Trigonometry/Calculus
|
|
- Rose Wells
- 6 years ago
- Views:
Transcription
1 /Calculus Dunmore School District Dunmore, PA
2 /Calculus Prerequisite: Successful completion of Algebra II In the first half of the course students will study., helps students develop skills sufficiently to write and use the definition of trigonometric functions; solve right and oblique triangles; use the unit circle; learn and apply the laws of sine and cosine; prove identities; solve trigonometric equations; and sketch the graphs of the trigonometric functions. The second half of the course is designed to introduce students to calculus. Students will begin by studying relations and functions. They will then study linear, polynomial, absolute value, square root, logarithmic, exponential, reciprocal and greatest integer functions. For each function they will learn domain, range, graphing and graph properties, followed by applications that apply to that function. The year will end with an introduction to derivatives and integrals where students will learn limits, power rules and applications. /Calculus Page 1
3 Year-at-a-glance Subject: /Calculus Grade Level: 12 Date Completed: 1/26/17 1 st Quarter with Right Triangles Unit Circle Definition of Trigonometric Topic Resources Standards Chapter 5 Sections 2-4 p Chapter 6 Sections 1-2 p CC.2.3.HS.A.7 G G HSG.SRT.C.6 HSG.SRT.C.7 HSG.SRT.C.8 HSF.TF.A.1 HSF.TF.A.2 HSF.TF.A.3 CC.2.2.HS.C.7 Graphs of Trigonometric Chapter 6 Sections 3-6 p HSF.TF.A.4 HSF.TF.B.5 CC.2.2.HS.C.8 /Calculus Page 2
4 Trigonometric Algebra Dunmore School District Chapter 7 Sections 1-4, 6-7 p , CC.2.2.HS.C.9 G G G HSF.TF.C.8 HSF.TF.C.9 /Calculus Page 3
5 2 nd Quarter Continue Trigonometric Algebra Topic Resources Standards Chapter 7 Sections 1-4, 6-7 p , CC.2.2.HS.C.9 G G G HSF.TF.C.8 HSF.TF.C.9 with General Triangles Introduction to Chapter 8 Sections 1-2 p Chapter 2 Section 3 p HSG.SRT.D.10 HSG.SRT.D.11 HSG.SRT.D.9 CC C.1 /Calculus Page 4
6 3 rd Quarter Linear Polynomial Absolute Value Topic Resources Standards Chapter 2 Section 4 p Chapter 3 Sections 1, 3-4 p , Chapter 1 Section 8 p CC.2.2.HS.C.5 CC.2.4.HS.B.3 CC.2.2.HS.C.5 Square Root Review Chapter Section 7 p Chapter 1 Section 6 p Chapter 2 Section 6 p.250 /Calculus Page 5
7 Logarithmic Dunmore School District Chapter 4 Sections 3-5 p /Calculus Page 6
8 4 th Quarter Exponential Reciprocal Topic Resources Standards Chapter 4 Sections 2, 5-6 p , CC.2.2.HS.C.5 Chapter 3 Section 5 p Greatest Integer Chapter 2 Section 6 p /Calculus Page 7
9 Introduction to Derivatives and Integrals Dunmore School District resources EK1.1A1 EK1.1B1 EK1.1C3 EK2.1A1 EK2.1A2 EK2.1A3 EK2.1A4 EK2.1C1 EK2.1C2 EK2.1C3 EK2.1C4 EK2.1C5 EK3.1A1 EK3.1A2 EK3.2A1 EK3.2A2 EK3.2C1 EK3.2C2 EK3.2C3 Final Review and Exam /Calculus Page 8
10 General Topic Anchor Descriptor PA Core Standards Eligible Content, Essential Knowledge, Skills & Vocabulary CC.2.3.HS.A.7 Introduction to Trigonometric with Right Apply trigonometric ratios to solve Ratios Triangles problems involving right triangles G Use the Pythagorean theorem to write and/or solve problems involving right triangles G Use trigonometric ratios to write and/or solve problems involving right triangles. HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Solving for a Side Solving for an Angle Solving the Triangle Application Problems Complementary Angles Reciprocal Ratios Special Right Triangles and Trigonometric Ratios Resources & Activities Chapter 5 Sections 2-4 p Assessments Suggested Time (In Days) 14 days HSG.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. /Calculus Page 9
11 Unit Circle Definition of Trigonometric HSF.TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. HSF.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Radians Unit Circle Definitions Trigonometric Values of Special Angles Quadrant Angles Reference Angles Chapter 6 Sections 1-2 p days HSF.TF.A.3 Use special right 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. CC.2.2.HS.C.7 Apply radian measure of an angle and the unit circle to analyze the trigonometric functions. /Calculus Page 10
12 Graphs of Trigonometric HSF.TF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. HSF.TF.B.5 Choose trigonometric functions to model periodic phenomena with specific amplitude, frequency, and midline. CC.2.2.HS.C.8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs. Graphs of sine, cosine and tangent Features of Sinusoidal from their Graphs Finding the Amplitude and Midline from their Formulas Periods of Sinusoidal Graphing Sinusoidal Constructing Sinusoidal Real World Problems Chapter 6 Sections 3-6 p days Trigonometric Algebra CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios. G Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction). G Use the Pythagorean Theorem to write and/or solve problems involving right triangles. Fundamental Identities Proving and Verifying Identities Sum and Difference Identities Double-Angle Identities Half-Angle Identities Solving Trigonometric Equations Chapter 7 Sections 1-4, 6-7 p , days /Calculus Page 11
13 G Use trigonometric ratios to write and/or solve problems involving right triangles. HSF.TF.C.8 Prove the Pythagorean identity sin 2 θ + cos 2 θ = 1 and use it to find sin θ, cos θ, or tan θ given sin θ, cos θ, or tan θ and the quadrant of the angle. with General Triangles HSF.TF.C.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. HSG.SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems. HSG.SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. HSG.SRT.D.9 Derive the formula A=1/2absinC for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Law of Sines Law of Cosines Solving Triangles Area Application Problems Chapter 8 Sections 1-2 p days /Calculus Page 12
14 Introduction to CC C.1 Define, evaluate, and compare functions. Interpret the effects transformations have on functions and find the inverses of functions. Definition Function Notation Evaluating Domain and Range Inverses Parent Function Graphs and Transformations Chapter 2 Section 3 p Chapter 4 Section 1 p days Linear Use the concept and notation of functions to interpret and apply them in terms of their context. Solving Linear Equations Solving Systems Of Equations Word Problems Linear Regression Chapter 2 Section 4 p days Graph and analyze functions and use their properties to make connections between the different representations. Graphing Linear Analyzing the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness /Calculus Page 13
15 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. Interpret functions in terms of the situations they model. Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Polynomial CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities. Quadratic Solving Graphing Application Problems Cubic Solving Graphing Application Problems Analyzing the Domain/Range Continuity Increasing/decreasing behav ior Symmetry Boundedness Local extrema Horizontal asymptotes Chapter 3 Sections 1, 3-4 p , days /Calculus Page 14
16 Interpret the effects transformations have on functions and find the inverses of functions CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. Interpret functions in terms of the situations they model. Vertical asymptotes End behavior x-intercepts y-intercepts Absolute Value Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities. Interpret the effects transformations have on functions and find the inverses of functions Solving Absolute Value Equations Graphing Absolute Value Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Chapter 1 Section 8 p days /Calculus Page 15
17 Interpret functions in terms of the situations they model. Square Root Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities. Solving Radical Equations Graphing Square Root Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Review Chapter Section 7 p Chapter 1 Section 6 p Chapter 2 Section 6 p days Interpret the effects transformations have on functions and find the inverses of functions Interpret functions in terms of the situations they model. /Calculus Page 16
18 Logarithmic Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities. Interpret the effects transformations have on functions and find the inverses of functions Solving Logarithmic Graphing Logarithmic Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Chapter 4 Sections 3-5 p days Interpret functions in terms of the situations they model. /Calculus Page 17
19 Exponential Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities. Interpret the effects transformations have on functions and find the inverses of functions Solving Exponential Equations Growth and Decay Interest Problems Graphing Exponential Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Chapter 4 Sections 2, 5-6 p , days CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. Interpret functions in terms of the situations they model. /Calculus Page 18
20 Reciprocal Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Write functions or sequences that model relationships between two quantities.. Interpret functions in terms of the situations they model. Solving Reciprocal Graphing Reciprocal Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Chapter 3 Section 5 p days Greatest Integer Use the concept and notation of functions to interpret and apply them in terms of their context. Graph and analyze functions and use their properties to make connections between the different representations. Evaluating Greatest Integer Graphing Greatest Integer Analyze the Function Domain/Range Continuity Increasing/decreasing behavior Symmetry Boundedness Local extrema Chapter 2 Section 6 p days /Calculus Page 19
21 Write functions or sequences that model relationships between two quantities. Interpret the effects transformations have on functions and find the inverses of functions Interpret functions in terms of the situations they model. Horizontal asymptotes Vertical asymptotes End behavior x-intercepts y-intercepts Introduction to Derivatives and Integrals EK1.1A1 Given A function f, the limit f(x) as x approaches c is a real number R f(x) can be made arbitrarily close to R by taking x sufficiently close to c (but not equal to c). If the limit exists and is a real number, then the common notation is lim x c f(x) = R. EK1.1B1 Numerical and graphical information can be used to estimate limits. Limits Power Rule for Derivatives Power Rule for Integrals Applications Area under the curve Displacement, velocity, acceleration resources. 15 days EK1.1C3 Limits of sums, differences, products, quotients, and composite functions can be found using the basic theorems of limits and algebraic rules. /Calculus Page 20
22 EK2.1A1 The difference quotients f(a+h) f(a) h and f(x) f(a) express the average rate x a of change of a function over an interval. EK2.1A2 The instantaneous rate of change of a function at a point can be expressed by lim f(a+h) f(a) h 0 h or lim f(x) f(a) x a x a provided that the limit exists. These are common forms of the definition of the derivative and are denoted f (a). EK2.1A3 The derivative of f is the functions whose value at x is lim provided this limit exists. f(a+h) f(a) h 0 h EK2.1A4 For y=f(x), notations for the derivative include dy dx, f (x), and y. EK2.1C1 Direct application of the definition of the derivative can be used to find the derivative for selected functions, including polynomial, power, sine, cosine, exponential, and logarithmic functions., /Calculus Page 21
23 EK2.1C2 Specific rules can be used to calculate derivatives for classes for functions, including polynomial, rational, power, exponential, logarithmic, trigonometric, and inverse trigonometric. EK2.1C3 Sums, differences, products, and quotients of functions can be differentiated using derivative rules. EK2.1C4 The chain rule provides a way to differentiate composite functions. EK2.1C5 The chain rule is the basis for implicit differentiation. EK3.1A1 An antiderivative of a function f is a function g whose derivative is f. EK3.1A2 Differentiation rules provide the foundation for finding antiderivatives. EK3.2A1 A Riemann sum, which requires a partition of an interval I, is the sum of products, each of which is the value of the function at a point in a subinterval /Calculus Page 22
24 multiplied by the length of that subinterval of the partition. EK3.2A2 The definite integral of a continuous function f over the interval [a, b], b denoted by f(x)dx = a n lim f(x i) x i where x i is a i=1 max x i 0 value in the ith subinterval, Δx i is the width of the ith subinterval, n is the number of subintervals, and maxδx i is the width of the largest subinterval. Another form of the definition is b a f(x)dx = lim n i=1 n where x i = b a n the ith subinterval. f(x i ) x i, and xi is the value in EK3.2C1 In some cases, a definite integral can be evaluated by using geometry and the connection between the definite integral and area. EK3.2C2 Properties of definite integrals include the integral of a constant times a function, the integral of the sum of two functions, reversal of limits of integration, and the integral of a function over adjacent intervals. /Calculus Page 23
25 Final Review EK3.2C3 The definition of the definite integral may be extended to functions with removable or jump discontinuities. 16 days /Calculus Page 24
Calculus Honors Curriculum Guide Dunmore School District Dunmore, PA
Calculus Honors Dunmore School District Dunmore, PA Calculus Honors Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Major topics include: limits, derivatives, integrals. Instruction
More informationRegion 16 Board of Education. Precalculus Curriculum
Region 16 Board of Education Precalculus Curriculum 2008 1 Course Description This course offers students an opportunity to explore a variety of concepts designed to prepare them to go on to study calculus.
More informationPre-Calculus EOC Review 2016
Pre-Calculus EOC Review 2016 Name The Exam 50 questions, multiple choice, paper and pencil. I. Limits 8 questions a. (1) decide if a function is continuous at a point b. (1) understand continuity in terms
More informationAlgebra II Curriculum Guide Dunmore School District Dunmore, PA
Algebra II Dunmore School District Dunmore, PA Algebra II Prerequisite: Successful completion of Geometry This course continues and reinforces the mathematical material learned in Algebra I. It deals with
More informationAlgebra II Honors Curriculum Guide Dunmore School District Dunmore, PA
Algebra II Honors Dunmore School District Dunmore, PA Algebra II Honors Prerequisite: Successful completion of Geometry Honors This course continues and reinforces the mathematical material learned in
More informationCC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of it. Calculator set builder notation, interval Unit 2:
Unit/Concepts Unit 1: Number Sets PA Eligible Content PA Common Core CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of it Resources Vocab 1.1 set, number sets (Natural,
More informationAlgebra II/Trigonometry
Algebra II/Trigonometry Scranton School District Scranton, PA Algebra II/Trigonometry Prerequisite: Successful completion of Honors Geometry, Geometry 9 or Geometry 10 Student must have earned an 80% or
More informationPre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives
Pre-Calculus MATH 119 Fall 2013 Learning Objectives Section 1.1 1. Use the Distance Formula 2. Use the Midpoint Formula 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables
More informationAP Calculus Curriculum Guide Dunmore School District Dunmore, PA
AP Calculus Dunmore School District Dunmore, PA AP Calculus Prerequisite: Successful completion of Trigonometry/Pre-Calculus Honors Advanced Placement Calculus is the highest level mathematics course offered
More informationMilford Public Schools Curriculum. Department: Mathematics Course Name: Precalculus Level 1
Milford Public Schools Curriculum Department: Mathematics Course Name: Precalculus Level 1 UNIT 1 Unit Description: Students will construct polynomial graphs with zeros and end behavior, and apply limit
More informationGrade 11 or 12 Pre-Calculus
Grade 11 or 12 Pre-Calculus Strands 1. Polynomial, Rational, and Radical Relationships 2. Trigonometric Functions 3. Modeling with Functions Strand 1: Polynomial, Rational, and Radical Relationships Standard
More informationWAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014)
WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014) COURSE NAME: Pre-Calculus UNIT: Chapter 1 NO. OF DAYS: KEY LEARNING (S): UNIT ESSENTIAL QUESTIONS: What methods are used to solve equations
More informationCURRICULUM GUIDE. Honors Algebra II / Trigonometry
CURRICULUM GUIDE Honors Algebra II / Trigonometry The Honors course is fast-paced, incorporating the topics of Algebra II/ Trigonometry plus some topics of the pre-calculus course. More emphasis is placed
More informationWest Windsor-Plainsboro Regional School District Algebra and Trigonometry Grades 11-12
West Windsor-Plainsboro Regional School District Algebra and Trigonometry Grades 11-12 Unit 1: Linear Relationships & Functions Content Area: Mathematics Course & Grade Level: Algebra & Trigonometry, 11
More informationHonors Algebra II/Trigonometry
Honors Algebra II/Trigonometry Scranton School District Scranton, PA Honors Algebra II/Trigonometry Prerequisite: Successful completion of Geometry or Honors Geometry Be in compliance with the SSD Honors
More informationCalculus I Curriculum Guide Scranton School District Scranton, PA
Scranton School District Scranton, PA Prerequisites: Successful completion of Elementary Analysis or Honors Elementary Analysis is a high level mathematics course offered by the Scranton School District.
More informationOverall Description of Course Trigonometry is a College Preparatory level course.
Radnor High School Course Syllabus Modified 9/1/2011 Trigonometry 444 Credits: 1 Grades: 11-12 Unweighted Prerequisite: Length: Year Algebra 2 Format: Meets Daily or teacher recommendation Overall Description
More informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More informationPC.FT.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π 3, π 4, and π 6,
FIRST NINE WEEKS Text: Blitzer Pre-Calculus Chapters 4, 5, 6 Unit 1 Introduction to : Sections 4.1, 4.2, 4.3, 4.4 PC.FT.1 Understand that the radian measure of an angle is the length of the arc on the
More informationWest Windsor-Plainsboro Regional School District Pre-Calculus Grades 11-12
West Windsor-Plainsboro Regional School District Pre-Calculus Grades 11-12 Unit 1: Solving Equations and Inequalities Algebraically and Graphically Content Area: Mathematics Course & Grade Level: Pre Calculus,
More informationPreCalculus Honors Curriculum Pacing Guide First Half of Semester
Unit 1 Introduction to Trigonometry (9 days) First Half of PC.FT.1 PC.FT.2 PC.FT.2a PC.FT.2b PC.FT.3 PC.FT.4 PC.FT.8 PC.GCI.5 Understand that the radian measure of an angle is the length of the arc on
More informationAP CALCULUS AB Study Guide for Midterm Exam 2017
AP CALCULUS AB Study Guide for Midterm Exam 2017 CHAPTER 1: PRECALCULUS REVIEW 1.1 Real Numbers, Functions and Graphs - Write absolute value as a piece-wise function - Write and interpret open and closed
More informationPolynomials and Rational Functions. Quadratic Equations and Inequalities. Remainder and Factor Theorems. Rational Root Theorem
Pre-Calculus Pre-AP Scope and Sequence - Year at a Glance Pre-Calculus Pre-AP - First Semester Pre-calculus with Limits; Larson/Hostetler Three Weeks 1 st 3 weeks 2 nd 3 weeks 3 rd 3 weeks 4 th 3 weeks
More informationMATHia Unit MATHia Workspace Overview TEKS
1 Function Overview Searching for Patterns Exploring and Analyzing Patterns Comparing Familiar Function Representations Students watch a video about a well-known mathematician creating an expression for
More informationWAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ALGEBRA II
UNIT: Review of Basic Algebra Skills as Needed SR1 and any Supplemental Materials UNIT : What skills from Algebra I are used in Algebra II? Review Algebra I Skills as Needed SR1 and any additional resources
More informationBemidji Area Schools Outcomes in Mathematics Analysis 1. Based on Minnesota Academic Standards in Mathematics (2007) Page 1 of 5
Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate. 9..1.1 9..1. 9..1.3 9..1.4 9..1.5 9..1.6 9..1.7
More informationIt is in Secondary Mathematics III Critical Area 1 Critical Area 2: Critical Area 3: Critical Area 4:
It is in Secondary Mathematics III that students pull together and apply the accumulation of learning that they have from their previous courses, with content grouped into four critical areas, organized
More informationHHS Pre-Calculus Reference Book
HHS Pre-Calculus Reference Book Purpose: To create a reference book to review topics for your final exam and to prepare you for Calculus. Instructions: Students are to compose a reference book containing
More informationMath Curriculum Map: Integrated Algebra II Unit: 1 Quarter: Time Frame: Review of Algebra 13 days Essential Questions: Key Concepts: Key Vocabulary:
Math Curriculum Map: Integrated Algebra II Unit: 1 Quarter: Time Frame: Review of Algebra 1 13 days Essential Questions: How does the order of operations help solve one- and two- step equations? How is
More informationALGEBRA & TRIGONOMETRY FOR CALCULUS MATH 1340
ALGEBRA & TRIGONOMETRY FOR CALCULUS Course Description: MATH 1340 A combined algebra and trigonometry course for science and engineering students planning to enroll in Calculus I, MATH 1950. Topics include:
More information, Precalculus, Quarter 1
2017.18, Precalculus, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency
More informationPre-Calculus & Trigonometry Scope and Sequence
Pre-Calculus & Trigonometry Scope and Sequence Domain INTERPRETING F.IF Understand the concept of a function, and use function notation. TRIGONOMETRIC F.TF BUILDING F.BF EXPRESSING GEOMETRIC PROPERTIES
More informationPrecalculus Review. Functions to KNOW! 1. Polynomial Functions. Types: General form Generic Graph and unique properties. Constants. Linear.
Precalculus Review Functions to KNOW! 1. Polynomial Functions Types: General form Generic Graph and unique properties Constants Linear Quadratic Cubic Generalizations for Polynomial Functions - The domain
More informationCurriculum Scope & Sequence
Book: Sullivan Pre-Calculus Enhanced with Graphing Utilities Subject/Grade Level: MATHEMATICS/HIGH SCHOOL Curriculum Scope & Sequence Course: PRE-CALCULUS CP/HONORS ***The goals and standards addressed
More informationCARLISLE AREA SCHOOL DISTRICT Carlisle, PA PRE-CALCULUS. GRADES 11 and 12
CARLISLE AREA SCHOOL DISTRICT Carlisle, PA 17013 PRE-CALCULUS GRADES 11 and 12 Date of Board Approval: April 17, 2014 CARLISLE AREA SCHOOL DISTRICT PLANNED INSTRUCTION COVER PAGE TITLE OF SUBJECT: Math
More informationPre-Calculus & Trigonometry Scope and Sequence
WHCSD Scope and Sequence Pre-Calculus/ 2017-2018 Pre-Calculus & Scope and Sequence Course Overview and Timing This section is to help you see the flow of the unit/topics across the entire school year.
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationHUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK
HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE / SUBJECT P r e c a l c u l u s ( A ) KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS and Graphs Polynomial, Power,
More informationChapter Lessons Standards Classical Methodologies
ACE GSE Precalculus Curriculum Map # of Days Chapter Lessons Standards Classical Methodologies Performance Tasks 12 1: from a Calculus Perspective 1: 2: Analyzing Graphs of and Relations 3: Continuity,
More informationTrigonometry. Unit 1 Trigonometry and Angles. Competencies. Trigonometric Functions
Unit 1 and Angles Estimated Time Frame for Unit 20 days Big Ideas Essential Question Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in
More informationAlgebra II. Key Resources: Page 3
Algebra II Course This course includes the study of a variety of functions (linear, quadratic higher order polynomials, exponential, absolute value, logarithmic and rational) learning to graph, compare,
More informationTopic Subtopics Essential Knowledge (EK)
Unit/ Unit 1 Limits [BEAN] 1.1 Limits Graphically Define a limit (y value a function approaches) One sided limits. Easy if it s continuous. Tricky if there s a discontinuity. EK 1.1A1: Given a function,
More informationPre-Calculus Mathematics Curriculum
Pre-Calculus Mathematics Curriculum First day introductions, materials, policies, procedures and Summer Exam (2 days) Unit 1 Estimated time frame for unit 1 Big Ideas Essential Question Competencies Lesson
More informationMath 121 Calculus 1 Fall 2009 Outcomes List for Final Exam
Math 121 Calculus 1 Fall 2009 Outcomes List for Final Exam This outcomes list summarizes what skills and knowledge you should have reviewed and/or acquired during this entire quarter in Math 121, and what
More informationPrecalculus. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGraw- Hill, ISBN:
Precalculus Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th edition, McGraw- Hill, 2008. ISBN: 978-0-07-331263-7. Course Description This course provides a working
More informationMATH 1040 Objectives List
MATH 1040 Objectives List Textbook: Calculus, Early Transcendentals, 7th edition, James Stewart Students should expect test questions that require synthesis of these objectives. Unit 1 WebAssign problems
More informationCourse Catalog. Pre-calculus Glynlyon, Inc.
Course Catalog Pre-calculus 2016 Glynlyon, Inc. Table of Contents COURSE OVERVIEW... 1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT 4: CIRCULAR
More informationMathematics High School Functions
Mathematics High School Functions Functions describe situations where one quantity determines another. For example, the return on $10,000 invested at an annualized percentage rate of 4.25% is a function
More informationUNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2
UNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2 Algebra II Unit 2 Overview: Trigonometric Functions Building on their previous work with functions, and on their work with trigonometric ratios
More informationMath Precalculus Blueprint Assessed Quarter 1
PO 11. Find approximate solutions for polynomial equations with or without graphing technology. MCWR-S3C2-06 Graphing polynomial functions. MCWR-S3C2-12 Theorems of polynomial functions. MCWR-S3C3-08 Polynomial
More informationPre-calculus 12 Curriculum Outcomes Framework (110 hours)
Curriculum Outcomes Framework (110 hours) Trigonometry (T) (35 40 hours) General Curriculum Outcome: Students will be expected to develop trigonometric reasoning. T01 Students will be expected to T01.01
More informationAlgebra 2 College Prep Curriculum Maps
Algebra 2 College Prep Curriculum Maps Unit 1: Polynomial, Rational, and Radical Relationships Unit 2: Modeling With Functions Unit 3: Inferences and Conclusions from Data Unit 4: Trigonometric Functions
More informationList of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015)
List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT 155 1 Absolute Value Equations P 7 P 3 2 Absolute Value Inequalities P 9 P 4 3 Algebraic Expressions:
More informationHS Trigonometry Mathematics CC
Course Description A pre-calculus course for the college bound student. The term includes a strong emphasis on circular and triangular trigonometric functions, graphs of trigonometric functions and identities
More informationPre Calculus Gary Community School Corporation Unit Planning Map
UNIT/TIME FRAME STANDARDS Functions and Graphs (6 weeks) PC.F.1: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities,
More informationAnalysis of Functions
Volusia County Mathematics Department Curriculum Map Analysis of Functions Course Number 1201310 Mathematics Department Analysis of Functions Curriculum Map Volusia County Schools 1201310 Revision 8-01-12
More informationLearning Objectives for Math 165
Learning Objectives for Math 165 Chapter 2 Limits Section 2.1: Average Rate of Change. State the definition of average rate of change Describe what the rate of change does and does not tell us in a given
More informationAlgebra 2 TN Ready Performance Standards by Unit. The following Practice Standards and Literacy Skills will be used throughout the course:
The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1. Make sense of problems and persevere
More informationPre AP Algebra. Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra
Pre AP Algebra Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra 1 The content of the mathematics standards is intended to support the following five goals for students: becoming
More informationAlgebra III. Mathematics Curriculum Framework. Revised 2004
Algebra III Mathematics Curriculum Framework Revised 2004 Title: Algebra III (Fourth-year Course) Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics Pre-requisite: Algebra II
More informationAlgebra 2 and Mathematics 3 Critical Areas of Focus
Critical Areas of Focus Ohio s Learning Standards for Mathematics include descriptions of the Conceptual Categories. These descriptions have been used to develop critical areas for each of the courses
More informationBusiness Calculus
Business Calculus 978-1-63545-025-5 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Senior Contributing Authors: Gilbert
More informationAlgebra 1 Part 1 Curriculum Guide Dunmore School District Dunmore, PA
Algebra 1 Part 1 Dunmore School District Dunmore, PA Algebra 1 Part 1 Prerequisite: Successful completion of Pre Algebra Algebra 1 Part 1 and Algebra 1 Part 2 K together create an Algebra course covered
More informationCurriculum Catalog
2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents PRE-CALCULUS COURSE OVERVIEW...1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT
More informationHow well do I know the content? (scale 1 5)
Page 1 I. Number and Quantity, Algebra, Functions, and Calculus (68%) A. Number and Quantity 1. Understand the properties of exponents of s I will a. perform operations involving exponents, including negative
More informationDue Date: Thursday, March 22, 2018
The Notebook Project AP Calculus AB This project is designed to improve study skills and organizational skills for a successful career in mathematics. You are to turn a composition notebook into a Go To
More informationMathematics - High School Algebra II
Mathematics - High School Algebra II All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in this course will
More informationPre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.2 Solving Quadratic Equations
Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.1.1 Solve Simple Equations Involving Absolute Value 0.2 Solving Quadratic Equations 0.2.1 Use the
More informationCLEP EXAMINATION: Precalculus
CLEP EXAMINATION: Precalculus DESCRIPTION OF THE EXAMINATION: The Precalculus examination assesses student mastery of skills and concepts required for success in a first-semester calculus course. A large
More informationCHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE TRIGONOMETRY / PRE-CALCULUS
CHINO VALLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL GUIDE TRIGONOMETRY / PRE-CALCULUS Course Number 5121 Department Mathematics Qualification Guidelines Successful completion of both semesters of Algebra
More informationVolusia County Mathematics Curriculum Map. Pre-Calculus. Course Number /IOD
Volusia County Mathematics Curriculum Map Pre-Calculus Course Number 1202340/IOD Mathematics Department Volusia County Schools Revised June 9, 2012 Pre- Calculus Curriculum Map 120234/IOD COMPONENTS OF
More informationDinwiddie County Subject: Trigonometry Scope and Sequence
Dinwiddie County Subject: Trigonometry Scope and Sequence GRADE: High School 9 WKS Topics Equations (linear, quadratic, and absolute value) and Radicals (simplest radical form, including rationalizing
More informationAlgebra II Learning Targets
Chapter 0 Preparing for Advanced Algebra LT 0.1 Representing Functions Identify the domain and range of functions LT 0.2 FOIL Use the FOIL method to multiply binomials LT 0.3 Factoring Polynomials Use
More informationThe American School of Marrakesh. AP Calculus AB Summer Preparation Packet
The American School of Marrakesh AP Calculus AB Summer Preparation Packet Summer 2016 SKILLS NEEDED FOR CALCULUS I. Algebra: *A. Exponents (operations with integer, fractional, and negative exponents)
More informationI. Content Standard: Number, Number Sense and Operations Standard
Course Description: Honors Precalculus is the study of advanced topics in functions, algebra, geometry, and data analysis including the conceptual underpinnings of Calculus. The course is an in-depth study
More informationG r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Exam
G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Exam G r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s Final Practice Exam Name: Student Number: For Marker
More informationSchool District of Marshfield Course Syllabus
School District of Marshfield Course Syllabus Course Name: Algebra II Length of Course: 1 Year Credit: 1 Program Goal: The School District of Marshfield Mathematics Program will prepare students for college
More informationAlgebra and Trigonometry
Algebra and Trigonometry 978-1-63545-098-9 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Jay Abramson, Arizona State
More informationObjectives List. Important Students should expect test questions that require a synthesis of these objectives.
MATH 1040 - of One Variable, Part I Textbook 1: : Algebra and Trigonometry for ET. 4 th edition by Brent, Muller Textbook 2:. Early Transcendentals, 3 rd edition by Briggs, Cochran, Gillett, Schulz s List
More informationCathedral Catholic High School Course Catalog
Cathedral Catholic High School Course Catalog Course Title: Pre-Calculus Course Description: This course is designed to prepare students to begin their college studies in introductory Calculus. Students
More informationAlgebra 2 CP and Algebra 2 A/B Curriculum Pacing Guide First Nine Weeks
Algebra CP and Algebra A/B Curriculum Pacing Guide 03-04 First Nine Weeks Unit Functions A.APR. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations
More informationPortable Assisted Study Sequence ALGEBRA IIB
SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The second half of
More informationTrimester 2 Expectations. Chapter (McGraw-Hill. CCSS covered Key Vocabulary Vertical. Alignment
Algebra 2 Trimester 2 Expectations Chapter (McGraw-Hill Algebra 2) Chapter 5 (Suggested Pacing 14 Days) Polynomials and Polynomial Functions Lesson 5-1: Operations with Polynomials Lesson 5-2: Dividing
More informationHarbor Creek School District
Unit 1 Days 1-9 Evaluate one-sided two-sided limits, given the graph of a function. Limits, Evaluate limits using tables calculators. Continuity Evaluate limits using direct substitution. Differentiability
More informationTRIGONOMETRY AND PRECALCULUS CURRICULUM Course 17008
TRIGONOMETRY AND PRECALCULUS CURRICULUM Course 17008 Students taking this course will concentrate on algebraic concepts and applications. The use of graphing calculators and other technologies is emphasized
More informationPre-Calculus H Unit 2: Trigonometry Functions
Pre-Calculus H Unit 2: Trigonometry Functions Unit #: APSDO-00019249 Duration: 7.0 Week(s) Date(s): Team: Melinda Litke (Author), Tracy Andreana, Sally degozzaldi, Jennifer Greene, Jeanine LaBrosse, Jaclyn
More informationMATHEMATICS Trigonometry. Mathematics 30-1 Mathematics (10 12) /21 Alberta Education, Alberta, Canada (2008)
MATHEMATICS 30-1 [C] Communication Trigonometry Develop trigonometric reasoning. 1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians. [CN, ME, R, V] 2. Develop
More information1 Analyzing Structure
1 Analyzing Structure Topic 1: Exploring and Analyzing Patterns Searching for Patterns Exploring and Analyzing Patterns Comparing Familiar Function Representations Students watch a video about a well-known
More informationAlgebra 2 (3 rd Quad Expectations) CCSS covered Key Vocabulary Vertical
Algebra 2 (3 rd Quad Expectations) CCSS covered Key Vocabulary Vertical Chapter (McGraw-Hill Algebra 2) Chapter 7 (Suggested Pacing 14 Days) Lesson 7-1: Graphing Exponential Functions Lesson 7-2: Solving
More informationMATHEMATICS LEARNING AREA. Methods Units 1 and 2 Course Outline. Week Content Sadler Reference Trigonometry
MATHEMATICS LEARNING AREA Methods Units 1 and 2 Course Outline Text: Sadler Methods and 2 Week Content Sadler Reference Trigonometry Cosine and Sine rules Week 1 Trigonometry Week 2 Radian Measure Radian
More informationReview Notes for IB Standard Level Math
Review Notes for IB Standard Level Math 1 Contents 1 Algebra 8 1.1 Rules of Basic Operations............................... 8 1.2 Rules of Roots..................................... 8 1.3 Rules of Exponents...................................
More informationCollege Algebra & Trig w Apps
WTCS Repository 10-804-197 College Algebra & Trig w Apps Course Outcome Summary Course Information Description Total Credits 5.00 This course covers those skills needed for success in Calculus and many
More informationUNIT 3 MATHEMATICAL METHODS ALGEBRA
UNIT 3 MATHEMATICAL METHODS ALGEBRA Substitution of Values Rearrangement and Substitution Polynomial Expressions Expanding Expressions Expanding Expressions by Rule Perfect Squares The Difference of Two
More informationAlgebra 2 (4 th Quad Expectations) Chapter (McGraw-Hill Algebra 2) Chapter 10 (Suggested Pacing 13 Days)
Algebra 2 (4 th Quad Expectations) Chapter (McGraw-Hill Algebra 2) Chapter 10 (Suggested Pacing 13 Days) Lesson 10-1: Sequences as Lesson 10-2: Arithmetic Sequences and Series Lesson 10-3: Geometric Sequences
More informationMATHEMATICAL ANALYSIS CURRICULUM GUIDE
MATHEMATICAL ANALYSIS CURRICULUM GUIDE Loudoun County Public Schools 2010-2011 Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet. INTRODUCTION
More informationAlbert Einstein High School Summer Task Cover Sheet
Albert Einstein High School Summer Task Cover Sheet Teacher(s): Chris Colwander Teacher(s) Contact Information: Chris_M_Colwander@mcpsmd.org, Chris.M.Colwander@mcpsmd.net Course: IB Pre-Calculus Purpose
More information1 Analyzing Structure
1 Analyzing Structure Topic 1: Exploring and Analyzing Patterns Searching for Patterns Exploring and Analyzing Patterns Comparing Familiar Function Representations Students watch a video about a well-known
More informationCommon Core State Standards. Clusters and Instructional Notes Perform arithmetic operations with complex numbers. 5.6
Algebra II Unit 1: Polynomial, Rational, and Radical Relationships This unit develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies
More information