Radnor High School Course Syllabus
Algebra 2 Honors 0453
Credits: 1 Grades: 9, 10, 11 Weighted: Length: 1 Year Format: Meets daily Prerequisite: 8th grade Algebra 1 with a “C” and Honors Geometry
Overall Description of Course
This course reviews and extends an understanding of the number system, formulas, equations and graphs. Subject matter includes quadratics, radicals, exponents, complex numbers, logarithms and exponential functions. An emphasis is placed on both the development of the concept of function and graphing functions using a transformational approach. The theory of equations and sequences and series are introduced during the course. Students are challenged to apply skills to new problems and to connect skills and concepts. Students are expected to handle a demanding workload. A graphing calculator is required.
Algebra 2 Honors is a Honors level course which is intended for the motivated math student who is very good with mathematics but needs more teacher guidance to assist in the mastery of the material. The course will involve accelerated pacing and a demanding workload with some written explanations expected. Students on this level will be prepared to take AP Calculus AB.
MARKING PERIOD ONE Common Core Standards N-VM.6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. N-VM.7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. N-VM.8. (+) Add, subtract, and multiply matrices of appropriate dimensions. N-VM.9. (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI.4. Solve quadratic equations in one variable. F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S-ID.8. Compute (using technology) and interpret the correlation coefficient of a linear fit.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills: Evaluate and write sigma notations Calculate absolute values Solve equations by using properties of equality Express solutions of equations as ordered pairs Apply properties of inequality Solve linear inequalities in one variable Graph solutions of inequalities on the number line Use midpoint and distance formulas Understand function notation Find domain and range of a function Multiply a matrix by a scalar Solve matrix equation Add, subtract and multiply matrices Calculate probability Use point-slope, slope-intercept and general linear forms of equations of lines Use slopes to determine if lines are perpendicular or parallel Solve system of linear equation graphically and algebraically Graph linear inequalities Find union and intersection of sets defined by inequalities Write equations that represent linear functions Recognize direct variation Fit a line to data by using linear regression in the calculator Recognize and graph compound (piecewise) functions Convert absolute value functions into piecewise functions and vice versa Multiply to form quadratics Remove common factors from expressions Factor trinomials and special products Graph quadratic functions Find the real zeros of quadratic functions Solve quadratic equations by factoring and quadratic formula Complete the square to find the maximum/minimum value of a quadratic function Complete the square to solve quadratic equations Analyze and solve problems involving maximum and minimum values Analyze and solve projectile motion
Materials & Texts
TEXTS Algebra 2 & Trigonometry, John Benson, McDougal Littell/Houghton Mifflin, 1991
Activities, Assignments, & Assessments
ACTIVITIES
Problem Solving Introduce Problem Solving Strategies Use Diagrams & Models to Solve Problems Find Patterns Use Sigma Notation to find Sums Write Sums in Sigma Notation
The Language of Algebra Simplify Expressions Solve Equations using Properties of Equality Solve & Graph Inequalities in One Variable Solve Absolute Value Equations & Inequalities Use Midpoint & Distance Formulas Understand Function Notation Perform Operations with Matrices Calculate Probabilities Simplify Expressions containing Exponents & Radicals
Linear Relationships Write Equations of Lines Graph Linear Equations Solve Systems of Linear Equations Graph Inequalities Recognize Direct Variation Find a Line of Best Fit Graph Compound Functions
Quadratic Functions Multiply Polynomials Factor Polynomials Graph Quadratic Functions Solve Quadratic Equations Complete the Square Solve Real World Problems using Quadratic Functions ASSIGNMENTS #01: Read the text and the examples in your book for the following sections: 1.1, 1.2, and 1.4. Be sure you read and under¬stand the handshake problem. Also make sure you copy an understandable definition and example of the following words and phrases: a. Model b. tree diagram c. digraph d. algorithm e. sigma notation #02: Find in Section 1.1 the FIVE MAIN THEMES of this course. Copy these into your notes. #03: Page 5: 2, 3, 4, 6 #04: Page 7: 1, 5, 6 #05: Page 14: 1, 2, 4, 6, 7(a) #06: Section 2.1: The Language of Expressions Page 26-29: 1-11 odd, 12-14, 17-28, 31(b), 32-34, 35, 39 #07: Section 2.2: Solving Equations Page 33-37: 1-9 odd, 10-12, 15, 16, 18, 19, 22-26, 29-37 odd, 38-44, 53 #08: Section 2.3: Solving Inequalities Page 40-44: 1-11 odd, 12, 13, 17, 18, 23, 26, 33, 36, 39, 42-48 even #09: Page 40-44: 14, 15, 19, 20, 22, 25, 34, 40, 43, 45, 53, 55, 59, 61 #10: Section 2.4: Introduction to Graphing Page 48-51: 1-5 odd, 7-11, 13-16, 19-25 odd, 26 #11: Section 2.5: Matrices Page 55-59: 1-7 odd, 9, 10, 17, 19, 21, 26, 27, 29, 33, 35 #12: Page 55-59: 11-16, 18, 22, 24, 30-32, 36 #13: Section 2.6: Probability Page 63-64: 1, 3-7, 9, 10, 12, 13, 15, 17, 19, 20 #14: Page 63-64: 8, 11, 14, 18, 21-23 #15: Page 66-68: 1-11, 14-18, 22-29, 33, 34, 36, 38-40 (Chapter Review) #16: Exponents & Radicals: Page 74-77: 1, 2, 4, 8, 9, 17, 23, 31, 34, 40 46, 49 #17: Page 74-77: 3, 7, 10, 11, 18, 24, 27, 32, 35, 41, 44, 47, 50 #18: Page 74-77: 5, 6, 12, 15, 19, 21, 25, 28, 36, 39, 42, 45, 51 #19: Page 74-77: 14, 16, 20, 29, 33, 37, 38, 43, 48, 52 #20: Section 3.1: Graphing Linear Equations Page 83-88: 1-11 odd, 13-17, 19-26, 29-31, 33 #21: Section 3.2: System of Linear Equations Page 90-93: 1-7 odd, 8, 10, 11, 13, 14, 16, 17-23 odd, 32 #22: Page 90-93: 9, 15, 18-24 even, 31 #23: Section 3.3: Graphing Inequalities Page 96-99: 1 -13 odd, 14, 16, 17, 20, 22, 27, 32 #24: Page 96-99: 2, 8, 10, 12, 15, 18, 28, 31 #25: Section 3.4: Functions and Direct Variations Page 103-6: 1 -7 odd, 9-11,13,15,16,19, 20, 22, 23, 25, 27-29, 35 #26: Page 103-6: 2-6 even, 12, 14, 17, 21, 24, 30, 31, 36, 37, 39, 42 #27: Section 3.5: Fitting a Line to Data Page 109-13: 1-5 odd, 6, 8, 9, 12-14, 16, 20, 28 #28: Section 3.6: Compound Functions Page 116-120: 1-13 odd, 14-19, 21, 23, 26, 27, 29, 33, 35, 37-39, 41, 42 45, 48, 49,54 56, 59 #29: Page 116-120: 2, 4, 10, 12, 20, 22, 25, 28. 30, 34, 36, 43, 44, 46, 50, 55, 57, 58, 60 #30: Page l22-124: 1-5, 7-9, 11-20, 22, 23, 27 (Chapter Review) #31: Section 4.1: What Are Quadratics? Page 130-134: 1-7 odd, 8, 9-15 odd, 16-24 even, 21, 25, 29, 33 #32: Section 4.2: Factoring Quadratics Page 137-141: 1-9 odd, 10-13, 15, 17, 20, 21, 24-28 even, 29, 33, 35-37, 39 #33: Page 137-141: 14-18 even, 19, 22, 23, 25, 30, 31, 34, 38, 40, 42, 43, 48 #34: Section 4.3: Graphing Quadratic Functions Page 145-148: 1, 3, 4, 6-8, 13, 15, 18, 20, 22, 25, 26, 29, 30, 34 #35: Page 146-148: 2, 5, 9-12, 14, 17, 19, 23, 24, 27, 28, 33, 36a, 37 #36: Section 4.4: Solving Quadratic Equations Page 152-156: 1, 3, 4-11, 13, 15, 16, 18-22, 24, 25, 28, 31-35 odd, 39 #37: Section 4.5: Complete the Square Page l60-163: 1-11 odd, 12-20 even, 19, 25-31 odd, 32, 34 #38: Page 160-163: 2-10 even, 13-17 odd, 22, 26-30 even, 35, 36, 38, 39 #39: Section 4.6: Applications of Quadratic Functions Page 168-170: 1 -5 odd, 7-13, 15-18, 20-22 #40: Section 4.7: Data Displays Page 174-176: 1-7, 9, 11, 12 #41: Page l78-180: 1, 3, 5, 7-10, 12, 13, 15, 16, 18, 19, 22-24, 26, 29, 31, 32,33, 36, 38
ASSESSMENTS Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and chapter tests.
Terminology sigma notation, absolute value, additive inverse, distribute, equation, equivalent expression, function, function notation, inequality, input, intercept, like-terms, linear equation, matrix, opposite, ordered pairs, output, probability, quadrant, scalar multiplication, compound function, constant of variation, direct variation, directly proportional, domain, intersection, line of best fit, linear function, range, regression line, system of linear equations, union, axis of symmetry, completing the square, discriminant, factoring, parabola, quadratic equation, quadratic expression, quadratic formula, quadratic function, real zero, root, vertex, vertex form, base, exponent, radical
Media, Technology, Web Resources Graphing calculator TI-83 or 84 MARKING PERIOD TWO Common Core Standards A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-REI.4. Solve quadratic equations in one variable. F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. F-BF.1. Write a function that describes a relationship between two quantities. F-BF.3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F-BF.4. Find inverse functions.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills: Represent relations Recognize functions Identify restrictions on the domain of a function Interpret composite functions Recognize inverse functions Find the inverse of a given function Recognize the relationship the graph of a function and its inverse Perform operations on the inputs and outputs of functions Use the factorial, permutation and combination functions Convert recursive definition to an equivalent closed form definition Graph absolute value functions Stretch, shrink, reflect and shift graphs Reflect objects graphed on a coordinate system Recognized symmetry with respect to a line or a point
Materials & Texts
TEXTS Algebra 2 & Trigonometry, John Benson, McDougal Littell/Houghton Mifflin, 1991 Activities, Assignments, & Assessments ACTIVITIES
Functions Represent Relations Recognize Functions Identify Domain & Range of a Function Interpret Composite Functions Recognize Inverse Functions Perform Operations on Functions Use Discrete Functions Use & Write Recursive Definitions of Functions
Graphing By Transformation Stretch, Shrink & Reflect Graphs Translate Graphs Recognize Symmetry
ASSIGNMENTS #42: Section 5.1: Relations and Functions Page 186-189: 1-9 odd, 12, 16, 18, 20, 22, 25, 26 #43: Page 186-189: 2-10 even, 11-19 odd, 23, 24, 27, 31 #44: Section 5.2: More About Functions Page 193-197: 1 (No Range for 1b or 1d), 3, 5, 8, 10, 11, 13, 14, 19, 21, 23, 25, 28 #45: Page 193-197: 4, 6, 7, 9, 12, 15-18, 20, 22, 24, 27, 29 #46: Section 5.3: Inverse Functions Page 201-205: 1-9 odd, 10-12, 14, 17, 21, 22, 24, 25, 28-30, 34 #47: Page 201-205: 2-8 even, 13, 15, 16, 19, 20, 23, 27, 31, 35, 37 #48: Section 5.4: Operations on Functions Page 209-212: 1-11 odd, 12-16 even, 19, 20, 26 #49: Page 209-212: 2-10 even, 13, 15, 17, 18, 21, 22, 24, 28 #50: Section 5.5: Discrete Functions Page 216-219: 1-9 odd, 11, 18, 19, 23, 24, 26, 29, 30, 33, 38 #51: Page 216-219: 2-10 even, 12-17, 20-22, 25, 27, 28, 32, 34 #52: Section 5.6: Recursively Defined Functions Page 224-227: 1, 3, 6, 9-11, 13, 16, 17, 20, 21, 24, 26 #53: Page 224-227: 2, 4, 5, 7, 8, 12(do algebraically), 14, 15, 18, 19, 22, 23, 25 #54: Section 5.7: Measures of Central Tendency and Percentiles Page 230-232: 1-5, 11-13 #55: Page 234-36: 1-4, 6-9, 11- 13, 16-21, 24-29, 31, 34 (Chapter Review) #56: Section 6.1: Beyond Plotting Points Page 242-245: 1-4, 9, 11, 12, 14, 16, 18, 22, 24, 26, 28, 33 #57: Page 242-245: 5-8, 10, 13, 15, 19, 20, 21, 23, 25, 27, 29, 30-32, 34 #58: Section 6.2: Translating Graphs Page 247-251: 1-21 odd, 23-25, 28, 30, 34-36, 39, 43, 49 #59: Page 247-251: 2-22 even, 26, 29, 31, 32, 37, 38, 41, 44, 47, 52 #60: Section 6.3: Reflections and Symmetry Page 256-259: 1-15 odd, 20-23, 27, 28, 30-32 #61: Page 256-259: 2-10 even, 14, 17-19, 24-26, 35-38, 40, 42 ASSESSMENTS Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and chapter tests. A midterm exam will be given at the end of the quarter.
Terminology Closed (explicit) form , combination, composition of functions, discrete functions, factorial, first/second differences, inverse function, permutation, recursive definition, reflection, relation, shift, shrink, stretch, symmetry
Media, Technology, Web Resources Graphing calculator TI-83 or 84 MARKING PERIOD THREE Common Core Standards N-RN.1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. N-RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. N-CN.1. Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. N-CN.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. N-CN.3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. N-CN.4. (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. N-CN.5. (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. N-CN.7. Solve quadratic equations with real coefficients that have complex solutions. N-CN.8. (+) Extend polynomial identities to the complex numbers. A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. A-REI.4. Solve quadratic equations in one variable. A-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. A-REI.8. (+) Represent a system of linear equations as a single matrix equation in a vector variable. A-REI.9. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills: Graph cubic, quartic, reciprocal and exponential functions Use system of equations to solve problems Solve systems of equations in three unknowns Graph equations that contains three variables Graph systems of inequalities Solve direct, inverse, joint and combined variation problems Solve nonlinear systems Factor by grouping Factor sum/difference of two cubes Solve equations by factoring Solve inequalities by factoring and interval testing Apply the properties of exponents to expressions with rational exponents Solve radical equations Perform operations on complex numbers
Materials & Texts
TEXTS Algebra 2 & Trigonometry, John Benson, McDougal Littell/Houghton Mifflin, 1991
Activities, Assignments, & Assessments ACTIVITIES
Graphing by Transformations Introduce Graphs of Cubic & Quartic Functions Graph Reciprocal Functions Graph Exponential Functions
Systems Use Systems of Equations to Solve Problems Solve Systems of Equations in 3 Unknowns Graph Equations that contain 3 Variables Graph Systems of Inequalities Solve Inverse Variation Problems Solve Systems containing Nonlinear Equations Factor the Sum or Difference of Two Cubes Solve Inequalities by Factoring
Extending the Real-Number System Simplify Expressions with Rational Exponents Solve Radical Equations Perform Operations on Complex Numbers
ASSIGNMENTS #62: Section 6.4: Graphing Other Functions Page 264-267: 1, 3-5, 8, 11-21 odd, 24, 25, 27, 29 #63: Page 264-267: 2, 6, 7, 9, 10-18 even, 22, 23, 26 #69: Section 7.1: Solving Problems with System of Equations Page 294-296: 1-9 odd, 10-14, 18, 19, 21, 24-26, 35 #70: Page 294-6: 2-8 even, 15, 16, 17, 20, 23, 27, 28-30, 34, 36, 37 #71: Section 7.2: Linear Systems with Three Variables Page 301-305: 1 -7 odd, 8, 10-13, 14, 17, 21, 23, 24 #72: Page 301-305: 2-6 even, 9, 15, 18, 19, 22, 25, 26, 28, 29 #73: Section 7.3: Systems of Inequalities Page 307-311: 1 - 5 odds, 7 - 14, 16, 17, 23, 25, 26, 28, 30, 33 #74: Linear Programming Worksheets #75: Section 7.4: Inverse Variations Page 314-317:1-7 odd, 9, 11, 13, 16, 18, 21 - 23, 27, 28, 29, 33 #76: Page 314-317: 2-14 even, 15, 17, 30, 32, 34, 37, 38, 39, 41, 43 #77: Section 7.5: Nonlinear Systems Page 320-323:1-9 odd, 10, 12, 13, 15 - 17, 19, 20, 22, 25, 26, 29, 31, 37, 39 #78: Chapter Review Page 332-334: 1-4, 6, 7, 9, 14, 16, 18, 20- 23, 25 #79: Factoring Page 339-341:1, 2, 4, 7, 8, 9, 11, 13, 14, 19, 21, 22-28 even, 35, 37 #80: Page 339-341: 3, 5, 6, 10, 12, 15, 16, 18, 20, 25, 27, 32, 34 #81: Section 8.1: Rational Exponents Page 345-348: 1-5 odd, 6-10, 14, 15, 19, 21, 23-28, 33 #82: Page 345-348: 2, 4, 11, 12, 16-18, 22, 29, 30, 32 #83: Section 8.2: Solving Radical Functions Page 352-356: 1-5 odd, 6, 8, 10, 12-16, 22-25, 30, 32, 38, 39, 45, 47, 51 #84: page 352-356: 2, 4, 7, 11, 17-21, 26-29, 31, 33-35, 40, 41, 46, 48, 49, 53, 54 #85: Section 8.3: Introduction to Complex Numbers Page 360-363: 1-5 odd, 6-14, 16, 18, 24, 27, 30, 34, 39, 42, 45 #86: Page 360-363: 2, 4, 15, 17, 19, 21-23, 25, 26, 28, 29, 33, 35- 37, 40, 44 #87: Section 8.4: Algebra of Complex Numbers Page 367-371: 1-5 odd, 7-9, 11, 12, 15, 16, 20, 22, 25, 30, 31, 34 #88: Page 367-371: 2, 4, 6, 13, 14, 17-19, 21, 23, 24, 26, 28, 29, 32, 33 #89: Chapter Review Page 377-378: 1-12, 14-16, 18, 20, 21, 23, 24, 27, 30, 31, 33-39, 41, 42
ASSESSMENTS Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and chapter tests.
Terminology cubic function, exponential function, horizontal asymptote, quartic function, reciprocal function, inverse, joint and combined variations, traces, complex numbers, conjugates, extraneous roots, pure imaginary numbers, radicand, root index, standard complex form
Media, Technology, Web Resources Graphing calculator TI-83 or 84 MARKING PERIOD FOUR Common Core Standards N-CN.7. Solve quadratic equations with real coefficients that have complex solutions. N-CN.8. (+) Extend polynomial identities to the complex numbers. N-CN.9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential functions. A-SSE.4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-APR.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. a(x) r(x) A-APR.6. Rewrite simple rational expressions in different forms; write /b(x) in the form q(x) + /b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. A-REI.2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. F-BF.1. Write a function that describes a relationship between two quantities. F-BF.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F-BF.5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. F-LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). F-LE.4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills: Divide a polynomial by a binomial Apply the remainder and factor theorems Perform synthetic and long divisions Find zeros of functions by factoring and using the quadratic formula Use the calculator to find the rational zeros of a function Determine the number of complex zeros a polynomial function has Determine the sum and product of the roots of a quadratic equation Apply the conjugate zero theorem Simplify, multiply, add, subtract and divide rational expressions Solve rational equations and inequalities Simplify complex fractions Graph exponential and logarithmic functions Use the properties of logarithms Solve exponential and logarithmic equations Use exponential and logarithmic functions as mathematical models Use appropriate base (10 or e) in certain problems Use sigma notation to express a series Find the value of an infinite series Compute any term in an arithmetic sequence Compute arithmetic means Evaluate arithmetic series Compute any term in a geometric sequence Compute geometric means Evaluate finite and infinite geometric series
Materials & Texts
TEXTS Algebra 2 & Trigonometry, John Benson, McDougal Littell/Houghton Mifflin, 1991
Activities, Assignments, & Assessments ACTIVITIES
Polynomials & Polynomial Functions Apply Remainder and Factor Theorems Perform Long & Synthetic Division Determine Number of Complex Zeroes of a Polynomial Function Determine the Sum & Product of the Roots of a Quadratic Equation Apply the Conjugate Zeroes Theorem
Rational Expressions, Equations and Functions Multiply and Divide Rational Expressions Solve Rational Equations and Inequalities Add and Subtract Rational Expressions With Like Denominators Add and Subtract Rational Expressions With Unlike Denominators Simplify Complex Fractions
Exponential and Logarithmic Functions Graph Exponential & Logarithmic Functions Use the Common Logarithmic and Natural Logarithmic Functions Use Properties of Logarithms Solve Exponential and Logarithmic Equations Solve Real World Problems using Exponential and Logarithmic Functions
Sequences and Series Introduce Sequences & Series Compute any Term in an Arithmetic or Geometric Sequence Evaluate Arithmetic & Geometric Series
ASSIGNMENTS
#90: Section 9.1: The Remainder and Factor Theorems Page 386-388: 6, 16, 21, 22, 24, 25, 27-31, 37-39, 42 #91: Page 386-388: 17, 19, 20, 23, 26, 32-36, 43, 45, 46 #92: Section 9.2: The Rational-Zero Theorem Page 392-395: 1-5 odd, 6, 8-10, 13, 14, 20, 21, 23, 27 #93: Page 392-395: 2, 11, 17,18, 22, 24-26, 29, 30, 33, 34 #94: Section 9.4: Four Useful Theorems Page 406-409: 1, 3, 5, 8, 9, 11, 12, 14, 17, 18, 21, 24, 26, 29, 31 #95: Page 406-409: 2, 4, 6, 7, 10, 13, 15, 19, 20, 25, 28, 33, 34a, 36 #96: Section 9.5: The Binomial Theorem Page 413-415: 1, 3, 5, 6, 8, 11, 12, 14, 16-18, 21, 24, 27, 34, 35, 40 #97: Page 413-415: 7, 9, 10, 13, 15, 19, 20, 22, 25, 26, 30, 32, 38, 39 #98: Chapter Review Page 423-24: 1, 4-6, 8-14, 17, 23, 26, 28 #99: Section 10.1: Multiplying and Dividing Rational Expressions Page 430-433: 1-17 odd, 22, 24, 28, 30, 32, 33, 36, 38 #100: Page 430-433: 2-20 even, 23, 25-27, 29, 31, 34, 40, 46 #101: Section 10.2: Rational Equations and Inequalities Page 438-441: 1-11 odd, 14, 16, 19, 22-26, 28-31, 36, 44, 47, 52, 53 #102: Page 438-441: 2, 4, 6, 10, 12, 15, 17, 18, 20, 27, 32, 33, 39-43, 48, 51, 54, 58 #103: Section 10.3: Adding and Subtracting Rational Expressions With Like Denominators Page 445-447: 1-11 odd, 16, 19, 21-24, 29, 31, 36, 37, 44, 51 #104: Page 445-447: 2-14 even, 15, 18, 25a, 27, 28, 30, 32, 38, 45, 48 #105: Section 10.4: Adding and Subtracting Rational Expressions With Unlike Denominators Page 450-453: 1-13 odd, 18, 21, 24, 25, 27, 28, 30, 33, 39, 42-45 #106: Page 450-453: 2-12 even, 15-17, 19, 20, 29, 31, 34, 35, 41, 48-51 #107: Section 10.5: Complex Fractions Page 457-460: 1-13 odd, 14, 17, 23, 24, 26, 30, 33, 35, 40, 42, 47 #108: Page 457-460: 2-12 even, 15, 16, 18, 25, 28, 29, 31, 38 #109: Chapter Review Page 462-464: 1, 3, 5-10, 12, 13, 15-19, 21, 23, 24, 27, 28, 30, 31, 33, 35, 36, 39, 41, 52 #110: Section 11.1: Definitions and Graphs of Exponential & Logarithmic Fns Page 476-479: 1-7 odd, 8-11, 14-17, 23, 28-31, 34, 37, 39-41 #111: Page 476-479: 2-6 even, 12, 18, 19-22, 24-27, 32, 43, 44(a & b), 45 #112: Section 11.2: Two Important Exponential and Logarithmic Functions Page 483-486: 1-13 odd, 14, 17, 27-30, 33, 39, 42, 43, 45 #113: Page 483-486: 2-10 even, 18, 20, 21, 22, 25, 31, 32, 34, 35, 38, 44, 46 #114: Section 11.3: Properties of Logarithms Page 490-493: 1-7 odd, 8-10, 12, 14, 15, 17-22, 24, 28, 30(a & b), 33, 36 #115: Page 490-493: 2-6 even, 11, 13, 23, 26, 27, 29(a & b), 32, 34 #116: Section 11.4: Solving Exponential and Logarithmic Equations Page 498-500: 1-9 odd, 10, 12, 15, 19, 21-24, 27, 29, 31, 32, 35 #117: Page 498-500: 2-8 even, 11, 17, 18, 26, 28, 30 #118: Section 11.5: Applications of Exponential and Logarithmic Functions Page 505-508: 2, 3, 6, 7, 9,12(a & b), 13, 17, 19, 23, 24 #119: Chapter Review Page 515-518: 1-6, 10-13, 17, 20, 23, 24, 26, 27, 32, 34, 35 (a & b) #120: Section 13.1: Sequences Page 566-569: 1-12, 17-19, 22, 26, 33-35, 37 #121: Section 13.2: Series Page 573-575: 3-5, 8-15, 17-20, 23, 30, 31, 36, 37 #122: Section 13.3: Arithmetic Sequences and Series Page 579-581: 1-15 odd, 18, 19, 25-27, 33, 35, 43 #123: Page 579-581: 2-16 even, 17, 22, 28-32, 34, 38, 39, 41 #124: Section 13.4: Geometric Sequences and Series Page 587-589: 1, 3, 6, 8-12, 21-24, 32, 33 #125: Page 587-589: 2, 4, 7, 13-15, 18-20, 29, 30 #126: Page 592-594: 1-3, 10-20, 22, 28, 38, 42-45 (Chapter Review)
ASSESSMENTS Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and chapter tests. A final exam will be given at the end of the school year.
Terminology factor theorem, fundamental theorem of algebra, multiplicity, remainder theorem, synthetic division, complex fractions, rational expressions, equations & inequalities, restricted values, anti-logarithms, base, base change formula, common logarithmic function, exponential equations/functions, logarithmic equations/functions, natural logarithmic function, arithmetic means, arithmetic sequences and series, common difference, common ratio, geometric means, geometric sequences and series, sequence of partial sums, sum of an infinite series
Media, Technology, Web Resources Graphing calculator TI-83 or 84