Algebra 2 CP Curriculum Pacing Guide

Transcription

1 SOUTH CAROLINA ACADEMIC STANDARDS FOR MATHEMATICS The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes. Standard IA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Indicators IA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately. IA-1.2 IA-1.3 IA-1.4 IA-1.5 IA-1.6 IA-1.7 Connect algebra with other branches of mathematics. Apply algebraic methods to solve problems in real-world contexts. Judge the reasonableness of mathematical solutions. Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic). Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams. Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs). COMMON CORE STATE STANDARDS FOR MATHEMATICS Indicators A-SSE.1 A-CED.2 A-CED.4 Interpret expressions that represent a quantity in terms of its context. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Anderson School District Five Page 1 Copyrigth July 1, 2012

2 Anderson School District Five Page 2 Copyrigth July 1, 2012

3 First Nine Weeks Unit 1 Numbers and Functions EA-2.5 EA-2.6 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions. Carry out a procedure to evaluate an expression by substituting a value for the variable. Identify and use properties of real numbers. Evaluate expressions using order of operations. PowerPoint Day 1 Critical Thinking Algebraic & Numeric Expressions EA-2.1 EA-3.4, EA-5.10 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers). Analyze the graph of a continuous function to determine the domain and range of the function. Analyze given information to determine the domain and range of a linear function in a problem situation. Classify numbers in the real number system. Find the domain, range, and inverse of a relation by using ordered pairs, tables, mapping, and graphs. Worksheet Introduction to Functions 1 EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph. Determine whether a relation and its inverse is a function. EA-3.2 EA-3.3 Use function notation to represent functional relationships. Carry out a procedure to evaluate a function for a given element in the domain. Write a function in function notation and evaluate it. PowerPoint Day 2 Function Notation Evaluating Functions 2 IA-2.5 Carry out procedures to perform operations on polynomial functions (including f(x) + g(x), f(x) g(x), f(x) g(x), and f(x)/g(x)). Perform operations with functions by evaluating Worksheet Operations with Functions Anderson School District Five Page 3 Copyrigth July 1, 2012

4 First Nine Weeks IA-2.6 A Apply a procedure to write the equation of a composition of given functions. Find the composition of two functions by evaluating. Worksheet Compositions of Functions PowerPoint Day 3 Transformations 2 cont d SC IA-2.7 SC IA-2.8 A F-BF.3 Carry out a procedure to graph translations of parent functions.. including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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. Review Test ). Given the graph of a function, perform transformations. Review Chapter 1 Study Guide Review for Test on Unit 1 Test A Test B 3 4 Anderson School District Five Page 4 Copyrigth July 1, 2012

5 First Nine Weeks Unit 2 Linear Functions EA-5.7 F-IF.6 EA-5.5 EA-5.1 EA-4.6 SC IA-2.7, SC IA-2.8 A F-BF.3 Apply the concept of slope as a rate of change to solve problems. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Carry out a procedure to determine the x- intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally. Carry out a procedure to graph a line when given the equation of the line. Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard). Carry out a procedure to graph translations of parent functions.. including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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 ). Identify linear functions as having a constant rate of change within ordered pairs, tables, and mappings using real world data. Find and analyze the slope of a linear function. Determine the slope, graph, and equations of horizontal and vertical lines. Use x- and y-intercepts to graph linear functions. Use slope intercept form to graph linear functions. Using a graph, write the equation in slope intercept form. Graph linear functions using the graphing calculator and transformations. Review Linear Equations Worksheet Modeling Linear Equations 4 cont d 5 6 Anderson School District Five Page 5 Copyrigth July 1, 2012

6 First Nine Weeks EA-3.4 EA-2.5 EA-4.7 SC IA-2.7, SC IA-2.8 A F-BF.3 EA-5.8 EA-4.8 from their graphs and algebraic expressions for them. Analyze the graph of a continuous function to determine the domain and range of the function. Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions. Carry out procedures to solve linear equations for one variable algebraically. Carry out a procedure to graph translations of parent functions.. including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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. Analyze the equations of two lines to determine whether the lines are perpendicular or parallel. Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution. ). Find the domain and range (using interval notation) of a linear function. Perform operations on linear functions. Solve linear equations and functions both algebraically and graphically. Write the equation of a line when given a point and a slope, two points, or a graph. Write the equation of a line that is parallel or perpendicular to a given line. Write, solve, and graph one and two variable linear inequalities. Operations with Linear Functions Function Operations Compositions & Inverses Function Inverses Solving Multi-Step Equations Solving Linear Functions Worksheet Finding the Slope and Writing the Equation of a Line Writing Equations of Lines Graphing Linear Inequalities Solving Inequalities Anderson School District Five Page 6 Copyrigth July 1, 2012

7 First Nine Weeks Review Review Study Guide Review Worksheet for Test 9 cont d Test 10 Anderson School District Five Page 7 Copyrigth July 1, 2012

8 First Nine Weeks Unit 3 System of Linear Equation SC IA-2.2 A-CED.3 SC IA-2.1 A-CED.3 SC IA-2.3 A-CED.3 Carry out a procedure to solve a system of linear inequalities graphically. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Carry out a procedure to solve a system of linear inequalities algebraically. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Analyze a problem situation to determine a system of linear inequalities that models the problem situation. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Identify a system as consistent, inconsistent, dependent, or independent. Solve a system of linear equations by graphing. Solve a system of linear equations by substitution. Solve a system of linear equations by elimination. Solve a system of linear equations (both two and three variable) using matrices. Solve real-world problems using systems of equations. Worksheet Solve by Graphing Systems of Two Equations Worksheet Mixed Practice on Solving Systems Worksheet Elimination and Substitution Systems of Three Equations Elimination Systems of Three Equations Substitution Systems of Equations Word Problems Anderson School District Five Page 8 Copyrigth July 1, 2012

9 First Nine Weeks Unit 3 System of Linear Equation continued SC IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically. Worksheet Systems of Inequalities Systems of Inequalities SC IA-2.4 A-CED.3 SC IA-2.3 A-CED.3 SC IA-2.4 A-CED.3 Use linear programming to solve contextual problems involving a system of linear inequalities. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Analyze a problem situation to determine a system of linear inequalities that models the problem situation. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Use linear programming to solve contextual problems involving a system of linear inequalities. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Review Graph a system of linear inequalities. Write and graph a set of constraints for a linear programming problem. Use linear programming to find the maximum or minimum value of an objective function. Worksheet Linear Programming (a) Worksheet Linear Programming (b) Worksheet Linear Programming (c) Project Rescue to Princess Review for the Test Test 19 Anderson School District Five Page 9 Copyrigth July 1, 2012

10 First Nine Weeks Review for Nine Weeks Test First Nine Weeks Test Exam Review Materials 22 Anderson School District Five Page 10 Copyrigth July 1, 2012

11 Second Nine Weeks Unit 4 Radical Functions EA-2.2 Apply the laws of exponents and roots to solve problems. Use all properties of exponents to multiply and divide monomials. Worksheet Properties of Exponents 23 IA-4.7 Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation). Write and simplify expressions with rational exponents in radical form and vice versa. Worksheet Simplifying Rational Exponents IA-4.5, IA-4.7 Carry out a procedure to simplify algebraic expressions involving rational exponents. Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation). Simplify expressions containing rational exponents. 24 Simplify a radical. More on Simplifying Radicals Simplify Radical Expression SC IA-4.9 A-REI.2 Carry out a procedure to solve radical equations algebraically. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Add, Subtract, and multiply radicals. Divide radicals and rationalize the denominator. More on Operations with Radicals Anderson School District Five Page 11 Copyrigth July 1, 2012

12 Second Nine Weeks SC IA-2.7 SC IA-2.8 B F-BF.3 SC IA-4.9 A-REI.2 Carry out a procedure to graph translations of parent functions.. including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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. Carry out a procedure to solve radical equations algebraically. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Review ). Graph radical functions using transformations. Determine the domain and range (using interval notation) of a radical function given the graph. Solve radical equations, verify solutions, and determine the domain restrictions. Worksheet Graphing Radical Transformations Worksheet Solving Radical Equations Jeopardy Review Review Chapter 7 Study Guide Review for Test 26 cont d Test Anderson School District Five Page 12 Copyrigth July 1, 2012

13 Second Nine Weeks Unit 5 Quadratic Functions Define quadratic functions. SC IA-3.5 B A-CED.1 A-CED.2 Analyze given information (including quadratic models) to solve contextual problems. Create equations and inequalities in one variable and use them to solve problems. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Graph quadratic functions using a graphing calculator and identify important features including the maximum/minimum, the zeros, and the intervals where the function is increasing/decreasing. Worksheet Introduction to Quadratics Properties of Parabolas Worksheet Word Problems and Solving with the Calculator 30 A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Determine the domain and range (using interval notation) for quadratic functions. A-CED.4 IA-3.3 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula). Factor quadratic expressions. Solve quadratic functions by factoring. Factoring Quadratic Form Factoring Quadratic Expressions Factoring by Grouping Factoring a Sum & Difference of Cubes Factoring All Techniques Worksheet Mixed Factoring Practice Worksheet Perfect Squares and Cubes and Graphing Wkst Factoring Trinomials Worksheet Solve by Factoring Worksheet Factoring and Solve by Factoring Quadratic Equations by Factoring Anderson School District Five Page 13 Copyrigth July 1, 2012

14 Second Nine Weeks Review for Test A Second Nine Weeks Test (if test is given before Christmas break) Review for Test Anderson School District Five Page 14 Copyrigth July 1, 2012

15 Second Nine Weeks Unit 5 Quadratic Functions continued SC IA-2.7 SC IA2.8 B F-BF.3 Carry out a procedure to graph translations of parent functions.. including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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. ). Complete the square to write a quadratic function in vertex form. Graph quadratic functions using vertex form. Determine the domain and range (using interval notation) for quadratic functions (with graphs). Completing the Square Worksheet Write in Vertex Form and Graph Worksheet Complete the Square to Find the Vertex Worksheet More on Completing the Square to Find the Vertex Worksheet Write in Vertex Form and Graph 34 SC IA-3.1 N-CN.1 SC IA-3.2 N-CN.2 Carry out a procedure to simplify expressions involving powers of i. Know there is a complex number i such that i 2 = -1, and every complex number has the form a + bi with a and b real. Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division). Use the relation i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Define and simplify complex numbers. Perform operations using complex numbers. Worksheet Complex Numbers Operations with Complex Numbers Properties of Complex Numbers Rationalizing Imaginary Denominators Anderson School District Five Page 15 Copyrigth July 1, 2012

16 Second Nine Weeks IA-3.3 SC IA-3.3 N-CN.7 IA-3.4 IA-3.6 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula). Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula). Solve quadratic equations with real coefficients that have complex solutions. Use the discriminant to determine the number and type of solutions of a quadratic equation. Carry out a procedure to write an equation of a quadratic function when given its roots. Review Solve quadratic functions by completing the square and using the square root method. Solve quadratic functions using the quadratic formula. Use the discriminant to determine the nature of the solutions. Write the equation of a quadratic function when given its roots. Worksheet Complete the Square to Solve Quadratics Worksheet Complete the Square to Find Vertex and Solve Quadratic Equations by Completing the Square Quadratic Equations Square Roots Worksheet Solve Using Quadratic Formula Quadratic Formula Activity Lab for Nature of Roots The Discriminant Worksheet Finding Eq from Roots Factors and Zeros 39 Chutes and Ladders Review for Quadratics Jeopardy Review Review Part B Test Review Midterm Exam (if test is given after Christmas break) Exam Review Materials 45 Anderson School District Five Page 16 Copyrigth July 1, 2012

17 Second Nine Weeks Anderson School District Five Page 17 Copyrigth July 1, 2012

18 Third Nine Weeks Unit 6 Polynomial Functions SC IA-4.1 A-APR.1 A-APR.6 SC IA-4.2 Carry out a procedure to classify polynomials by their degree and number of terms. Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions. 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. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(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. Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions. Classify polynomials Add, subtract, and multiply polynomial functions. Divide polynomial functions using long division. Divide polynomial functions using synthetic division. Polynomial Basics 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. Describe the shapes of their graphs 48 F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Anderson School District Five Page 18 Copyrigth July 1, 2012

19 Third Nine Weeks SC IA-4.2 F-IF.4 SC IA-4.4 C SC IA-4.3 A-SSE.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of quantities, and sketch graphs showing key features given a verbal description of the relationship. Analyze given information (including polynomial models) to solve contextual problems. Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes). Use the structure of an expression to identify ways to rewrite it. Identify and describe important features of the graph of a polynomial function including absolute and relative maximum/minimum points, intervals where the function is increasing/decreasing, zeros (including the multiplicity of each), domain and range (in interval notation), and end behavior. Factor and solve polynomial functions. Graphing Polynomial Functions Basic Shape Graphing Polynomial Functions Review 7.1 to cont d 49 F-1F.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Use the rational root theorem and the complex conjugate root theorem to find the zeros of a polynomial function. The Remainder Theorem Rational Room Theorem More on Factors, Zeros, and Dividing Irrational and Imaginary Root Theorems Descartes Rule of Signs Analyzing and Solving Polynomial Equations Worksheet Rational Root Theorem (A) to Solve Worksheet Rational Root Theorem (B) to Solve Worksheet Last Practice Rational Root 50 Anderson School District Five Page 19 Copyrigth July 1, 2012

20 Third Nine Weeks Theorem to Find All Roots Review Chapter 6 Study Guide Review 51 Review for Test Test 52 Anderson School District Five Page 20 Copyrigth July 1, 2012

21 Third Nine Weeks Unit 7 Rational Functions SC IA-4.8 A-APR.7 SC IA-2.9 C F-IF.7 SC IA A-REI.2 Carry out a procedure to perform operations with rational expressions (including addition, subtraction, multiplication, and division). (+) 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. Carry out a procedure to graph discontinuous functions (including piecewise and step functions). Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Carry out a procedure to solve rational equations algebraically. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Review Identify and evaluate rational functions. Multiply and divide rational expressions including complex fractions. Add and subtract rational expressions. Graph a rational function and find its domain and range (in interval notation), write equations for its asymptotes, and identify any holes in its graph. Solve rational equations. Worksheet Multiply and Divide Rational Exp Worksheet Review of Operations Worksheet More on Adding and Subtracting Worksheet Add and Subtract with Like Denominators Mixed Review of Operations Worksheet Graphing Rationals (a) Worksheet Graphing Rationals (b) Worksheet Graphing Rationals (c) Worksheet More on Solving Rational Exp Worksheet Solving Rational Exp Review Chapter 9 Study Guide Review Graphing and Operations Review Operations & Solving Rational Anderson School District Five Page 21 Copyrigth July 1, 2012

22 Third Nine Weeks Equations Review Test 58 Anderson School District Five Page 22 Copyrigth July 1, 2012

23 Third Nine Weeks Unit 8 Exponential Functions & Logarithmic Functions SC IA F-IF-7c SC IA F-IF.7e SC IA F-LE.4 IA-4.6 SC IA A-CED.1 Carry out a procedure to graph exponential functions. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Carry out a procedure to graph exponential functions. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude Carry out a procedure to graph logarithmic functions. For exponential models, express as a logarithm the solution to ab ct =d where a, c, and d are numbers and the base b Carry out a procedure to simplify algebraic expressions involving logarithms. Carry out a procedure to solve logarithmic equations algebraically. Create equations and inequalities in one variable and use them to solve problems. Graph exponential functions using transformations. Find the domain and range (in interval notation) and the equation of the horizontal asymptote for an exponential function Solve exponential equations with like bases. Graph the inverse of the exponential function and define the logarithmic function. Find the domain and range (in interval notation) and the equation of the vertical asymptote for a logarithmic function Rewrite logarithmic equations. Simplify and evaluate expressions involving logarithms using the properties of logarithms. Use the definitions of exponential and logarithmic functions to solve equations. Classify an exponential Worksheet Exponential Graphs Worksheet Exponential Eq with Like Bases Worksheet Intro to Logs Worksheet Practice with Log Properties and Solving Log Equations Review 1st Half Through Log Properties Worksheet Basic Log Equations with No Calculator Worksheet Logs Worksheet Worksheet More on Logs Anderson School District Five Page 23 Copyrigth July 1, 2012

24 Third Nine Weeks SC IA-4.10 SC IA F-BF.4 Carry out a procedure to solve logarithmic equations algebraically. Carry out a procedure to solve logarithmic equations graphically. Find inverse functions. Review function as representing a growth or a decay. Solve equations involving logarithms algebraically and graphically. Solve exponential equations using common logs algebraically and graphically. Calculate the growth of investments under various conditions using exponential and natural exponential functions. Write and evaluate exponential expressions to model growth and decay situations. Review Log Equations and Exponential Equations using Logs Worksheet Exponential Eq with Unlike Bases Worksheet Compound Interest and Exp. Funcitons Worksheet Growth & Decay Solve for New Variable Activity Shedding Light on the Subject Activity Spreading Rumors Worksheet More Word Problems Worksheet Word Problems Finding Other Variables Jeopardy Review Station Rotation Test Quiz on Logs Third Nine Weeks Test Exam Review Materials Anderson School District Five Page 24 Copyrigth July 1, 2012

25 Third Nine Weeks Anderson School District Five Page 25 Copyrigth July 1, 2012

26 Fourth Nine Weeks Unit 9 Sequence and Series IA-6.1 Categorize a sequence as arithmetic, geometric, or neither. Categorize a sequence as arithmetic, geometric, or neither. Introduction to Sequences IA-6.2 Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence. Carry out a procedure to write a specified term of an arithmetic sequence when given the nth term of the sequence. IA-6.3 IA-6.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence. Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence. Write a specified term or formula for the nth term of an arithmetic sequence when given at least four consecutive terms of the sequence. Write a formula for the nth term of an arithmetic sequence when given at least four terms of the sequence IA-6.7 Carry out a procedure to determine consecutive terms of a sequence that is defined recursively. Determine consecutive terms of a sequence that is defined recursively. IA-6.8 IA-6.9 Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence. Translate between the explicit form and the recursive form of sequences. Define a sequence recursively when given four or more consecutive terms of the sequence Translate between the explicit form and the recursive form of sequences. Worksheet Arithmetic Seq and Series Arithmetic Sequence Arithmetic Series Anderson School District Five Page 26 Copyrigth July 1, 2012

27 Fourth Nine Weeks IA-6.3 IA-6.4 SC IA-6.5 A-SSE.4 SC IA-6.6 A-SSE.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence. Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence. Represent an arithmetic or geometric series by using sigma notation. 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. Carry out a procedure to calculate the sum of an arithmetic or geometric series written in sigma notation. 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. Write a specified term of an geometric sequence when given the nth term of the sequence. Write a specified term or formula for the nth term of an geometric sequence when given at least four consecutive terms of the sequence. Write a formula for the nth term of an geometric sequence when given at least four terms of the sequence Represent an arithmetic or geometric series by using sigma notation. Calculate the sum of an arithmetic or geometric series written in sigma notation Review of Arithmetic and Geometric Arithmetic and Geometric Means Geometric Sequences Finite Geometric Series Infinite Geometric Series Review Mid-Chapter Review Test 74 Anderson School District Five Page 27 Copyrigth July 1, 2012

28 Fourth Nine Weeks Unit 10 Piecewise Functions and Modeling SC IA-2.9 D F-IF.7b Carry out a procedure to graph discontinuous functions (including piecewise and step functions). Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Define and graph piecewise functions. Worksheet Graphing Piecewise Functions 75 SC IA-2.10 F-IF.5 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Identify the domain and range (in interval notation) of piecewise functions. Anderson School District Five Page 28 Copyrigth July 1, 2012

29 Fourth Nine Weeks SC IA-2.7 SC IA-2.8 D F-BF.3 Carry out a procedure to graph translations of parent functions, including 2 1 y x, y x, y x, y x, y x Carry out a procedure to graph transformations of parent functions (including y x, y x 2, and y x Identify the effect on the graph of replacing 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. ). Define an absolute value function. Graph an absolute value function using transformations and identify the domain and range (in interval notation) Solve absolute value equations. Graphing Absolute Value Equations Solving Absolute Value Equations Worksheet Graphing & Solving Absolute Value Equations 76 Define and graph a step function. SC IA F-IF.5 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions). Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Identify the domain and range (in interval notation) of step functions. 77 Anderson School District Five Page 29 Copyrigth July 1, 2012

30 Fourth Nine Weeks SC IA-3.5 SC IA-4.4 A-CED.1 Analyze given information (including quadratic models) to solve contextual problems. Analyze given information (including polynomial models) to solve contextual problems Create equations and inequalities in one variable and use them to solve problems. Analyze given information and scatterplots to determine the appropriate model to use to solve contextual problems using the regression feature of the graphing calculator. These should include all previously learned functions. Activity Growing by Leaps and Bounds Worksheet More on Nonlinear Modeling Problems Worksheet (a) Modeling Nonlinear Worksheet Nonlinear Modeling Using the Calculator Review Review for Test on Piecewise Functions Test 80 Anderson School District Five Page 30 Copyrigth July 1, 2012

31 Fourth Nine Weeks Unit 11 Conic Sections IA-5.2 IA-5.1 Carry out a procedure to write an equation of a circle centered at the origin when given its radius. Carry out a procedure to graph the circle whose equation is the form x 2 y 2 r 2 Classify a conic section as the intersection of a plane and a double cone. Write an equation for a circle. Given an equation of a circle, graph it and label the radius and the center Worksheet Parabola and Circle 81 IA-5.2 IA-5.3 IA-5.4 IA-5.6 IA-5.5 Carry out a procedure to write an equation of a circle centered at the origin when given its radius. Carry out a procedure to graph the ellipse whose equation is the form x 2 a 2 y 2 b 2 1 Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices. Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices. Carry out a procedure to graph the hyperbola whose equation is the form x 2 a 2 y 2 b 2 1 Complete the square to change the equation of a circle from general form to standard form. Write the standard equation of an ellipse. Given an equation of an ellipse, graph it and label the center, vertices, covertices, and foci. Complete the square to change the equation of an ellipse from general form to standard form. Write the standard equation for a hyperbola. Graph the equation of a hyperbola and identify the center, foci, vertices, and covertices. Worksheet Ellipse Worksheet - Hyperbola 82 Anderson School District Five Page 31 Copyrigth July 1, 2012

32 Fourth Nine Weeks IA-5.6 IA-5.7 SC IA A-REI.11 Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices. Match the equation of a conic section with its graph. Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function). Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Review Complete the square to change the equation of a hyperbola from general form to standard form. Identify a conic section from its equation. Mixed product. Solve a system of equations containing first or second degree equations in two variables. Review Circle, Hyperbola, Ellipse Review Parts of Conics Activity Parabola Race Game Review for Test 82 cont d Test Exam Review Final Exam Exam Review Materials Anderson School District Five Page 32 Copyrigth July 1, 2012