Course:  Algebra II, 1st Semester

Text: Algebra 2, Holt, Rinehart and Winston

Cost: $48.75

Prerequisite:  Geometry

 

Grade Distribution:

Homework/Classwork     15%

Quizzes                             15%

Tests                                 50%

Performance Final              5%

Multiple Choice Final         15%

 

Curricular goals interwoven throughout the mathematics program are that students will:

            learn to communicate mathematically (QCC)

            learn to use mathematics in their daily lives (QCC)

            become proficient with appropriate computational tools and techniques (QCC)

            learn to reason mathematically (QCC)

            become mathematical problem solvers (QCC)

 

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

 

Chapter 1: Data and Linear Representations (pp. 2-83)                                                           

·    use graphs to solve linear and quadratic equations and inequalities (QCC, SAT I) (MAAA_A2001-1)

Ÿ         identify, write, solve and graph absolute value, step and constant functions

      (QCC, SAT I, ACT) (MAAA_A2001-4)

·    solve and graph linear and quadratic equations and inequalities in one and two variables (QCC, SAT I) (MAAA_A2001-5)

·        (revised) investigate, solve and graph direct, joint, inverse and combined variation problems (QCC, ACT)(MAAA_A2001-6)

·    transform data to make interpretations and predictions (MAAA_C2001-11)

·    compare and contrast linear, quadratic, exponential, logarithmic and power functions (MAAA_E2001-27)

·        solve formulas for one variable (QCC ) (MAAA_A2003-1)

·        (revised) identify and graph linear equation in one and two variables including vertical and horizontal lines, and write equations for lines using various combinations of given information (QCC) (MAAA_A2003-5)

·        determine if a relation is linear based on an equation, data table, or graph (QCC) (MAAA_E2003-22)

·        solve and graph linear inequalities in one variable, including compound inequalities and absolute value equations and inequalities (QCC) (MAAA_A2003-9)

 

Chapter 2: Numbers and Functions (pp. 84-153)                                                                        

·    identify domain and range for algebraic and transcendental functions (QCC) (MAAA_E2001-26)

·    determine and graph compositions and inverses of functions, using multiple notation formats, such as f [g(x)] and (f g)(x) (QCC, ACT) (MAAA_E2001-24)

·    analyze transformations of functions and relations and determine the effects on graphs and equations (QCC) (MAAA_B2001-9)

·    compare and contrast linear, quadratic, exponential, logarithmic and power functions (MAAA_E2001-27)

Ÿ         identify, write, solve and graph absolute value, step and constant functions

      (QCC, SAT I, ACT) (MAAA_A2001-4)

·    describe functional relationships (QCC) (MAAA_A2001-2)

·    develop and investigate axiomatic systems (MAAA_F2001-28)

·        (revised) evaluate and simplify expressions containing integral and rational exponents (QCC) (MAAA_A2003-3)

·        identify the inverse of relations algebraically and graphically, and determine if the inverse relation is a function (QCC ) (MAAA_A2003-8)

·        identify, define and graph relations that are functions, and evaluate functions for given input values (QCC) (MAAA_E2003-24)

 

 

Chapter 3: Systems of Linear Equations and Inequalities (pp. 154-213)                                  

(Omit 3.5 and 3.6)

·    (revised) solve, graph, apply, and interpret systems of linear and non-linear equations and inequalities in two and three variables using a variety of methods (QCC, SAT I, ACT) (MAAA_A2001-3)

·        determine the number of solutions for a system of linear equations, and recognize the system as consistent (dependent or independent) or inconsistent (QCC) (MAAA_A2003-10)

 

 

Chapter 4: Matrices (pp. 214-271) (Omit 4.5)

·        (revised) solve, graph, apply, and interpret systems of linear and non-linear equations and inequalities in two and three variables using a variety of methods (QCC, SAT I, ACT) (MAAA_A2001-3)

·        evaluate the results of matrix operations, such as addition, multiplication and scalar operations, when defined (MAAA_A2003-2)

·        find sums and products of matrices (QCC) (MAAA_F2003-36)

Ÿ         find determinants of 2 x 2 and 3 x 3 matrices (QCC) (MAAA_F2003-37)

Ÿ         find and apply inverses of  2 x 2 and 3 x 3 matrices (QCC) (MAAA_F2003-38)

Ÿ         apply matrices to practical situations (QCC) (MAAA_F2003-39)

 

 

Chapter 5: Quadratic Functions (pp. 272-351)                                                                           

·    use graphs to solve linear and quadratic equations and inequalities (QCC, SAT I) (MAAA_A2001-1)

·    solve and graph linear and quadratic equations and inequalities in one and two variables (QCC, SAT I) (MAAA_A2001-5)

·        fit and model linear and nonlinear curves to data (QCC) (MAAA_A2003-7)

Ÿ         perform operations with complex numbers, including adding, subtracting, multiplying, dividing and find additive inverses, conjugates, and absolute values (QCC, ACT) (MAAA_E2001-20)

Ÿ         solve quadratic equations and inequalities using various methods including factoring, completing the square, the quadratic formula, and graphing tools and methods (QCC) (MAAA_E2003-29)

Ÿ         graph quadratic functions and determine their maximum or minimum values, the number of zeros, and whether the zeros are real or imaginary (QCC) (MAAA_E2003-30)

Ÿ         solve problems using quadratics, such as problems involving motion and minimum/maximum values, and make predictions using data and regression techniques (QCC) (MAAA_E2003-31)

Ÿ         analyze the nature of the roots of quadratic equations by using the discriminant and the relationship between roots and coefficients (QCC) (MAAA_E2003-32)

 

Chapter 6: Exponential and Logarithmic Functions (pp. 352-421)                                            

·    recognize and apply the inverse relationship of exponential and logarithmic functions and graph and model each function (QCC, ACT) (MAAA_E2001-25)

·    compare and contrast linear, quadratic, exponential, logarithmic and power functions (MAAA_E2001-27)

·        model and solve exponential and logarithmic problems involving growth, decay, and compound interest, and make predictions from collected data using regression techniques (QCC) (MAAA_E2003-33)

·        apply the definition and properties of logarithms and exponents to evaluate logarithms and solve exponential and logarithmic equations (QCC) (MAAA_E2003-35)

Course:  Algebra II, 2nd Semester

Text: Algebra 2, Holt, Rinehart and Winston

Cost: $48.75

Prerequisite:  1st Semester Algebra II

 

Curricular goals interwoven throughout the mathematics program are that students will:

            learn to communicate mathematically (QCC)

            learn to use mathematics in their daily lives (QCC)

            become proficient with appropriate computational tools and techniques (QCC)

            learn to reason mathematically (QCC)

            become mathematical problem solvers (QCC)

 

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

 

Chapter 7: Polynomial Functions (pp. 422-477)                                                                          

·    develop algorithms and analyze functions using the Fundamental Theorem of Algebra (QCC) (MAAA_E2001-23)

·        determine quotients of polynomials using appropriate techniques (monomial divisor, long or synthetic division) or graphing tools (QCC) (MAAA_E2003-20)

·        apply theorems, including Remainder, Factor, Rational Root and the Fundamental Theorem of Algebra, to polynomial equations (QCC ) (MAAA_E2003-21)

·        approximate real roots of polynomial equations using calculators or computers (QCC) (MAAA_E2003-23)

 

Chapter 8: Rational Functions and Radical Functions (pp. 84-153)                                          

·    identify domain and range for algebraic and transcendental functions (QCC) (MAAA_E2001-26)

·        describe functional relationships (QCC) (MAAA_A2001-2)

·        (revised) evaluate and simplify expressions containing integral and rational exponents (QCC) (MAAA_A2003-3)

·    (revised) investigate, solve, and graph direct, joint, inverse and combined variation problems (ACT) (MAAA_A2001-6)

·        (new) solve rational equations and simplify rational expressions and their products, quotients, sums and differences (QCC, SAT I, ACT)(MAAA_E2004-1)

·        solve radical equations with one or two radical terms (QCC) (MAAA_E2003-19)

·        simplify radical expressions and their products, quotients, sums and differences, including rationalizing denominators by using properties of radicals (QCC) (MAAA_E2003-27)

·        determine real or imaginary nth roots of real numbers (QCC)(MAAA_E2003-26)

 

Chapter 9: Conic Sections (pp. 560-625)                                                                                    

·        (revised) solve, graph, apply, and interpret systems of linear and non-linear equations and inequalities in two and three variables using a variety of methods (QCC, SAT I, ACT) (MAAA_A2001-3)

·    (revised) apply the Pythagorean Theorem, distance and midpoint formulas as they pertain to conics (QCC, SAT I) (MAAA_B2001-7)

·    (revised) identify, compare, graph and solve problems involving conic sections (QCC, ACT) (MAAA_B2001-8)

·    analyze transformations of functions and relations and determine the effects on graphs and equations (QCC) (MAAA_B2001-9)

·    compare and contrast linear, quadratic, exponential, logarithmic and power functions (MAAA_E2001-27)

 

Chapter 10: Counting Principles and Probability (pp. 626-687)                                                 

·    design, conduct and interpret a statistical experiment (QCC) (MAAA_C2001-13)

·    discriminate between and determine the number of permutations and combinations of n things taken r at a time (QCC, SAT I, ACT) (MAAA_D2001-14)

·    solve numeration and finite probability problems, including finding the probability of mutually-exclusive events occurring (QCC, ACT) (MAAA_D2001-15)

·    apply theoretical and conditional probabilities to find the probability of an event by determining the sample space of all possible outcomes and the number of successful outcomes (QCC, ACT) (MAAA_D2001-16)

·    distinguish among odds, probabilities, and change and find the odds associated with given events (QCC, HSGT, SAT I) (MAAA_D2001-18)

·    find theoretical and conditional probability, and determine probability of independent, dependent, and conditional events (QCC, SAT I) (MAAA_D2001-19)

·    apply basic counting principles and solve basic and compound counting problems (QCC) (MAAA_F2001-29)

·        define probability in terms of sample spaces, outcomes and events (MAAA_D2003-15)

 

Chapter 11: Series and Patterns (pp. 688-761)                                                                          

·    apply the Binomial Theorem and relate it to Pascal’s Triangle (MAAA_D2003-16)

·        expand and simplify binomial expressions (QCC) (MAAA_D2003-17)

·        interpret arithmetic and geometric sequences and series (QCC, SAT I, ACT)(MAAA_F2004-2)

 

Chapter 12: Statistics (pp. 762-825) Only sections 12.1, 12.4, 12.5, 12.6                                 

·    analyze the effects of data transformation on measures of central tendency and variability (MAAA_C2001-12)

·    design, conduct and interpret a statistical experiment (QCC) (MAAA_C2001-13)

·        analyze data by using measures of central tendency and standard deviations (MAAA_C2003-14)

·        conduct binomial experiments (QCC) (MAAA_D2001-17)

·        explore normal distributions (QCC) (MAAA_D2003-18)