Course:  Honors Algebra II, 1st Semester

Text: Algebra II (Holt, Rinehart and Winston)

Cost: $48.75

Prerequisite: Honors Geometry (MAHG)

 

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.

 

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

Ÿ         investigate families of lines with different slopes and y-intercepts (QCC, ACT) (MAHA_A2001-2)

Ÿ         investigate parallel and perpendicular lines (QCC) (MAHA_D2003-16)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

Ÿ         fit linear and nonlinear curves to data (QCC, SAT I) (MAHA_B2001-5)

Ÿ         investigate direct, inverse, joint and quadratic variation (QCC, SAT I) (MAHA_D2003-22)

 

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

·      analyze translations, rotations and reflections of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-1)

·      translate among tabular, symbolic and graphical representations of data (MAHA_D2001-14)

·      graph and model piecewise functions (QCC) (MAHA_D2001-18)

Ÿ         apply and graph absolute value functions (QCC) (MAHA_D2003-15)

·      apply absolute value, step and constant functions (QCC) (MAHA_D2001-19)

Ÿ         analyze scale changes of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-3)

·      apply patterns of functional model (QCC) (MAHA_D2001-20)

·      find and graph compositions and inverses of functions (QCC) (MAHA_D2001-21)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

·      describe and analyze functional relationships (QCC) (MAHA_D2001-17)

·      simplify expressions containing integral exponents (QCC) (MAHA_G2001-37)

Ÿ         evaluate and simplify expressions with fractional exponents (QCC) (MAHA_D2003-13)

 

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

·      formulate linear and quadratic equations and inequalities for given conditions (QCC, SAT I, ACT) (MAHA_D2001-24)

·      solve and graph linear and quadratic equations and inequalities in two variables (QCC, SAT I, ACT) (MAHA_G2001-44)

·        apply linear programming models (MAHA-D2001-15)

 

Chapter 4: Matrices (pp. 214-271)                                                                                              

·      find sums and products of matrices (MAHA_E2003-18)

Ÿ         find determinants of 2 x 2 and 3 x 3 matrices (QCC) (MAHA_E2003-19)

Ÿ         find and apply inverses of 2 x 2 and 3 x 3 matrices (QCC) (MAHA_E2003-20)

Ÿ         use matrices to solve systems of equations and inequalities (QCC) (MAHA_E2001-31)

 

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

·      apply the Pythagorean theorem, distance and midpoint formulas (QCC) (MAHA_A2001-4)

·      fit linear and nonlinear curves to data (QCC, SAT I) (MAHA_B2001-5)

·      formulate linear and quadratic equations and inequalities for given conditions (QCC, SAT I) (MAHA_D2001-24)

·      use graphs to solve linear and quadratic equations and inequalities (QCC, SAT I, ACT) (MAHA_G2001-43)

·      find roots and intercepts of quadratic functions algebraically (QCC, SAT I, ACT) (MAHA_D2001-25)

·      make connections among different representations of linear and quadratic functions (QCC, SAT I, ACT) (MAHA_D2001-26)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

·      determine maximum and minimum points of a graph and interpret the results in problem situations (QCC) (MAHA_D2001-29)

·      investigate complex numbers (QCC, SAT I) (MAHA_G2001-41)

·      perform operations with complex numbers (QCC, SAT I) (MAHA_G2001-42)

Ÿ         analyze the nature of the roots of quadratic equations by using the discriminant and the relationship between roots and coefficients (QCC) (MAHA_D2003-17)

 

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

·      model exponential and logarithmic situations (QCC) (MAHA_B2001-6)

·      compare and contrast linear, quadratic, exponential, logarithmic and power functions (MAHA_D2001-16)

Ÿ         analyze translations, rotations and reflections of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-1)

Ÿ         analyze scale changes of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-3)

·      describe and analyze functional relationships (QCC) (MAHA_D2001-17)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

Ÿ         apply the definitions and properties of logarithms (QCC) (MAHA_B2003-3)

Ÿ recognize the inverse relationship of logarithms and exponential functions and graph each function (QCC) (MAHA_B2003-4)

Ÿ determine values of common and natural logarithms and antilogarithms and apply the change of base rule (QCC) (MAHA_B2003-5)

Ÿ solve exponential and logarithmic equations (QCC) (MAHA_B2003-6)

 

 

 

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

·      explore polynomial functions, including finding roots and intercepts (QCC, SAT I) (MAHA_D2001-28)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

·      determine maximum and minimum points of a graph and interpret the results in problem situations (QCC) (MAHA_D2001-29)

Ÿ         determine quotients of polynomials using appropriate techniques (QCC)

      (MAHA_D2003-12)

·      factor polynomials (QCC, SAT I) (MAHA_G2001-40)

·      solve polynomial equations using the following theorems:  Remainder, Factor, Rational Root and Fundamental Theorem of Algebra (QCC) (MAHA_G2001-45)

Ÿ         fit polynomials to data (MAHA_B2003-7)

 

 

 

 

 

 

Course:  Honors Algebra II, 2nd Semester

Text: Algebra II (Holt, Rinehart and Winston)

Cost: $48.75

Prerequisite: 1st Semester Honors 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 8: Rational Functions and Radical Functions (pp. 478-559)                                        

·      investigate direct, inverse, joint and quadratic variation (QCC, SAT I) (MAHA_D2001-22)

·      formulate, solve and graph equations for variation (QCC) (MAHA_D2001-23)

Ÿ         identify domain and range for algebraic functions (QCC) (MAHA_D2003-11)

·      simplify rational and irrational expressions (QCC) (MAHA_G2001-38)

Ÿ         solve equations with one or more radical terms (QCC) (MAHA_D2003-14)

Ÿ         solve problems involving rational and irrational equations (QCC) (MAHA_G2001-39)

 

 

 

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

Ÿ         apply the Pythagorean theorem, distance and midpoint formulas (QCC) (MAHA_A2001-4)

·      translate among tabular, symbolic and graphical representations of data (MAHA_D2001-14)

Ÿ         identify and compare conic sections and sketch their graphs (MAHA_F2003-21)

Ÿ         analyze translations, rotations and reflections of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-1)

Ÿ         analyze scale changes of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-3)

·      graph and solve problems involving circles, ellipses, hyperbolas and parabolas (MAHA_D2001-30)

·      solve and graph linear and quadratic equations and inequalities in two variables (QCC, SAT I) (MAHA_G2001-44)

 

 

 

 

 

 

Chapter 10: Counting Principles and Probability (pp. 625-687)                                                 

·      apply theoretical and conditional probabilities (QCC) (MAHA_C2001-9)

·      use permutations and combinations (QCC, SAT I) (MAHA_2001-12)

·      solve numeration and finite probability problems (QCC, SAT I) (MAHA_C2001-13)

Ÿ         (new) determine probability of independent, dependent and conditional probabilities (MAHA_C2003-9)

 

 

 

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

·      apply Pascal’s triangle and its properties to binomial experiments (QCC)

      (MAHA_C2001-11)

Ÿ         use the Binomial Theorem to expand and simplify expressions (MAHA_C2003-10)

Ÿ         analyze arithmetic and geometric sequences and series (QCC) (MAHA_E2001-34)

 

 

 

Chapter 12: Statistics (pp. 762-825)                                                                                            

·      analyze the effects of data transformations on measures of central tendency and variability (SAT I) (MAHA_B2001-7)

·      conduct and analyze binomial experiments (QCC) (MAHA_C2001-10)

Ÿ         analyze data using measures of central tendency and standard deviations (QCC) (MAHA_B2003-2)

Ÿ         explore normal distributions (MAHA_C2003-8)

Ÿ         transform data to make interpretations and predictions (SAT I) (MAHA_B2001-8)

 

 

 

Chapter 13: Trigonometric Functions (pp. 826-883)                                                      15 days

Ÿ         (new) convert measures of angles between radians and degrees (MAHA_F2003-22)

Ÿ         determine maximum and minimum points of a graph and interpret the results in problem situations (QCC) (MAHA_D2001-29)

Ÿ         solve problems using trigonometric ratios (QCC, ACT) (MAHA_F2001-36)

·      develop, graph and apply the six trigonometric functions (QCC) (MAHA_F2001-35)

Ÿ         analyze translations, rotations and reflections of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-1)

Ÿ         analyze scale changes of functions and relations and determine the effects on graphs and equations (QCC) (MAHA_A2001-3)

 

 

Chapter 14: Further Topics in Trigonometry (pp. 884-939)                                           10 days

Ÿ         apply laws of sines and cosines (MAHA_F2003-23)

Ÿ         represent coordinates in trigonometric and polar form (QCC) (MAHA_A2003-1)