HEMPFIELD AREA SCHOOL DISTRICT. Planned Course Guide. For HONORS PRE-CALCULUS GRADE 11

Transcription

1 HEMPFIELD AREA SCHOOL DISTRICT Planned Course Guide For HONORS PRE-CALCULUS GRADE Prepared by: Curriculum Design Team

2 ACKNOWLEDGEMENTS The Hempfield Area School District would like to acknowledge and express appreciation for the development of the Mathematics Curriculum to the following staff members. Administration: Terry J. Foriska Assistant Superintendent George Vollrath Principal - Wendover Teaching Staff: Richard Albright Hempfield Area High School Jan Byers Hempfield Area High School Jamie Caldwell Wendover Middle School Susan Ciarimboli West Point Elementary Gary Dzendzel West Hempfield Middle School Felicity Filicky Bovard Elementary Mary Flannery Fort Allen Elementary Patty Fordyce Stanwood Elementary Elizabeth Hawk Fort Allen Elementary Barbara J. Marin Assistant Superintendent Thomas Daugherty Asst. Principal - High School Jill Hixson Fort Allen Elementary Tracy Hutchison Stanwood Elementary Denise Johnson Harrold Middle School Marylyn Korinko West Hempfield Elementary Richard Kozain Wendover Middle School Debbie Kuhar Wendover Middle School Shannon Lippa East Hempfield Elementary Amy McCormick Hempfield Senior High School Monica Methven Maxwell Elementary Donald McIlvaine Principal - Fort Allen Elementary Georgene Miller West Hempfield Elementary Beth Murphy Stanwood Elementary Jim Nescot West Hempfield Middle School Ginny Parker Maxwell Elementary Tom Piper Hempfield Area High School Joe Scheuermann Hempfield Area High School Frannie Sellers Hempfield Area High School Arlene Senger Bovard Elementary Jan Southern West Hempfield Elementary

3 GOAL STATEMENT The Honors Pre-Calculus Course of Study is designed to provide a thorough and rigorous study of trigonometry as well as topics from advanced algebra and analytic geometry. The course is designed to provide the necessary foundation for the AP Calculus course. During this course, the students will: 1. Develop an understanding of trigonometric functions and their graphs, inverse trigonometric functions and their graphs, trigonometric identities, trigonometric equations, the trigonometric form of complex numbers and applications of trigonometry to various fields of study. 2. Examine vectors and parametric equations. 3. Explore the characteristics of various types of functions and their graphs. 4. Solve systems of equations and inequalities using several methods. 5. Examine the polar coordinate system. 6. Explore exponential and logarithmic functions and their graphs. 7. Examine conic sections, their equations and their graphs. 8. Utilize the T1-83+ graphing calculator to enhance the development of mathematical concepts. 1

4 CURRICULUM STRANDS I. Functions and Their Graphs (5 weeks) Write and graph linear equations and inequalities. Identify domain and range of functions Evaluate functions Sketch graphs of polynomial functions and identify increasing and decreasing intervals and relative minima and maxima using a graphing calculator Graph step functions and piecewise-defined functions Identify even and odd functions Identify basic parent graphs of functions Identify translations and dilations of functions Perform basic arithmetic operations with functions Find composition of two functions Find inverse functions and verify two functions are inverses both graphically and algebraically II. Polynomial and Rational Functions (5 weeks) Graph quadratic functions and identify maximum and minimum values Identify end behavior of functions Perform operations with complex numbers Find all zeros of polynomial functions using the Fundamental Theorem of Algebra, The Rational Root Theorem, Descartes s Rule of Signes, The Location Principal and the Upper and Lower Bound Theorem Graph rational functions Graph rational inequalities III. Exponential and Logarithmic Functions (3 weeks) Graph exponential and logarithmic functions Use properties of logarithms to evaluate and simplify expressions Use properties of natural logarithms Solve exponential and logarithmic equations IV. Trigonometric Functions 4 weeks) Convert radian measure to degree measure and visa versa Find and sketch coterminal angles Find arc length and linear and angular velocity Define and evaluate the six trigonometric functions 2

5 Solve problems using the trigonometric functions of special angles and reference angles Solve right triangles Graph trigonometric functions and inverse trigonometric functions V. Analytic Trigonometry (4 weeks) Identify basic trigonometric identities and use them to solve problems Verify other trigonometric identities using the basic identities Solve trigonometric equations VI. Additional Trigonometry Topics (4 weeks) Use Law of Sines and Cosines to solve triangles Develop vector terminology Find equal opposite and parallel vectors Perform operations with vectors both algebraically and geometrically Write the trigonometric form of a complex numbers Find products, quotients, powers, and roots of complex numbers in trigonometric form VII. Analytic Geometry (5 weeks) Write standard and general form of equations of circles, parabolas, ellipses and hyperbolas Graph circles, parabolas, ellipses and hyperbolas Recognize conics by their equations Graph translated and rotated conics Graph and solve systems of second-degree equations Write parametric equations Graph polar coordinates and polar equations and identify the type of curve Convert from polar coordinates to rectangular and visa versa VIII. Linear Systems and Matrices Solve systems of equations graphically and algebraically Solve systems of three equations graphically and algebraically Decompose an algebraic fraction into partial fractions Develop matrix vocabulary Solve systems of equations using augmented matrices Find determinants and inverses of 2x2 and 3x3 matrices (4 weeks) 3

6 Mathematics Curriculum Map Grade/Course Honors Pre-Calculus Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 1 st Quarter Apply the concept of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Functions Relations Use appropriate terminology and notation to define functions and their properties Algebraic Symbols Use function properties to evaluate functions Define and evaluate functions, domains and ranges Compare and apply numerical, symbolic and graphical properties of a variety of functions Cartesian Coordinate Plane Perform operations with functions Identify and find various types of functions Graph various types of functions Find the maximum or minimum value of a function defined for a polygonal convex set Perform operations with functions Find composite and inverse functions Identify and graph odd, even, polynomial, absolute value and step functions Solve problems using zeros and slopes of linear functions Graph inverse and rational functions Determine continuity or discontinuity of functions Describe end behavior of graphs Determine intervals where functions are increasing or decreasing Use a variety of algebraic and graphical methods to solve equations, inequalities and systems Equations Inequalities Solve linear equations and inequalities and related problems Solve systems of linear equations and inequalities and related problems Write linear equations and inequalities given various data Solve linear equations and inequalities algebraically and graphically Solve practical problems involving linear equations and inequalities Solve systems of linear equations and inequalities algebraically and graphically Solve systems of equations using matrices Solve practical problems using systems of linear equations and inequalities Graph polynomial, radical and absolute value inequalities 1

7 Mathematics Curriculum Map Grade/Course Honors Pre-Calculus Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 1 st Quarter (Cont d) Analyze geometric shapes and spatial relationships by applying problem solving techniques and mathematical reasoning Use visualization, spatial reasoning and geometric modeling to solve problems Geometric Terms Geometric Shapes And Forms Identify and use various types of symmetry Determine symmetry with respect to the origin, x-axis, y-axis, y=x or y=-x and use to complete a graph Use coordinate geometry to represent geometric figures and analyze them algebraically Deductive Reasoning Prove geometric theorems analytically Prove geometric theorems involving slope, distance, midpoints, parallel and perpendicular lines analytically Analyze the effect of transformations on objects Transformations Apply transformations to families of graphs Use linear and geometric transformations to graph families of graphs Understand and apply measurement using various tools, systems and units Fluently calculate measurements by applying appropriate formulas Linear Measurement Apply the distance formula Use the distance formula to solve problems 2

8 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) II, III Benchmark Objective(s) II: 1, 2, 3; III: 4 Performance Indicator(s) II: 1-1A, 1-1B; 2-2A; 3-3A, 3-3B III: 4-4B Strand: Linear Relations and Functions (Quarter 1) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Define, perform operations with, and evaluate functions, domains, and ranges Identify, find domain and range, evaluate, and graph composition and inverse functions Write and graph linear equations and inequalities Prove geometric theorems involving parallel and perpendicular lines analytically NOTE: Bold print indicates objectives critical to Essential Learning Targets 3

9 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II Benchmark Objective(s) I: 3; II: 3 Performance Indicator(s) I: 3-3A, 3-3B II: 4-4B Strand: Systems of Equations and Inequalities (Quarter 1) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Solve systems of equations algebraically, graphically, and using matrices Solve systems of inequalities NOTE: Bold print indicates objectives critical to Essential Learning Targets 4

10 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) II, III Benchmark Objective(s) II: 1, 2, 3; III: 3 Performance Indicator(s) II: 1-1A, 2-2A; 3-3A III: 3-3A Strand: Functions and their graphs (Quarter 1) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Identify and graph odd, even, polynomial, absolute value, and step functions Modify graphs of polynomial, absolute value, and step functions using various linear and geometric transformations Graph rational functions Determine continuity and discontinuity of functions and identify end behavior Graph polynomial, absolute value, and radical inequalities NOTE: Bold print indicates objectives critical to Essential Learning Targets 5

11 Mathematics Curriculum Map Grade/Course Honors Pre-Calculus Time- Frame Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets 2 nd Quarter Understand numbers, their representation and relationships, and the meaning and use of operations, in order to estimate, compute and solve problems Compute fluently with a variety of forms and make reasonable estimates Operations Number Representation Comparisons and Relationships Compare angle measures in degrees and radians Convert between radian measure and degree measure Apply the concepts of patterns, equations, inequalities, functions, and relations to solve problems using algebraic symbols Use appropriate terminology and notation to define functions and their properties Functions Relations Trigonometric function of definitions Define the six trigonometric functions Compare and apply numerical, symbolic and graphical properties of a variety of functions Cartesian Coordinate Plane Define and use various types of trigonometric angles Find trigonometric function values of any size angle Examine continuity and end behavior of functions Find zeros of polynomial functions Define trigonometric angles and identify properties of standard position and angles Identify and use quadrantal and co-terminal angles Use reference angles to find the value of trigonometric functions of angles Use remainder, factor, rational root, upper and lower bound and location theorems, and Descartes Rule of Signs to find the zeros of a polynomial function Use a variety of algebraic and graphical methods to solve equations, inequalities and systems Equations Inequalities Algebraic Symbols Apply appropriate problem-solving strategies for given situations Identify and explain processes to derive solutions Understand and apply basic algebraic principles and symbols Apply operations to algebraic terms, expressions, equations and functions Solve various types of equations and inequalities Explore real life situations using algebraic concepts Graph various types of inequalities Solve quadratic equations by factoring, graphing, completing the square and quadratic formula Use the discriminate to describe the roots of quadratic equations Graph quadratic equations and inequalities Solve rational equations and inequalities and use them to solve practical problems Solve radical equations and inequalities and use them to solve practical problems Decompose rational expressions into partial fractions 6

12 Mathematics Curriculum Map Grade/Course Honors Pre-Calculus Time- Frame 2 nd Quarter (Cont d) Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Analyze geometric shapes and spatial relationships by applying problem-solving techniques and mathematical reasoning Use visualization, spatial reasoning and geometric modeling to solve problems Right Triangle relationships Apply properties of geometry to right triangles to solve problems Find exact values for the six trigonometric functions of special angles Solve right triangles Understand and apply measurement using various tools, systems, and units Fluently calculate measurements by applying appropriate formulas Linear Measurement Area Angles Apply the proper formula and calculate the requested value for problems involving sectors, arcs, and velocities Solve real life problems involving right triangles using trigonometric functions Solve problems involving arc length and area of sector of a circle Solve problems involving linear and angular velocity Analyze oblique triangle problems and apply the proper formula to calculate sides, angles and areas Solve oblique triangles using the Laws of Sines and Cosines Analyze and solve the Ambiguous Case of the Sine Law Solve practical problems involving oblique triangles using the Laws of Sines and Cosines Find the area of triangles using Heron s Formula or the Area of a Triangle Formula 7

13 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II Benchmark Objective(s) I: 3; II: 3 Performance Indicator(s) II: 3-3A, III: 3-3A; 3-3B Strand: Polynomial and rational Functions (Quarter 2) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Solve and graph quadratic equations and inequalities Solve radical equations and inequalities Solve rational equations and inequalities Decompose a rational expression into partial fractions Find the factors of polynomials using the remainder and factor theorems Find all of the zeros of a polynomial function using the rational root theorem, Descartes rule of signs, upper and lower bonds theorem, and the location theorem NOTE: Bold print indicates objectives critical to Essential Learning Targets 8

14 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, III, IV Benchmark Objective(s) I: 3; II: 1, 2; III: 2; IV: 2 Performance Indicator(s) I: 3-3A; II: 1-1B; 2-2A III: 2-2B2; 2-2B3; IV: 2-2A Strand: The Trigonometric Functions (Quarter 2) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Convert between radian and degree measure of angles Find co-terminal angles and reference angles Solve problems involving ARC length and area of a sector Solve problems involving linear and angular velocity Define the six trigonometric functions Solve problems involving trigonometric functions of special angles Solve right triangles Use Laws of Sines and Cosines to solve any triangles Find areas of triangles and circular segments NOTE: Bold print indicates objectives critical to Essential Learning Targets 9

15 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 3 rd Quarter Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Compare and apply numerical, symbolic and graphical properties of a variety of functions Cartesian coordinate plane Graph trigonometric functions Construct the graphs of the six trigonometric functions over specified intervals of values for x Construct graphs of families of trigonometric functions: 7=asin*b(x-c)+d** *or cos, tan, csc, sec, cot **a, b, c, d represent any real number Identify amplitude, period, vertical translation, and phase shift of trigonometric function graphs, and use them to write equations for these function graphs Use the six trigonometric function graphs to solve practical problems Functions Relations Algebraic symbols Evaluate and apply inverse trigonometric functions Evaluate inverse trigonometric functions Evaluate the composition of inverse trigonometric functions Find principal values of inverse trigonometric functions Write equations for inverse trigonometric, functions Graph inverse trigonometric functions Use inverse trigonometric functions to solve practical problems Use TI-82 calculator to analyze trigonometric function and inverse trigonometric function graphs Equations Patterns Functions Relations Algebraic Symbols Understand and apply trigonometric identities Use the basic trigonometric identities, the sum and difference, the double-angle, and the half angle identities to find values of trigonometric functions Use the basic trigonometric identities, the sum and difference, the double-angle and the halfangle identities to verify other identities 10

16 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 3 rd Quarter (Cont d) Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Use a variety of algebraic and graphical methods to solve equations, inequalities, and systems Solve trigonometric equations Write linear equations in normal form Solve trigonometric equations involving one function Solve trigonometric equations involving two functions Solve trigonometric equations involving multiple angles Solve trigonometric equations involving more than one variable Write the normal form of a linear equation Understand and apply using various tools, systems, and units Linear measurement Apply the formula for distance from a point to a line Find the distance from a point to a line Find the distance between parallel lines Fluently calculate measurements by applying appropriate formulas 11

17 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) III Benchmark Objective(s) III: 3, 4 Performance Indicator(s) III: 3-3A, 4-4A Strand: Graphs of Trigonometric Functions (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Graph trigonometric functions using amplitude, period, phase shift, and vertical translation Write equations of trigonometric functions from their graphs NOTE: Bold print indicates objectives critical to Essential Learning Targets 12

18 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) II, III Benchmark Objective(s) II: 1, 2; III:3, 4 Performance Indicator(s) II: 1-1B, 2-2A, III: 3-3A, 4-4A Strand: Inverse Trigonometric Functions (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Evaluate inverse trigonometric functions Find principal values of inverse trigonometric functions Graph inverse trigonometric functions Write equations for inverse trigonometric functions NOTE: Bold print indicates objectives critical to Essential Learning Targets 13

19 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, III Benchmark Objective(s) I: 3; II: 2; III: 1 Performance Indicator(s) I: 3-3A; II: 2-2A; III: 1-1B Strand: Trigonometric Identities (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Identify basic trigonometric identities and use them to solve problems Verify other trigonometric identities using the basic identities Solve problems and verify identities using the sine, cosine, and tangent sum and difference identities Solve problems and verify identities using the double-angle and half-angle identities NOTE: Bold print indicates objectives critical to Essential Learning Targets 14

20 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, Benchmark Objective(s) I: 3; II: 3 Performance Indicator(s) I: 3-3A; II: 3-3A; Strand: Trigonometric Equations (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Solve trigonometric equations involving one or two trigonometric functions or multiple angles Convert between standard and normal form of a linear equation Use the normal form of a linear equation to find distances and to write anglebisector equations NOTE: Bold print indicates objectives critical to Essential Learning Targets 15

21 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, III Benchmark Objective(s) I: 3; II: 2; III: 2, 4 Performance Indicator(s) I: 3-3A; II: 2-2A; III: 2-2A, 4-4A Strand: Vectors and Parametric Equations (Quarter 3) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Develop knowledge of vector terminology Find equal, opposite, and parallel vectors Add and subtract vectors geometrically Represent vectors using ordered pairs Add, subtract, multiply, and find magnitude of vectors algebraically Find perpendicular vectors using inner product Write vector and parametric line equations NOTE: Bold print indicates objectives critical to Essential Learning Targets 16

22 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 4 th Quarter Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Understand numbers, their representation and relationships, and the meaning and use of operations, in order to estimate, compute and solve problems Compute fluently with a variety of forms and make reasonable estimates Complex numbers Perform operations on complex numbers in rectangular form Compare complex numbers in rectangular and polar forms Perform operations on complex numbers in polar form Apply complex numbers Add, subtract, multiply, and divide complex numbers in rectangular form Change complex numbers from rectangular to polar form and vie-versa Multiply and divide complex numbers in polar form Use DeMoivre s theorem to find powers of complex numbers in polar form Find roots of complex numbers in polar form Use complex numbers to solve real-life problems Exponents Apply properties of exponents Use properties of integral exponents Simplify expressions containing rational exponents Evaluate expressions containing irrational exponents Apply the concepts of patterns, equations, inequalities, functions and relations to solve problems using algebraic symbols Compare and apply numerical symbols and graphical properties of a variety of functions Polar coordinates Graph polar coordinates Express coordinates in equivalent forms Graph polar equations Express equations in equivalent forms Graph polar coordinates List other pairs of coordinates that represent the same point Convert from polar coordinates to rectangular coordinates and vice-versa Graph polar equations Identify the classical curve based on its polar equation Use the Tl-82 calculator to graph polar equations Convert linear equations from rectangular form to polar form and vice-versa Exponential Functions Use properties of exponential functions Define exponential function Discover properties of exponential functions Define and use the exponential function y=e א Apply exponential function to the solution of reallife problems 17

23 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 4 th Quarter Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Graph exponential functions Graph exponential functions using their properties Graph exponential inequalities Use the Tl-82 calculator to graph exponential functions Logarithmic functions Use properties of logarithmic functions Define logarithmic function Use properties of logarithms to evaluate expressions Apply logarithmic functions to the solution of reallife problems Express logarithmic functions in equivalent forms Graph logarithmic functions Convert from exponential form to logarithmic form and vice-versa Use change of base formula to evaluate logarithms of numbers Graph logarithmic functions Graph logarithmic inequalities Use the Tl-82 calculator to graph logarithmic functions Common logarithms Apply common logarithms Find common logarithms and antilogarithms of numbers Use common logarithms to computer powers and roots Use common logarithms to solve real-life problems Natural logarithms Apply natural logarithms Find natural logarithms and anti-natural logarithms of numbers Use natural logarithms to solve real-life problems 18

24 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 4 th Quarter Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Use a variety of algebraic and graphical methods to solve equations, inequalities, and systems Second-degree equations and inequalities Solve systems of second-degree equations and inequalities Solve systems of second-degree equations and inequalities algebraically Solve systems of second-degree equations and inequalities graphically Exponential equations and inequalities Solve exponential equations and inequalities Solve exponential equations using properties of exponents Solve exponential equations and inequalities using common logarithms Solve exponential equations using natural logarithms Use the Tl-82 calculator to solve exponential equations and inequalities Analyze geometric shapes and spatial relationships by applying problem-solving techniques and mathematical reasoning Use coordinate geometry to represent geometric figures and analyze them algebraically Logarithmic equations and inequalities Circles Parabolas Solve logarithmic equations and inequalities Use the standard and general forms of the circle equation Graph circles Use the standard and general forms of the parabola equation Graph parabolas Solve logarithmic equations and inequalities using common logarithms Solve logarithmic equations using natural logarithms Write the standard circle equation satisfying a given set of conditions Write the general and standard circle equations, given three (3) points on the circle Graph circles using center and radius Use the Tl-82 calculator to graph circles Write the standard parabola equation satisfying a given set of conditions Use the parabola equations to identify key parts of the parabola Graph parabolas using vertex, focus, directrix, axis, and lotus?? rectum Use the Tl-82 calculator to graph parabolas 19

25 Mathematics Curriculum Map Grade/Course Honors Precalculus Time- Frame 4 th Quarter Standards & Benchmarks Key Content Processes & Skills Essential Learning Targets Ellipses Use the standard and general forms of the ellipse equation Write the standard ellipse equation satisfying a given set of conditions Use the ellipse equations to identify key parts of the ellipse Hyperbolas Graph ellipses Graph ellipses using center, vertices, foci, major and minor axes Use the Tl-82 calculator to graph ellipses Use the standard and general forms of the hyperbola equation Write the standard hyperbola equation satisfying a given set of conditions Use the hyperbola equations to identify key parts of the hyperbola Graph hyperbolas Graph hyperbolas using center, foci, vertices, and asymptotes Use the Tl-82 calculator to graph hyperbolas Equilateral hyperbolas Write the equation for a graph equilateral hyperbolas Conic sections Recognize conics Distinguish among conics using their equations Identify eccentricity Find the eccentricity of each conic section Analyze the effects of transformation of objects Transformation of conics Apply translations and rotations to conic sections Find the equations of translated or rotated conics Find the angles of rotated conics 20

26 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, III Benchmark Objective(s) I: 3; II: 1, 2, 3; III: 4 Performance Indicator(s) I: 3-3A; II: 1-1A, 2-2A, 3-3B III: 4-4A Strand: Polar Coordinates and Complex Numbers (Quarter 4) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Graph polar coordinates and simple polar equations Graph polar equations and identify Convert between polar and rectangular coordinates Write and graph the polar form of a linear function Perform algebraic operations on complex numbers in rectangular form Convert complex numbers between rectangular and polar form Find products, quotients, powers, and roots of complex numbers in polar form NOTE: Bold print indicates objectives critical to Essential Learning Targets 21

27 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) II, III Benchmark Objective(s) II: 3; III: 3, 4 Performance Indicator(s) II: 3-3A; III: 3-3A III: 4-4A, 4-4B Strand: Conics (Quarter 4) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Write standard and general form equations of circles, parabolas, ellipses, and hyperbolas Graph circles, parabolas, ellipses, and hyperbolas Recognize conics by their equations Find graphs of translated and rotated conics Graph and solve systems of second-degree equations and inequalities NOTE: Bold print indicates objectives critical to Essential Learning Targets 22

28 HEMPFIELD AREA SCHOOL DISTRICT LESSON GUIDE Grade/Subject: HONORS PRECALCULUS STANDARDS LINK/HIGH SCHOOL Standard(s) I, II, III Benchmark Objective(s) I: 2, 3; II: 1, 2, 3; III: 3, 4 Performance Indicator(s) I: 2-2A, 3-3A; II: 1-1A, 2-2A, 3-3A III: 3-3A, 4-4A Strand: Exponential and Logarithmic Functions (Quarter 4) INSTRUCTIONAL OBJECTIVE(S): Date Completed The student will: Use properties of exponents and logarithms to evaluate and simplify expressions Solve exponential and logarithmic equations and inequalities Find and use common logarithms and antilogarithms of numbers Find and use common logarithms and antilogarithms of numbers NOTE: Bold print indicates objectives critical to Essential Learning Targets 23