CURRICULUM PACING GUIDE ALG. II WITH TRIG (GRADES 10-12) 1st Nine Weeks 1

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1 b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. 15 days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in Context of One-to-one function ACT Quality Core Unit 2: Linear Equations McGraw Hill Algebra 2: 2.1 Relations and Functions Increasingly Complex Mathematical and Real-World 2.2 Linear Relations and Functions Problems 2.3 Rate of Change and Slope a. Apply problem-solving skills (e.g., identifying irrelevant 2.4 Writing Linear Equations or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. 2.5 Scatter Plots/Lines of Regression 2.6 Special Functions 2.7 Parent Functions/Transformations 2.8 Graphing Linear and Absolute Value Inqeualities Onto function Discrete relation Continuous relation Vertical line test Independent variable Dependent variable Function notation Linear relations Linear equations Linear function Standard form y-intercept x-intercept rate of change slope slope-intercept form point-slope form parallel perpendicular bivariate data scatter plot dot plot positive correlation negative correlation line of fit prediction equation regression line correlation coefficient Mid-Chapter 2 Test Chapter 2 Test Benchmark 1+E29 1st Nine Weeks 1

2 Suggested 10 Days g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize date, develop concepts, explore relationships, decrease time spent on computations after a skill has been established. D. Exploring Expressions, Equations, and Functions in the First Degree 1. Expressions, Equations, and Inequalities a. Solve linear inequalities containing absolute value. (CCRS-27) b. Solve compound inequalities containing and, or and graph the solution set. (CCRS-27) c. Solve Algebraically a system containing three variables. (CCRS-27) 2. Graph, Relations and Functions a. Graph a system of linear inequalities in two variables with and without technology. (CCRS-21, 22) b. Solve linear programming problems by finding maximum and minimum values of a function over a region defined by linear inequalities. (CCRS-20, 21) H. Organizing and Analyzing Data and Applying Probability 2. Sequences and Series piecewise-defined function piecewise-linear function step function greatest integer function absolute value function family of graphs parent graph parent function constant function identity function quadratic function translation reflection line of reflection dilation linear inequality boundary Sequence Term Finite Sequence Infinite Sequence Arithmetic Sequence Common difference Geometric Sequence ACT Quality Core Unit 1: Functions, Graphs, and Their Transformations McGraw Hill Algebra Sequences as Functions 10.2 Arithmetic Sequences/Series 10.3 Geometric Sequences/Series 10.6 Binomial Theorem Mid-Chapter 10 Test Chapter 10 Test 1st Nine Weeks 2

3 a. Find the nth term of an arithmetic or geometric sequence b. Find the position of a given term of an arithmetic or geometric sequence c. Find sums of a finite arithmetic or geometric series d. Use sequences and series to solve real-world problems e. Use sigma notation to express sums Geometric Sequence Common ratio Arithmetic Series Partial sum Sigma notation Geometric means Geometric series 10.6 Binomial Theorem 10.7 Proof by Mathematical Induction 10 Days D. Exploring Expressions, Equations, and Functions in System of Equations ACT Quality Core Unit 3: What is a the First Degree 1. Expressions, Equations, and Inequalities c. Solve Algebraically a system containing three variables. (CCRS-21) I. Using Matrices to Organize Data and Solve Problems 1. Matrices a. Add, Subtract, and multiply matrices. (CCRS-8, 9, 10) b. Use addition, subtraction and multiplication of matrices to solve real-world problems. (CCRS-8, 10) c. Calculate the determinant of 2x2 and 3x3 matrices. (CCRS-11) d. Find the inverse of a 2x2 matrix. (CCRS-11) Break-even point Consistent Inconsistent Independent Dependent Substitution Method Elimination Method Linear Programming Feasible region Optimize Unbound Ordered triple Matrix Element Dimensions Row Cell Matrix-Really? McGraw Hill Algebra 2: 3.1 Solving Systems of Equations 3.2 Solving Systems of Inequalities by Graphing 3.3 Optimization with Linear Programming 3.4 Systems of Equations in Three Variables 3.5 Operations with Matrices 3.6 Multiplying Matrices Mid-Chapter 3 Test Chapter 3 Test Benchmark 1 1st Nine Weeks 3

4 e. Solve systems of equations by using matrices and determinants. (CCRS-11, 26) f. Use technology to perform operation on matrices, find determinants, and find inverses. (CCRS-7, 8, 9, 10) Spreadsheet Scalar Scalar multiplication Zero Matrix Additive inverse 1st Nine Weeks 4

5 35 Days ACT Quality Core +B14 Standards B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in Context of Increasingly Complex Mathematical and Real-World Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. ACT Quality Core Academic Quality Core Unit 4 Parabola Focus Directrix Latus rectum Standard form General form Circle Center Radius Ellipse Foci Major Axis Constant sum Verticles Co-vertices Constant difference Mid-Chapter 9 Test Chapter 9 Test Mid-Chapter 4 Test Chapter 4 Test Benchmark 2 d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize date, develop concepts, explore relationships, decrease time spent on computations after a skill has been established. C. Establishing Number Sense and Operation Skills 1. Foundations c. Simplify quotients of complex numbers. (CCRS-4) E. Exploring Quadratic Equations and Functions 2. Graphs, Relations and Functions Quality Core Unit 5 Quadratic Function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex Maximum value Minimum value Quadratic Equations Standard form Root Zero Factored Form FOIL Method Imaginary Unit Pure Imaginary Number Complex Number Complex Conjugate 2nd Nine Weeks 5

6 ACT Quality Core +B14 Standards a. Determine the domain and range of a quadratic function: graph the function with and without technology. (CCRS-21, 29) b. Use transformations (e.g., translation, reflection) to draw the graph of a relation and determine a relation that fits a graph. (CCRS-29, 34) 3. Conic Sections a. Identify conic sections (e.g., parabola, ellipse, hype rbola) from their equation in standard form. (CCRS-28, 28a, 31) b. Graph circles and parabolas and heir translations from given equation or characteristics with and without technology. (CCRS-28, 28a, 31) c. Determine characteristics of circles and parabolas from their equations and graphs. (CCRS-31) d. Identify and write equations for circles and parabolas from given characteristics and graphs. (CCRS-28, 28a, 31) E. Exploring Quadratic Equations and Functions 1. Equations and Inequalities a. Solve quadratic equations and inequalities using various techniques, including competing the square and using the quadratic formula (CCRS-20) b. Use the discriminant to determine the number and types of roots for a given quadratic equation. c. Solve quadratic equations with complex number solutions d. Solve quadratic systems graphically and algebraically with and without technology. (CCRS-20) 2. Graphs, Relations and Functions b. Use transformations (e.g., translation, reflection) to draw the graph of a relation and determine a relation that fits a graph (CCRS-29) c. Graph a system of quadratic inequalities with and without technology to find the solution set to the system. (CCRS-21, 22) ACT Quality Core Academic Completing the Square Quadratic Formula Discriminant Vertex Form Quadratic Inequality 2nd Nine Weeks 6

7 35 Days B. Exploring the Skills and Strategies Underlying Mathematics 1. Mathematical Processes Learned in Context of Increasingly Complex Mathematical and Real-World Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize date, develop concepts, explore relationships, decrease time spent on computations after a skill has been established. Unit 6 Simplify Degree of a Polynomial Synthetic Division Polynomial in one variable Leading coefficient Polynomial function Power function End behavior Quartic function Quantic function Relative maximum Relative minimum Extrema Turning points Prime polynomials Quadratic form Identity Polynomial identity Synthetic substitution Depressed polynomial Unit 7 Composition of Functions Inverse Relation Inverse Function Square Root Inequality Nth Root Radical sign Index Radicand Principal root Rationalizing the denominator Like Radical Expresssions Conjugate Radical Equation Extraneous Solution ACT Quality Core Unit 6: Polynomials McGraw Hill Algebra 2: 5.1 Operations with Polynomials 5.2 Dividing Polynomials 5.3 Polynomial Functions 5.4 Analyzing Graphs of Polynomial Functions 5.5 Solving Polynomial Equations 5.6 The Remainder and Factor Theorem 5.7 Roots and Zeros ACT Quality Core +A1 Unit 7: Rational and Radical Expressions/Equations McGraw Hill Algebra 2: 6.1 Operations on Functions 6.2 Inverse Functions and Relations 6.3 Square Root Functions and Inequalities 6.4 nth Roots 6.5 Operations with Radical Expressions 6.6 Rational Exponents 6.7 Solving Radical Equations and Inequalities (7 days) 8.1 Multiplying and Dividing Rational Expressions 8.2 Adding and Subtracting Rational Expressions 8.3 Graphing Reciprocal Functions 8.4 Graphing Rational Functions 8.5 Variation Functions 8.6 Solving Rational Equations and Inequalities (7 days) Mid-Chapter 5 Test Chapter 5 Test Mid-Chapter 6 Test Chapter 6 Test Mid-Chapter 8 Test Chapter 8 Test Benchmark 3 3rd Nine Weeks 7

8 F. Exploring Polynomial Expressions, Equations and Functions 1. Expressions and Equations a. Evaluate and simplify polynomial expressions and equations. (CCRS-16) b. Factor polynomials using a variety of methods (e.g., factor theorem, synthetic division, long division, sums and differences of cubes, grouping) (CCRS-13, 17) 2. Functions a. Determine the number and type f rational zeros for a polynomial function. (CCRS-17) b. Find all rational zeros of a polynomial function. (CCRS-17, 19) c. Recognize the connection among zeros of a polynomial function, x-intercepts, factors of polynomials, and solutions of polynomials equations. (CCRS-6) d. Use technology t graph a polynomial function and approximate the zeros, minimum, and maximum; determine domain and range of the polynomial function. (CCRS-17, 30) G. Exploring Advanced Functions 1. Rational and Radical Expressions, Equations, and Functions a. Solve mathematical and real-world rational equation problems (e.g., work or rate problems). (CCRS-12, 12a, 12b, 20) b. Simplify radicals that have various indices. (CCRS- 24) c. Use properties of roots and rational exponents to evaluate and simplify expressions. (CCRS-13, 24) d. Add, subtract, multiply and divide expressions containing radicals. (CCRS-24) Extraneous Solution Radical Inequality Rational Expression Complex Fraction Reciprocal Function Hyperbola Asymptote Rational Function Point Discontinuity Direct Variation Constant of Variation Rational Equations Rational Inequalities Weighted Average Inverse Function 3rd Nine Weeks 8

9 e. Rationalize denominators containing radicals and find the simplest common denominator. (CCRS-24) f. Evaluate expressions and solve equation containing nth roots or rational exponents. (CCRS- 24) g. Evaluate and solve radical equation given a formula for a real-world situation (CCRS-24) 3rd Nine Weeks 9

10 35 Days B. Exploring the Skills and Strategies Underlying Exponential Function Mathematics 1. Mathematical Processes Learned in Context of Increasingly Complex Mathematical and Real-World Problems a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making conjectures, extracting mathematical meaning, recognizing and performing multiple steps when needed, verifying results in the context of the problem) to the solution of real-world problems. b. Use a variety of strategies to set up and solve increasingly complex problems c. Represent data, real-world situations and solutions in increasingly complex contexts (e.g., expressions, formulas, tables, charts, graphs, relations, functions) and understand the relationships. d. Use the language of mathematics to communicate increasingly complex ideas orally and in writing, using symbols and notations correctly. e. Make appropriate use of estimation and mental mathematics in computations and to determine the reasonableness of solutions to increasingly complex problems. f. Make mathematical connections among concepts, across disciplines, and in everyday experiences. Exponential Growth Asymptote Growth Factor Exponential Decay Decay Factor Exponential Equation Compound Interest Exponential Inequality Logarithm Logarithmic Function Logarithmic Equation Logarithmic Inequality Common Logarithm Change of Base Formula Natural Base e Natural Base Exponential Function Natural Logarithm Rate of Continuous Growth Rate of Continuous Decay Logistic Growth Model Trigonometry Angle of Depression Standard Position Initial Side Terminal Side Coterminal Angles Radian Central Angle ACT Quality Core Unit 8: Exponential and Logarithmic Functions McGraw Hill Algebra 2: 7.1 Graphing Exponential Growth 7.2 Solving Exponential Equations and Inequalities 7.3 Logarithms and Logarithmic Functions 7.4 Solving Logarithmic Equations and Inequalities 7.5 Properties of Logarithms 7.6 common Logarithms 7.7 Base e and Natural Logarithms 7.8 Using Exponential and Logarithmic Functions (9.5 Days) Mid-Chapter 7 Test Chapter 7 Test Benchmark 4 g. Demonstrate the appropriate role of technology (e.g., calculators, software) in mathematics (e.g., organize date, develop concepts, explore relationships, decrease time spent on computations after a skill has been established. 4th Nine Weeks 10

11 C. Establishing Number Sense and Operation Skills 1. Foundations d. Perform operations on functions, including function composition, and determine domain and range for each of the given functions. (CCRS 33/33a) G. Exploring Advanced Functions 2. Exponential and Logarithmic Functions a. Graph exponential Functions with and without technology. (CCRS-30) b. Convert exponential functions to logarithmic form and logarithmic equations to exponential form. (CCRS-36) H. Organizing and Analyzing Data and Applying Probability 1. Data Relations, Probability, and Statistics a. Use the fundamental counting principal to count the number of ways an event can happen. (CCRS-41, 42, 43) b. Use counting techniques, like combinations and permutations, to solve problems (e.g., calculate probabilities) (CCRS-41, 42, 43, 50) c. Find the probability of mutually exclusive and nonmutually exclusive events. (CCRS-41, 42, 43) d. Find the probability of independent and dependent events. (CCRS-44, 42, 45, 46, 48, 49) e. Use unions, intersections, and complements to find probabilities (CCRS-41, 42, 43) Combinations Permutations Probabilities Mutually exclusive Independent/dependent events Union Intersection Complement Conditional probability Fundamental counting principle ACT Quality Core Unit 10: Probability and Data Analysis McGraw Hill Algebra 2: Chapter Chapter 10 Test Benchmark 4 4th Nine Weeks 11

12 4th Nine Weeks 12

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices

ALGEBRA 2. Background Knowledge/Prior Skills Knows what operation properties hold for operations with matrices ALGEBRA 2 Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number