear Algebra Std. 3.0 & 6.0)* 3.3 Linear Inequalities in Two Variables 3.4 Systems of Linear Inequalities [Std 2.0] 3.5 Linear Programming (optional) 3.6 Parametric Equations (optional for Honors only, Math Analysis standard 7.0) 2

3 CHAPTER FIVE - QUADRATIC FUNCTIONS 16 DAYS 5.1 Introduction to Quadratic Functions [Std 8.0 &10.0] 5.2 Solving Quadratic Equations [Std 8.0 & 10.0] 5.3 Factoring Quadratics [Std 4.0 & 8.0] 5.4 Completing the Square [Std 8.0] 5.5 Quadratic Formula [Std 8.0] 5.6 Quadratic Equations & Complex Numbers [Std 5.0, 6.0 & 8.0] 5.8 Solving Quadratic Inequalities (Honors only) CHAPTER SIX - EXPONENTIAL AND LOGARITHMIC FUNCTIONS 11 DAYS 2.2 Properties of Exponents (review) [Std 12.0] 6.1 Exponential Growth & Decay [Std 12.0] 6.2 Exponential Functions [Std 12.0] 6.3 Logarithmic Functions [Std 11.0] 6.4 Properties of Logarithmic Functions [Std 14.0] 6.5 Applications of Common Logarithms [Std 13.0] 6.6 The Natural Base e (Honors only) 6.7 Solving Equations and Modeling (base e part for Honors only) [Std 15.0] CHAPTER SEVEN - POLYNOMIAL FUNCTIONS 8 DAYS 7.1 Introduction to polynomials [Std 3.0] 7.2 Polynomial Graphs & Functions 7.3 Products & Factors of Polynomials [Std 3.0 & 4.0] 7.4 Solving Polynomial Equations (Math Analysis Std 6.0) 7.5 Zeros of Polynomial Functions (Honors only, Math Analysis Std 4.0) * Using Graphing Calculators 2 DIAGNOSTIC DAYS 73 INSTRUCTIONAL DAYS 5 DISCRETIONARY DAYS 5 FINALS AND REVIEW DAYS END OF FIRST SEMESTER (85 STUDENTS DAYS) 3

4 SECOND SEMESTER CHAPTER EIGHT - RATIONAL FUNCTIONS 17 DAYS Optional suggestion to separate and into two smaller units. 8.1 Inverse, Joint, and Combined Variation (Optional) [on SAT] 8.2 Rational Functions and Graphs (Math Analysis Std 6.0) 8.3 Multiplication & Division of Rational Expressions [Std 7.0] 8.4 Addition & Subtraction of Rational Expressions [Std 7.0] 8.5 Solving Rational Equations (Inequalities is Honors only) [Std 15.0] 8.6 Radical Expressions and Radical Functions (Optional) 8.7 Simplifying Radical Expressions 8.8 Solving Radical Expressions (Inequalities is Honors only) [Std 15.0] CHAPTER NINE - CONIC SECTIONS 17 DAYS 5.4 Completing the Square (review) 9.1 Introduction to Conic Sections [Std 16.0 & 17.0] 9.2 Parabolas [Std 16.0 & 17.0] 9.3 Circles [Std 16.0 & 17.0] 9.4 Ellipses [Std 16.0 & 17.0] 9.5 Hyperbolas [Std 16.0 & 17.0] 9.6 Solving Non-Linear Systems CHAPTER 10 - COUNTING PRINCIPLES AND PROBABILITY 12 DAYS 10.1 Introduction to Probability (Probability & Statistics Standard 3) [Std 18.0] 10.2 Permutations [Std 18.0] 10.3 Combinations [Std 18.0] 10.4 Using Addition w/probability 10.5 Independent Events (Probability & Statistics Standard 1.0) 10.6 Dependent Events & Conditional Probability (Probability & Statistics 2.0) 10.7 Experimental Probability and Simulation (Optional intro for AP Stats) CHAPTER 11 - SERIES & PATTERNS 15 DAYS 11.1 Sequences and Series 11.2 Arithmetic Sequences 11.3 Arithmetic Series [Std 22.0 & 23.0] 11.4 Geometric Sequences 11.5 Geometric Series & Mathematical Induction (separate day) [Std 21.0 & 22.0 & 23.0] 11.6 Infinite Geometric Series [Std 22.0] 11.7 Pascal s Triangle, Combinations & Permutations w/probability [Std 19.0] 11.8 The Binomial Theorem [Std 20.0] 4

5 CHAPTER 13 - TRIGONOMETRIC FUNCTIONS 15 DAYS Strongly recommended emphasis on the Unit Circle 13.1 Right-Triangle Trigonometry (Trigonometry 5.0, 6.0, 12.0) 13.2 Angles of Rotation (Trigonometry 1.0) 13.3 Trigonometric Functions of Any Angle (Trigonometry 2.0 & 9.0) 13.4 Radian Measure and Arc Length (Trigonometry 1.0) 13.5 Graphing Trigonometric Functions; brief overview (Trigonometry 2.0 & 5.0) 13.6 Inverses of Trigonometric Functions (Trigonometry 8.0) CHOOSE ANY OF THESE TOPICS OF THE FOLLOWING TWO UNITS IF TIME PERMITS. HONORS COURSES ARE EXPECTED TO COMPLETE BOTH OF THE FOLLOWING UNITS: CHAPTER 12 - STATISTICS 12.1 Measures of Central Tendency, briefly covered (Probability & Statistics Standard 6.0) 12.2 Stem-and-Leaf Plots, Histograms, and Circle Graphs, briefly covered (Probability & Statistics Standard 8.0) 12.3 Box-and-Whisker Plots (Probability & Statistics Standard 8.0) 12.4 Measures of Dispersion (Probability & Statistics Standard 4.0, 5.0 & 7.0) 12.5 Binomial Distributions (Probability & Statistics Standard 4.0 & 5.0) 12.6 Normal Distributions (Probability & Statistics Standard 4.0 & 5.0) CHAPTER 14 - FURTHER TOPICS IN TRIGONOMETRY 14.1 The Law of Sines (Trigonometry 13.0) 14.2 The Law of Cosines (Trigonometry 13.0) 14.3 Fundamental Trigonometric Identities (Trigonometry 3.0) 14.6 Solving Trigonometric Equations (Great Closure for the year) 76 INSTRUCTIONAL DAYS 6 DAYS TESTING (SAT/STAR/ ) 10 DISCRETIONARY DAY 5 DAYS FINALS AND REVIEW END OF SECOND SEMESTER (97 STUDENT DAYS) 5

6 RESOURCES 1.0 Students solve equations and inequalities involving absolute value. Students will write, solve and graph absolute-value equations and inequalities. 1.8 Each honors extension will allow students to apply identified algebraic standards to move advanced concepts of trigonometry, math analysis, probability, and statistics. Technology: pg 2D 2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. Students will solve systems by graphing or substitution. 3.1 Students will solve systems of linear inequalities. 3.4 Students will solve linear programming. 3.5 Students will solve systems with matrix equations. 4.4 Students will be expected to challenge the more advanced problems provided in each section of the text as well as complete advanced problems created by instructor. Technology: pg 154D Internet: pg 159, 183, 186, 191, 235, Students are adept at operations on polynomials, including long division. Students will identify, evaluate, add and subtract polynomials. Students will classify polynomials and describe the shapes of their graphs. 7.1 Students will identify products and factors of polynomials. 7.3 Technology: pg 422D Internet: pg 431, Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Students will factor quadratic equations. 5.3 Students will identify products and factors of polynomials. 7.3 Technology: pg 272D, 422D Internet: pg 298, 443 Page 6

7 RESOURCES 5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically, in particular, they can plot complex numbers as points in the plane. Students will classify and identify roots of quadratic equations and complex numbers. Students will graph and perform operations on complex numbers. 5.6 Technology: pg 272D Internet: pg Students add, subtract, multiply, and divide complex numbers. Students will solve quadratic equations and complex numbers. 5.6 Technology: pg 272D Internet: pg Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Students will multiply and divide rational expressions. 8.3 Students will add and subtract rational expressions. 8.4 Technology: pg 478D 8.0 Students solve and graph quadratic equations by Page 7 Students will identify and graph quadratic function. 5.1 Students will solve and factor Technology: pg 272D Internet: pg 284, 298, 306,

8 RESOURCES factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. quadratic equations. 5.2 Students will use completing the square to solve quadratic equations. 5.3 Students will use the quadratic formula to find real roots of quadratic equations. 5.4 Students will classify and find all roots of quadratic equations. Students will perform operations on complex numbers Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(xb) 2 +c. Students will write and graph the standard equation of a parabola. 9.2 Technology: pg 560D Internet: pg Students graph quadratic functions and determine the maxima, minima, and zeros of the function. Students will graph and identify quadratic functions. Students will multiply linear binomials to produce quadratic expressions. 5.1 Technology: pg 272D 11.0 Students prove simple laws of Students will write equivalent forms for exponential and logarithmic Technology: pg 352D Page 8

9 RESOURCES logarithms Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms, and exponents. equations. Students will use the definitions of exponential and logarithmic functions to solve equations. 6.3 Students will evaluate natural exponential and natural logarithmic functions. Students will investigate model exponential growth and decay processes Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. Students will model and solve real world problems involving exponential and logarithmic relationships Students know the laws of fractional exponents, understand exponential functions, and use these functions in Page 9 Students will evaluate and simplify expressions involving exponents. 2.2 Students will determine the multiplier for exponential growth and decay. 6.1 Students will calculate the growth of Technology: pg 352D Internet: pg 365

10 RESOURCES problems involving exponential growth and decay. investments under various conditions Students use the definition of logarithms to translate between logarithms in any base. Students will define and use the common logarithmic function to solve exponential and logarithms equations. 6.5 Technology: pg 352D Internet: pg Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. Students will simplify and evaluate expressions involving logarithms. Students will solve equations involving logarithms. 6.4 Technology: pg 352D 15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always, true, or never true. Students will solve logarithmic and exponential equations by using algebra and graphs. 6.7 Students will solve a rational equation or inequality by using algebra or a graph. 8.5 Students will solve radical equations 8.8. Students will model exponential growth and decay processes. Students will evaluate natural exponential and natural logarithmic functions. 6.6 Students will solve problems by using a rational equation or inequality. 8.5 Students will solve for Radical equations and radical inequalities. 8.8 Technology: pg 352D, 478D Internet: pg 403, 409, 519, 539 Page 10

11 RESOURCES 16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. Students will graph and label the vertex, focus, and directive of parabolas. 9.2 Given an equation of a circle, students will graph and label the radius and center. 9.3 Students will graph the equation of a hyperbolas and identify the center foci, vertices, and co-vertices. 9.5 Technology: pg 560D Internet: pg 578, Given a quadratic equation of the form ax 2 +by 2 +cx+dy+e=0 students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation. Students will graph and label the vertex, focus, and directive of parabolas. 9.2 Given an equation for a circle, students will graph and label the radius and center 9.3. Student will graph and label the center, vertices, and co-vertices of an ellipse. 9.4 Students will graph the equation of a hyperbolas and identify the center foci, vertices, and co-vertices. 9.5 Students will solve nonlinear systems. 9.6 Technology: pg 560D Internet: pg 578, 583, 589, Students use fundamental counting principles to compare combinations and permutations. Page 11 Students will find the theoretical Probability of an event. Students will apply the fundamental counting principal Students will solve problems involving linear permutations of distinct or indistinguishable objects. Technology: pg 626D Internet: pg 635, 639, 649

12 RESOURCES 10.2 Students will solve problems by distinguishing between permutations and combinations Students use combinations and permutations to compute probabilities. Students will find entries in Pascal s triangle. Students will use Pascal s triangle to find combinations and probabilities Technology: pg 688D 20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. Students will use the Binomial Theorem to expand (x+y) n. Students will use the Binomial Theorem to compute a probability Technology: pg 688D Internet: pg Students apply the method of mathematical induction to prove general statements about the positive integers. Students will use mathematical induction to prove general statements about natural numbers Technology: pg 688D 22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite Page 12 Students will find the sum of the first (n) terms of an arithmetic series Students will find the sum of the first (n) terms of a geometric series Students will find the sum of an Technology: pg 688D Internet: pg 734

13 RESOURCES geometric series. infinite geometric series if one exists Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. Students will find the sum of the first (n) terms of a geometric series Technology: pg 688D Internet: pg Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. Students will graph a relation, state its domain and range, and tell whether it is a function. 2.3 Students will perform operations with functions, write new functions and find the composite of two functions. 2.4 Students will find the inverse of a relation or function and determine whether the inverse of a function is a function. 2.5 Technology: pg 84D Internet: pg 107, 110, 132 Students will write, graph and apply special functions: piecewise, step and absolute value Students use properties from number systems to justify steps in combining and simplifying functions. Students will solve operations with numbers. 2.1 Technology: pg 84D Page 13

14 RESOURCES Trigonometry Standards 1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. Students will find co-terminal and reference angles. Students will find the trigonometric functions values of angles in standard potion Students will convert from degree measure to radian measure. Students will find arc length Technology: pg 826D Internet: pg Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions. Students will find exact values for trigonometric functions of special angles and their multiples. Students will find approximate values for trigonometric functions of any angle Students will graph the sine, cosine and tangent function and their transformations Technology: pg 826D Internet: pg 850, Students know the identity cos 2 (x) + sin 2 (x) = 1 Students will prove fundamental trigonometric identities Technology: pg 884D 5.0 Students know the definitions of the tangent and cotangent functions and can graph them. Page 14 Students will define and discuss cosecant, cotangent and secants. 13.1

15 RESOURCES 12.0 Students use trigonometry to determine unknown sides or angles in right triangles. Students will find the trigonometric functions of acute angles Technology: pg 826D Internet: pg 829, Students know the law of sines and the law of cosines and apply those laws to solve problems. Students will solve mathematical and real world problems by using the law of sines Students will use the law of cosines to solve triangles Students will solve trigonometric equations algebraically and graphically Technology: pg 884D Internet: pg 888, 901 Probability Standards 1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces. Students will find the probability of two or more independent events Technology: pg 626D 2.0 Students know the definition of conditional probability and use it to solve for probabilities of Page 15 Students will find conditional probabilities Technology: pg 626D Internet: pg 667

16 RESOURCES finite sample spaces. 4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families. Students will calculate and use measure of dispersion, such as range, mean, deviation, variance and standard deviation Students will find the probability of (n) successes in (n) trials of a binomial experiment Students will find the probability of an event given that the data is normally distributed and its mean and standard deviation are known Technology: pg 762D Internet: pg 798, Students determine the mean and the standard deviation of a normally distributed random variable. Students will calculate and use measure of dispersion, such as range, mean, deviation, variance and standard deviation Students will find the probability of (n) successes in (n) trials of a binomial experiment Students will find the probability of an event given that the data is normally distributed and its mean and standard deviation are known Technology: pg 762D Internet: pg 798, Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations. Students will find or estimate the mean from a frequency table of data Technology: pg 762D Internet: pg 771 Page 16

17 RESOURCES 7.0 Students compute the variance and the standard deviation of a distribution of data. Students will calculate and use measures of dispersion, such as range, mean deviation, variance, and standard deviation Technology: pg 762D Internet: pg Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stemand-leaf displays, scatterplots, and box-and-whisker plots. Students will make a stem-and-leaf plot, a histogram or a circle graph for a data set Technology: pg 762D Math Analysis Standards 4.0 Students know the statement of, and can apply, the fundamental theorem of algebra. Students will use the fundamental theorem of algebra to write a polynomial function given sufficient information about its zeros. 7.5 Technology: pg 422D 6.0 Students find the roots and poles of a rational function and can graph the Page 17 Students will graph a rational function, find its domain, write equations for its asymptoms and identify any holes in its graphs. 8.2 Students will solve polynomial equations. 7.4 Technology: pg 422D, 478D Internet: pg 453, 455, 493

18 RESOURCES function and locate its asymptotes. 7.0 Students demonstrate an understanding of functions and equations defined parametrically and can graph them. Students will graph a pair of parametric equations and use them to model real world applications. 3.6 Technology: pg 154D Linear Algebra Standards 2.0 Students interpret linear systems as coefficient matrices and the Gauss- Jordan method as row operations on the coefficient matrix. Students will use matrices to solve systems of linear equations in mathematical and real world situations. 4.4 Technology: pg 214D Internet: pg 235, Students perform addition on matrices and vectors. Students will represent mathematical and real world data in a matrix. 4.1 Technology: pg 214D Internet: pg Students perform matrix multiplication and multiply vectors by matrices and by Page 18 Students will use matrix multiplication to solve mathematical and real world problems. 4.2 Technology: pg 214D Internet: pg 226

19 RESOURCES scalars. 9.0 Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations. Students will find and use the inverse of a matrix. 4.3 Students will find and use the determinant of a matrix. 4.3 Technology: pg 214D Internet: pg 233 Honors Activities Students will identify the transformations from one function to another. 2.7 Technology: pg 84D Students will write, solve, and graph a quadratic inequality in one variable. 5.8 Technology: pg 272D Internet: pg 333, 337 Page 19 Students will evaluate natural exponential and natural logarithmic functions. 6.6 Technology: pg 352D

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