Honors Pre-Calculus (Course #341)

Transcription

1 Honors Pre-Calculus (Course #341) Course of Study Findlay City Schools June 2016

2 TABLE OF CONTENTS 1. Findlay City Schools Mission Statement and Beliefs 2. Honors Pre-Calculus Course of Study 3. Honors Pre-Calculus Pacing Guide Honors Pre-Calculus Course of Study Writing Team Lori Cole Ellen Laube Judy Lentz Karen Ouwenga Textbok: James Stewart: Lothar Redlin: Saleem Watson; Precalculus: Mathematics for Calculus, 7 th Edition Student Edition: ISBN-10: Teacher Edition: ISBN-13:

3 FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) Honors Pre-Calculus Grade / Course 12 th Grade Unit of Study Chapter 1 Fundamentals Pacing 25 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS N.CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. N.CN.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, ( i) 3 = 8 because ( i) has modulus 2 and argument 120. 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 Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

4 Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Find (N.CN.3) Conjugate of a complex number Remember Use (N.CN.3) The conjugate with the quotient of complex Apply numbers Represent (N.CN.5) Addition, subtraction, multiplication and Understand conjugation of complex numbers geometrically on the complex plane. Use (N.CN.5) Properties of addition, subtraction, multiplication Apply and conjugation for computations Understand (A.APR.7) Rational expressions are closed under addition, Understand subtraction, multiplication, and division by a nonzero rational expression Add (A.APR.7) Rational expressions Apply Subtract (A.APR.7) Rational expressions Apply Multiply (A.APR.7) Rational expressions Apply Divide (A.APR.7) Rational expressions Apply Vocabulary Resources Real Numbers Natural Numbers Textbook with Supplementals Enhanced WebAssign Integers Rational Numbers Irrational Numbers Additive Identity Set Union Intersection Open Interval Absolute Value Distance Rationalizing Denominator Variable Algebra Expression

5 Monomial Binomial Trinomial Polynomial Fractional Expression Rational Expression Domain Range Compound Fraction Solutions Roots Linear Equation Quadratic Equation Zero Product Property Quadratic Type Slope Point-Slope Form Slope-Intercept From Overview Chapter 1 reviews the real numbers, equations, and the coordinate plane. Students are probably already familiar with these concepts, but it is helpful to get a fresh look at how these ideas work together to solve problems and model (or describe) real-world situations. Understanding/Corresponding Big Ideas Real Numbers Exponents and radicals Algebraic expressions Rational expressions Equations Inequalities Coordinate Geometry Lines

6 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 2 Functions 20 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.IF. 7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. F.BF. 1c Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F.BF. 4b Verify by composition that one function is the inverse of another. F.BF. 4c Read values of an inverse function from a graph or a table, given that the function has an inverse. F.BF. 4d Produce an invertible function from a non-invertible function by restricting the domain. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

7 Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Graph (F.IF.7d) Rational function Create Identify (F.IF.7d) Zeroes and asymptotes Create Show (F.IF.7d) Show end behaviors Create Compose (F.BF.1c) Functions Analyze Verify (F.BF.4b) By composition that one function is the inverse of Analyze the other Read (F.BF.4c) Values of an inverse function from a graph or table Analyze Produce (F.BF.4d) Invertible function from a non-invertible function by restricting the domain. Create Vocabulary Function Domain Range Piecewise Function Greatest Integer Function Local Maximum Local Minimum Composite Functions Continuous Functions Vertical Line Test Increasing Decreasing Linear Function Composite Function One-to-one Function Horizontal line Test Overview Perhaps the most useful mathematics idea for modeling the real world is the concept of functions, which is discussed in this chapter. Resources Textbook with Supplementals Enhanced WebAssign Understanding/Corresponding Big Ideas Functions Graphs of functions Getting information from the graph of a function Average rate of change of a function

8 Linear functions and models Transformations of functions Combining functions One-to-one functions and their inverses

9 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 3 Polynomial and Rational Functions 15 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.IF. 7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. N.CN. 9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. N.CN. 8 Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x - 2i). Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Graph (F.IF.7d) Rational function Create Identify (F.IF.7d) Zeroes and asymptotes Create Show (F.IF.7d) Show end behaviors Create Extend (N.CN.8) Polynomial identities to the complex numbers Apply Know (N.CN.9) Fundamental Theorem of Algebra Remember

10 Show (N.CN.9) Polynomial Function Quadratic Function Minimum Value Maximum Value Degree of a polynomial function End Behavior Zeros Long Division Synthetic Division Remainder Theorem Factor Theorem Descartes Rule of Signs Vocabulary Fundamental Theorem of Algebra is true for Understand quadratics. Resources Lower Bound Textbook with Supplementals Upper Bound Enhanced WebAssign Multiplicities Rational Functions Asymptotes Vertical Asymptotes Horizontal Asymptotes Transformations Polynomials Inequalities Cut Points Rational Inequality Overview Functions defined by polynomial expressions are called polynomial functions. The graphs of polynomial functions are beautiful, smooth curves that are used in design processes. Rational functions are studied in this chapter, which are quotients of polynomial functions. It will also be shown that rational functions also have many useful applications. Understanding/Corresponding Big Ideas Quadratic functions and models Polynomial functions and their graphs Diving polynomials Complex zeros and the Fundamental Theorem of Algebra Rational functions Polynomial and rational inequalities

11 FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Subject(s) Honors Pre-Calculus Grade / Course 12 th Grade Unit of Study Chapter 4 Exponential and Logarithmic Functions Pacing 15 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.BF. 4b Verify by composition that one function is the inverse of another. F.BF. 4c Read values of an inverse function from a graph or a table, given that the function has an inverse. F.BF. 5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Verify (F.BF.4b) By composition that one function is the inverse of Analyze the other Read (F.BF.4c) Values of an inverse function from a graph or table Analyze

12 Understand (F.BF.5) Use (F.BF.5) Vocabulary Annual Percentage Yield Natural Exponential Function Continuously Compounded Interest Logarithmic Function Change of Base Formula Exponential Equations Exponential Growth Relative Growth Radioactive Decay Newton s Law of Cooling Logarithmic Scale PH Scale Richter Scale Overview This chapter looks at a class of functions called exponential functions. Exponential functions are appropriate for modeling population growth for all living things, from bacteria to elephants. Logarithmic functions, which are inverses of exponential functions, will also be explored. Inverse relationship between exponents and Understand logarithms The relationship between exponents and Analyze logarithms to solve problems Resources Textbook with Supplementals Enhanced WebAssign Understanding/Corresponding Big Ideas Exponential functions The natural exponential function Logarithmic functions Laws of logarithms Exponential and logarithmic equations Modeling with exponential functions Logarithmic scales

13 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 5 Trigonometric Functions: Unit Circle Approach 15 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.TF. 3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number. F.TF. 4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F.TF. 6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. F.TF. 7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. F.TF. 9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

14 Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Use (F.TF.3) Special right triangles to determine geometrically Apply the values of sine, cosine and tangent for /3, /4, and /6 Use (F.TF.3) The unit circle to express the values of sine, cosine, Apply and tangents for x, +x, and 2-x Use (F.TF.4) Unit circle to explain symmetry of the periodicity Analyze of trig functions Understand (F.TF.6) Restricting a trig function to a domain on which it Understand is always increasing or decreasing allows its inverse to be constructed. Use (F.TF.7) Inverse functions to solve trig equations Apply Evaluate (F.TF.7) The solutions using technology Evaluate Interpret (F.TF.7) Solutions in terms of context Analyze Prove (F.TF.9) The addition and subtraction formulas for sine, Evaluate cosine, and tangent Use (F.TF.9) The addition and subtraction formulas to solve problems Apply Unit Circle Terminal Points Reference Number Periodic Sine Cosine Tangent Cotangent Secant Cosecant Cancellation Properties Cycle Amplitude Vocabulary Resources Textbook with Supplementals Enhanced WebAssign

15 Period Frequency Damped Harmonic Motion Phase Horizontal Shift Phase Difference Overview In Chapters 5 and 6, new functions called trigonometric functions are introduced. The trig functions can be defined in two different, but equivalent ways as functions of angles (Chapter 6) or functions of real numbers (Chapter 5). Both approaches are studied because different applications require that trig functions are viewed differently. The approach in this chapter lends itself to modeling periodic motion. Understanding/Corresponding Big Ideas The Unit Circle Trigonometric functions of real number Trigonometric graphs More trigonometric graphs Inverse trigonometric functions and their graphs

16 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 6 Trigonometric Functions: Unit Circle Approach 15 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.TF. 3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number. F.TF. 4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. F.TF. 6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. F.TF. 7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. F.TF. 9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

17 Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Use (F.TF.3) Special right triangles to determine geometrically Apply the values of sine, cosine and tangent for /3, /4, and /6 Use (F.TF.3) The unit circle to express the values of sine, cosine, Apply and tangents for x, +x, and 2-x Use (F.TF.4) Unit circle to explain symmetry of the periodicity Analyze of trig functions Understand (F.TF.6) Restricting a trig function to a domain on which it Understand is always increasing or decreasing allows its inverse to be constructed. Use (F.TF.7) Inverse functions to solve trig equations Apply Evaluate (F.TF.7) The solutions using technology Evaluate Interpret (F.TF.7) Solutions in terms of context Analyze Prove (F.TF.9) The addition and subtraction formulas for sine, Evaluate cosine, and tangent Use (F.TF.9) The addition and subtraction formulas to solve problems Apply Angle Degree Radians Standard Position Coterminal Linear Speed Angular Speed Hypotenuse Opposite Leg Adjacent Leg Reference Angle Law of Sines Ambiguous Case Vocabulary Resources Textbook with Supplementals Enhanced WebAssign

18 Law of Cosines Bearing Heron s Formula Semiperimeter Overview In Chapters 5 and 6, new functions called trigonometric functions are introduced. The trig functions can be defined in two different, but equivalent ways as functions of angles (Chapter 6) or functions of real numbers (Chapter 5). Both approaches are studied because different applications require that trig functions are viewed differently. The approach in this chapter lends itself to geometric problems involving finding angles and distances. Understanding/Corresponding Big Ideas Angle measure Trigonometry of right triangles Trigonometric functions of angles Inverse trigonometric functions and right triangles The Law of Sines The Law of Cosines

19 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 7 Analytic Geometry 20 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS F.TF. 6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. F.TF. 7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. F.TF. 9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Understand (F.TF.6) Unwrapped Concepts (Students need to know) Restricting a trig function to a domain on which it is always increasing or decreasing allows its inverse to be constructed. Bloom s Taxonomy Levels Understand

20 Use (F.TF.7) Inverse functions to solve trig equations Apply Evaluate (F.TF.7) The solutions using technology Evaluate Interpret (F.TF.7) Solutions in terms of context Analyze Prove (F.TF.9) The addition and subtraction formulas for sine, Evaluate cosine, and tangent Use (F.TF.9) The addition and subtraction formulas to solve problems Apply Vocabulary Identity Trigonometric Identity Double Angle Formula Half-Angle Formula Product-Sum Formula Overview This chapter studies the algebraic aspect of trigonometry, which is, simplifying and factoring expressions and solving equations that involve trigonometry functions. The basic tools in the algebra of trigonometry are trigonometric identities. Resources Textbook with Supplementals Enhanced WebAssign Understanding/Corresponding Big Ideas Trigonometric identities Addition and subtraction formulas Double-angle, half-angle, and product-sum formulas Basic trigonometric equations More trigonometric equations

21 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 10 Systems of Equations and Inequalities 20 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING 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. N.VM. 10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. N.VM. 12 Work with 2 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. 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).

22 Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Use (N.VM.6) Matrices to represent and manipulate data Remember Multiply (N.VM.7) Matrices by scalars Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Understand (N.VM.9) Matrix multiplication is not commutative Understand Understand (N.VM.10) Zero and identity matrix plays a role in matrix Understand addition and multiplication similar to zero and 1 in real numbers. Work (N.VM.12) With 2x2 matrices as transformations of the plane Understand Interpret (N.VM.12) Absolute value of the determinant in terms of area Applying Represent (A.REI.8) System of linear equations as a single matrix Understand equation in a vector variable Find (A.REI.9) The inverse of a matrix Apply Use (A.REI.9) the inverse to solve systems of linear equations Apply System of equations Solution Substitution method Elimination method Vocabulary Reduced row-echelon form Gauss-Jordan Elimination Leading variable Equivalent matrices Resources Textbook with Supplementals Enhanced WebAssign

23 Graphical method Dependent Independent Inconsistent Triangular form Matrix Rows Columns Augmented matrix Gaussian Elimination Row-echelon form Scalar multiplication Scalar product Inner product Identity matrix Inverse matrix Coefficient matrix Square matrix Determinant Cramer s Rule Overview Many real-world situations have too many variables to be modeled by a single equation. For example, weather depends on many variables, including temperature, wind speed, air pressure, humidity, and so on. So to model (and forecast) the weather, scientists use many equations, each having many variables. Such systems of equations work together to describe the weather. Systems of equations with hundreds or even thousands of variables are also used extensively in the air travel and telecommunications industries to establish consistent airline schedules and to find efficient routing for telephone calls. Understanding/Corresponding Big Ideas Systems of linear equations in two variables Systems of linear equation in several variables Matrices and systems of linear equations The algebra of matrices Inverses of matrices and matrix equations Determinants and Cramer s Rule Partial fractions Systems of nonlinear equations

24 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 11 Conic Sections 15 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS G.C.4 Construct a tangent line from a point outside a given circle to the circle. G.GPE.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Use (N.VM.6) Matrices to represent and manipulate data Remember Multiply (N.VM.7) Matrices by scalars Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Add (N.VM.8) Matrices of appropriate dimensions Understand Understand (N.VM.9) Matrix multiplication is not commutative Understand

25 Understand (N.VM.10) Zero and identity matrix plays a role in matrix Understand addition and multiplication similar to zero and 1 in real numbers. Work (N.VM.12) With 2x2 matrices as transformations of the plane Understand Interpret (N.VM.12) Absolute value of the determinant in terms of area Applying Represent (A.REI.8) System of linear equations as a single matrix Understand equation in a vector variable Find (A.REI.9) The inverse of a matrix Apply Use (A.REI.9) the inverse to solve systems of linear equations Apply parabola vertex axis of symmetry focus directrix latus rectum focal diameter ellipse foci vertices Vocabulary major axis minor axis center eccentricity hyperbola branches transverse axis asymptotes shifted conic general equation Resources Textbook with Supplementals Enhanced WebAssign Overview Conic sections are the curves that are made when a straight cutes is made in a double cone. The goal of this chapter is to find equation whose graphs are the conic sections. Understanding/Corresponding Big Ideas Parabolas Ellipses Hyperbolas Shifted Conics

26 Subject(s) Grade / Course Unit of Study Pacing FINDLAY CITY SCHOOLS Curriculum Design Grades 6 12 Honors Pre-Calculus 12 th Grade Chapter 8 Polar Coordinates and Parametric Equations 10 days ESSENTIAL UNDERSTANDINGS AND SUPPORTING STANDARDS 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. 8 Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x - 2i). Mathematical Practices: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unwrapped Skills (Students need to be able to do) Unwrapped Concepts (Students need to know) Bloom s Taxonomy Levels Represent (N.CN.4) Complex number on the complex plane in Remember rectangular and polar form including real and imaginary numbers. Explain (N.CN.4) Why the rectangular and polar form of a given Understand complex number represents the same number. Extend (N.CN.8) Polynomial identities to the complex numbers Apply

27 Vocabulary Polar Coordinate System Polar Equations Cardioid Modulus Absolute Value Polar Form Trigonometric Form DeMoivre s Theorem Parameter Cycloid Closed Curve Lissajous Figure Overview This chapter studies polar coordinates, which is a new way of describing the location of points in a plane. Resources Textbook with Supplementals Understanding/Corresponding Big Ideas Polar coordinates Graphs of polar equations Polar form of complex numbers; DeMoivre s Theorem Plan curves and parametric equations

28 Chapter 1 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 1.1 Real Numbers Exponents and Radicals Algebraic Expressions Rational Expressions Equations Complex Numbers Inequalities The Coordinate Plane; Graphs of Equations; Circles Lines 2 TOTAL DAYS 25

29 Chapter 2 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 2.1 Functions Graphs of Functions Getting Information from the Graph of a Function Average Rate of Change of a Function Linear Functions and Models Transformations of Functions Combining Functions One-to-One Functions and Their Inverses 2 TOTAL DAYS 20

30 Chapter 3 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 3.1 Quadratic Functions and Models Polynomial Functions and Their Graphs Diving Polynomials Real Zeros of Polynomials Complex Zeros and the Fundamental Theorem of 1 Algebra 3.6 Rational Functions Polynomial and Rational Inequalities 2 TOTAL DAYS 15

31 Chapter 4 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 4.1 Exponential Functions The Natural Exponential Function Logarithmic Functions Laws of Logarithms Exponential and Logarithmic Equations Modeling with Exponential Functions Logarithmic Scales 1 TOTAL DAYS 15

32 Chapter 5 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 5.1 The Unit Circle Trigonometric Functions of Real Numbers Trigonometric Graphs More Trigonometric Graphs Inverse Trigonometric Functions and Their Graphs 2 TOTAL DAYS 15

33 Chapter 6 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 6.1 Angle Measure Trigonometry of Right Triangles Trigonometric Functions of Angles Inverse Trigonometric Functions and Right 2 Triangles 6.5 The Law of Sines The Law of Cosines 1 TOTAL DAYS 15

34 Chapter 7 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 7.1 Trigonometric Identities Addition and Subtraction Formulas Double-Angle, Half-Angle, and Product-Sum 2 Formulas 7.4 Basic Trigonometric Equations More Trigonometric Equations 2 Review 1 Test 1 TOTAL DAYS 15

35 Chapter 10 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 10.1 Systems of Linear Equations in Two Variables Systems of Linear Equations in Several Variables Matrices and Systems of Linear Equations The Algebra of Matrices Inverses of Matrices and Matrix Equations Determinants and Cramer s Rule Partial Fractions Systems of Nonlinear Equations 2 Review 1 Test 1 TOTAL DAYS 20

36 Chapter 11 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 11.1 Parabolas Ellipses Hyperbolas Shifted Conics 1 Test 1 TOTAL DAYS 15

37 Chapter 8 HONORS PRE-CALCULUS PACING GUIDE Section Chapter Title Days 8.1 Polar Coordinates Graphs of Polar Equations Polar Form of Complex Numbers; DeMoivre s 1 Theorem 8.4 Plane Curves and Parametric Equations 2 Project 2 TOTAL DAYS 10