SECONDARY MATHEMATICS CURRICULUM GUIDE. AP Calculus AB
|
|
- Christal Bell
- 5 years ago
- Views:
Transcription
1 # % <! $ ± Θ Δ Π Σ SECONDARY MATHEMATICS CURRICULUM GUIDE AP Calculus AB Textbook: Calculus Concepts and Calculators, 2 nd edition Best, Carter, Crabtree, Venture Publishing HILLSBOROUGH COUNTY SCHOOL DISTRICT # % <! $ ± Θ Δ Π Σ
2 GRAPHING CALCULATORS: Students are expected to use a graphing calculator throughout the course, and to learn the paper-and-pencil techniques of calculus. County exams, as well as the AP exam, will have both calculator and non-calculator parts. Students are expected to be able to do the following on their graphing calculator: Plot the graph of a function within an arbitrary viewing window; Find the zeros of functions (solve equations numerically); Numerically calculate the derivative of a function; and Numerically calculate the value of a definite integral. It is imperative that the teacher establish a level of rigor appropriate to the demands of this course. Cumulative District exams are provided for Semester 1 and Semester 2. Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the District semester exam. This outline is based on material supplied by the textbook publisher. It is provided as a general guideline to the teacher. The suggested problems are not meant to be exclusionary. The timeline is approximate. The following points are offered: The teacher may wish to reduce the amount of time suggested for Chapter 1 Functions and Graphs, and instead review these topics within the study of the Calculus. Please make note of the cut-off point for material on the SDHC Semester One exam. Some topics are required for AP Calculus BC only, and not for AP Calculus AB. Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 2 of 9
3 BEGINNING OF SEMESTER ONE Ch 1 Functions and Graphs (21 days) What is a Function Page 5: 1 4; 7,11, What is a Function Page 5: 5, 9, 12-17, Basic Functions and Transformations Page 7: 18, 19, 21, 23; Page 12: 1-19 odd Basic Functions and Transformations Page 8: 20; Page 13: 20, 21, 22ab, 24, 26 & Read Linear Functions and Models Page 14: 25; Page 22: 1-17 odd Linear Functions and Models Page 22: 2 10 even, 16; Page 76: 4,11,14,16,20,27,30a 7 Test Exponential Functions Page 30: 1, 3a-e, 5-15 odd Exponential Functions Page 30: 4 18 even, Compound Interest and e Page 37: 1 17 odd; Page 33: Compound Interest and e Page 37: 2-18 even; Page 33: Inverse Functions Page 42: 1 27 odd Inverse Functions Page 42: 2-28 even Logarithms Page 49: 1 4; 5,7,9,11, Logarithms Page 49: 6, 10, 12, 14, 17, odd 16 Supp Review Page 76: 8, 9, 15, 24, 30b 17 Test Polynomial and Rational Functions Page 58: 1-8,10,15, Composition of Functions Page 58: 11,13,16,21; Page 66: 1, 2, 4, 7, 9, 10, 12, Trigonometric Functions Page 66: 8, 14, 16; Page 73: 1-6, 7, 9, 11,12 21 Supp Review Page 73: 14, 17; Page 76: 1, 2, 3, 5, 12, 13, 17, 18, 23, 25, Test Chapter 1 Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 3 of 9
4 Ch 2 Derivative Functions (19 days) Average and Instantaneous Velocity Page 87: 1 13 odd Average and Instantaneous Velocity Page 87: 2 12 even; Page 79: 19, Derivative of a Function at a point Page 97: 1 8, 10 a, b, c Derivative of a Function at a point Page 98: 9, 10 d,e,f; 11 17, The Derivative Function Page 105: 1 19 odd, The Derivative Function Page 105: 2 12 even, 21,23,26, Calculating Derivative Numerically Page 105: 28,29; Page 112: 1 13 odd Calculating Derivative Numerically Page 112: 2 12 even 31 Test Critical Numbers; Relative Max/Min Page 116: 1 15 odd, Critical Numbers; Relative Max/Min Page 116: 8 18 even, 23, Inflection points and Second Derivative Page 125: 1, 2, 4, 5, 7, 9, 10, Inflection points and Second Derivative Page 125: 6, 12-17, The Limit of a Function Page 137: 1-29 odd Continuity Page 145: 1 15 odd, 16,17, Supp Review Page 149: 1, 3, 5, 9,10,13,16, 17,20,21,25,29,33 39 Test Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 4 of 9
5 Ch 3 The Definite Integral (10 days) Calculating Distance Traveled Page 163: 1 6, Calculation Areas; Riemann Sums Page 163: 7, 9; Page 169: 1 9 odd Riemann Sums Page 169: 2-10 even, Definite Integrals Page 176: 1, 2, 3, 5-17 odd Definite Integrals Page 177: 8-18 even; page 179 lab project The Fundamental Theorem of Calculus Page 184: 1-13 odd The Fundamental Theorem of Calculus Page 184: 2, 4, 8, 10, 12, 15, Supplementary Problems Page 187: 1,3,4, 7, 10,13, 16, 18, Test Chapter 3 Ch 4 Differentiation Rules (16 days) Derivative Rules for Basic Functions Page 200: 1, 5, 9, 13, 17, 19, 21, 23, 25, 27, 29, Derivative Rules for Basic Functions Page 200: 3, 7, 15, 18, 20, 22, 24, 26,28, 30, Differentiating Exponential Functions Page 206: 1 21 odd The Product and Quotient Rule Page 206: 4, 6, 10, 14, 16, 18, 20; Page 215: 1, 3, 5, 7, 10, The Product and Quotient Rule Page 215: 2, 4, 6, 12, 15-23,odd; 26, Test The Chain Rule Page 215: 31, 32, 35, 37; Page 223: 1 21 odd The Chain Rule Page 217: 36, 39; Page 223: 2, 4, 10; even; 25, 27, The Chain Rule Page 224: 23; even; 35, 39, 40, 43, Functions Defined Implicitly Page 223: 37, 41, 44; Page 229: 3 19 odd Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 5 of 9
6 Ch 4 Differentiation Rules (continued) Functions Defined Implicitly Page 229: 4, 8, even 60 Supplementary Problems Page 230: 21, 24, 27; Page 245: 2, 5, 8, 9, 10, 15, 16, 20, Test Related Rates of Change Page 235: 3, 5, 7, 9, 11, 12, Related Rates of Change Page 235: 4, 8, 10, 15, 18, Approximations Page 243: 1-9 odd Approximations Page 243: 4, 6, 8, 11, 13, 14, 16, * Derivative of Inverse Functions Supplement Ch 5 More Applications of the Derivative (14 days) Increasing and Decreasing Functions Page 260: 1; 5 11 odd;15, 17, 19; odd Increasing and Decreasing Functions Page 260: 6, 8, 10, 18; 28 36; 38, 41, Test and Applications of the Second Derivative Page 268: 2 4; 8 11; 17, 18, 20, 21, 22; Page 260: 12, 23, 24, Applications of the Second Derivative Page 269: 13, 15, 16, 19, 25, 28, 31, Limits at Infinity Page 268: 24, 26, 29; Page 275: 1 19odd Optimization Problems Page 275: 4, 8, 12, 16; Page 281: 1, 4, 7, Optimization Problems Page 281: 2, 5, 10, 11, 12, 13, Test The Mean Value Theorem Page 282 : 15, 17; Page 285: 1 11 odd Antiderivatives Page 285: 4, 8, 12; Page 291: 1 19 odd Antiderivatives Page 291: 4, 8, 12, 16, 18, 20, 21, 23 END OF SEMESTER ONE CUT-OFF FOR MATERIAL, SEMESTER ONE EXAM Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 6 of 9
7 BEGINNING OF SEMESTER TWO Ch 6 Integrals (9 days) The Definite Integral Again Page 304: 1-17 odd Functions Defined by Integrals Page 304: 4, 8, 12, 16; Page 312: 1-11 odd The Fundamental Theorem Again Page 318: 1 13 odd; Page 325: 6, 9, The Fundamental Theorem Again Page 318: 2-10 even; Page 325: 18, 19, 21, Test 5.5, 5.6 and Areas of Plane Regions Page 324: 1, 5, 9, 13, 15, 17, 19, Areas of Plane Regions Page 324: 4, 8, 12, 14, 16, 18, 20, 21 Ch 7 Finding Antiderivatives (14 days) Antiderivatives Page 332: 1-29 odd Antiderivatives Page 332: 2-30 even The Chain Rule Page 333: 31, 33; Page 336: 3-33 by 3's The Chain Rule Page 336: 2, 5, 8, 11, 14, 17, 20, 23, 28, 31, Integration by Parts (BC required) Page 336: 32, 34, 36, 37; Page 340: 1, 3, 5, 9-17 odd Integration by Parts (BC required) Page 340: 2-18 even, Review Page 325: 7, 8, 10 Page 361: 3, 5, 6, 9, 11, 12, 15, 18, 20, 29, Test 6.4 and Trig Functions and Inverses Page 348: 1, Trig Functions and Inverses Page 348: 4, 8, 12, 20, 21, 23-26, Numerical Integration Page 349: 29, 30; Page 357: 1-9 odd; 13, 17, Supp Review Page 348: 14-16; 22, 27; Page 357: 2, 6, 10, 14, 16, 18, 20 Page 361: 28, 43, Test Chapter 7 Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 7 of 9
8 Ch 8 Using the Definite Integral (10 days) Net and Total Distance Traveled Page 370: 1-15 odd Volume by Slicing Page 370: 12, 14; Page 377: Volume by Slicing Page 377: 5-19 odd Volume by Shell Method Page 378: 12, 16, 18; Page 382: 1-13 odd Average Value of a Function Page382: 6, 8, 10, 14; Page 385: 1-13 odd More Applications of the Definite Page 385: 8, 10, 12; Page 388: 1, 3, 5, 7 Integral 104 Supp Review Page Page 389: 6, 9; page 390: 1, 3, 5, 8, 9, 11, Test Chapter 8 Ch 9 Differential Equations (9 days) Introduction Page 397:1-11 odd Slope Fields Page 397: 6, 10; Page 402: Euler's Method (BC required) Page 403: 4, 5, 7: Page 408: 1, Euler's Method (BC required) Page 408: Separation of Variables Page 411: 1-9 odd Separation of Variables Page 411: 2-10 even; Page 415: 1, Supp Review Page 413: 1-14; Page 415: 4, Test Chapter 9 END OF NEW MATERIAL Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 8 of 9
9 Following the end of new material, approximately at the end of Quarter 3, the remaining time before the AP Exam should be spent preparing for the exam through use of practice exams from various publishers, and through use of released exams. RESOURCES Check the College Board s Acorn Book, which is updated annually, for the AP Course Description. The following books are good sources of activities and problems: Barnes, Mary, Investigating Change. Curriculum Corporation, Reprinted Best, George and Richard Lux, Preparing for the Calculus (AB) Exam 2004 Edition, Venture Publishing. Finney, Calculus: Graphical, Numeric, Algebraic, Pearson/Prentice Hall Hughes-Hallet, Deborah. Calculus. John Wiley & Sons, Hyun, Thomas, Acing AP Calculus AB and BC, Greenhall Publishing, 2007 The Ithaca College Group, Calculus An Active Approach with Projects. John Wiley & Sons, Note: The Instructor s Guide for Calculus An Active Approach with Projects has several quizzes and examinations in the back which contain some of the new types of questions. Thomas-Finney, Calculus 9th Edition. Addison Wesley, Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam.. Page 9 of 9
HW#02 (18 pts): All recommended exercises from JIT (1 pt/problem)
Spring 2011 MthSc103 Course Calendar Page 1 of 7 January W 12 Syllabus/Course Policies BST Review Th 13 Basic Skills Test F 14 JIT 1.1 1.3: Numbers, Fractions, Parentheses JIT 1.1: 2, 6, 8, 9 JIT 1.2:
More informationAnalytic Geometry/ Trigonometry
Analytic Geometry/ Trigonometry Course Numbers 1206330, 1211300 Lake County School Curriculum Map Released 2010-2011 Page 1 of 33 PREFACE Teams of Lake County teachers created the curriculum maps in order
More informationMAT 140 SYLLABUS - ANALYTIC GEOMETRY AND CALCULUS I
MAT 140 SYLLABUS - ANALYTIC GEOMETRY AND CALCULUS I ANDREW SCHWARTZ, PH.D. Catalog Description: 140-04 Analytic Geometry and Calculus I (Fall 2010) Analytic geometry, functions, limits, derivatives and
More informationAP CALCULUS AB - CHAPTERS 1 & Worksheet: 1(a, c), 2(a, c), 3a, 4, 5, 10a, 11b, (Solving inequalities)
AP CALCULUS AB - CHAPTERS 1 & 2 1. Worksheet: 1(a, c), 2(a, c), 3a, 4, 5, 10a, 11b, 12-15 (Solving inequalities) 2. Pg. 25-26: 1, 3, 7, 13, 14 (Functions. Abs. Val., Piece-wise) Pg. 59-62: 3, 7, 13, 19,
More informationMath Lecture 2 Inverse Functions & Logarithms
Math 1060 Lecture 2 Inverse Functions & Logarithms Outline Summary of last lecture Inverse Functions Domain, codomain, and range One-to-one functions Inverse functions Inverse trig functions Logarithms
More informationExponential and Logarithmic Functions. Copyright Cengage Learning. All rights reserved.
5 Exponential and Logarithmic Functions Copyright Cengage Learning. All rights reserved. 5.3 Properties of Logarithms Copyright Cengage Learning. All rights reserved. Objectives Use the change-of-base
More information171S5.4p Properties of Logarithmic Functions. November 20, CHAPTER 5: Exponential and Logarithmic Functions. Examples. Express as a product.
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions
More informationTennessee Senior Bridge Mathematics
A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts
More informationInstructor Notes for Chapter 4
Section 4.1 One to One Functions (Day 1) Instructor Notes for Chapter 4 Understand that an inverse relation undoes the original Understand why the line y = xis a line of symmetry for the graphs of relations
More informationMath 122: Final Exam Review Sheet
Exam Information Math 1: Final Exam Review Sheet The final exam will be given on Wednesday, December 1th from 8-1 am. The exam is cumulative and will cover sections 5., 5., 5.4, 5.5, 5., 5.9,.1,.,.4,.,
More informationDouble Integrals over More General Regions
Jim Lambers MAT 8 Spring Semester 9-1 Lecture 11 Notes These notes correspond to Section 1. in Stewart and Sections 5.3 and 5.4 in Marsden and Tromba. ouble Integrals over More General Regions We have
More informationPREREQUISITE/PRE-CALCULUS REVIEW
PREREQUISITE/PRE-CALCULUS REVIEW Introduction This review sheet is a summary of most of the main topics that you should already be familiar with from your pre-calculus and trigonometry course(s), and which
More information2. Be able to evaluate a trig function at a particular degree measure. Example: cos. again, just use the unit circle!
Study Guide for PART II of the Fall 18 MAT187 Final Exam NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 5 multiple choice questions. You will be
More informationMATH 20C: FUNDAMENTALS OF CALCULUS II FINAL EXAM
MATH 2C: FUNDAMENTALS OF CALCULUS II FINAL EXAM Name Please circle the answer to each of the following problems. You may use an approved calculator. Each multiple choice problem is worth 2 points.. Multiple
More informationCollege Pre-Calc Lesson Plans
January 4-8 January 11-15 January 18-22 January 25-29 Sections 9.2 Area of a Triangle Mixed Trig Exercises Section 14.1 Matrix Addition & Scalar Multiplication Section 14.5 Transition Pg 342: 1, 3, 7-13,
More informationLogarithmic Functions and Their Graphs
Logarithmic Functions and Their Graphs Accelerated Pre-Calculus Mr. Niedert Accelerated Pre-Calculus Logarithmic Functions and Their Graphs Mr. Niedert 1 / 24 Logarithmic Functions and Their Graphs 1 Logarithmic
More informationJEFFERSON COLLEGE COURSE SYLLABUS ETC104 AC CIRCUITS. 5 Credit Hours. Prepared by: Ronald S. Krive. Revised Date: October 2007 by Dennis Eimer
JEFFERSON COLLEGE COURSE SYLLABUS ETC104 AC CIRCUITS 5 Credit Hours Prepared by: Ronald S. Krive Revised Date: October 2007 by Dennis Eimer Division of Technology Dr. John Keck, Dean Ms. Brenda Russell,
More informationMath 210: 1, 2 Calculus III Spring 2008
Math 210: 1, 2 Calculus III Spring 2008 Professor: Pete Goetz CRN: 20128/20130 Office: BSS 358 Office Hours: Tuesday 4-5, Wednesday 1-2, Thursday 3-4, Friday 8-9, and by appointment. Phone: 826-3926 Email:
More informationMathematics UNIT FIVE Trigonometry II. Unit. Student Workbook. Lesson 1: Trigonometric Equations Approximate Completion Time: 4 Days
Mathematics 0- Student Workbook Unit 5 Lesson : Trigonometric Equations Approximate Completion Time: 4 Days Lesson : Trigonometric Identities I Approximate Completion Time: 4 Days Lesson : Trigonometric
More informationAlgebra 2/Trigonometry Review Sessions 1 & 2: Trigonometry Mega-Session. The Unit Circle
Algebra /Trigonometry Review Sessions 1 & : Trigonometry Mega-Session Trigonometry (Definition) - The branch of mathematics that deals with the relationships between the sides and the angles of triangles
More informationPreparing Smart Teachers to Teach with SMART TM Technology. NCTM Annual Conference April 26, 2012 Philadelphia, PA
Preparing Smart Teachers to Teach with SMART TM Technology NCTM Annual Conference Philadelphia, PA Mary Lou Metz (mlmetz@iup.edu) Edel Reilly Francisco Alarcon Indiana University of PA Metz, Reilly & Alarcon
More information3.3 Properties of Logarithms
Section 3.3 Properties of Logarithms 07 3.3 Properties of Logarithms Change of Base Most calculators have only two types of log keys, one for common logarithms (base 0) and one for natural logarithms (base
More informationKeystone Exams: Algebra I Assessment Anchors and Eligible Content. Pennsylvania Department of Education
Keystone Exams: Algebra I Assessment Anchors and Pennsylvania Department of Education www.education.state.pa.us 2010 PENNSYLVANIA DEPARTMENT OF EDUCATION General Introduction to the Keystone Exam Assessment
More informationReview Sheet for Math 230, Midterm exam 2. Fall 2006
Review Sheet for Math 230, Midterm exam 2. Fall 2006 October 31, 2006 The second midterm exam will take place: Monday, November 13, from 8:15 to 9:30 pm. It will cover chapter 15 and sections 16.1 16.4,
More informationNUMBER THEORY AMIN WITNO
NUMBER THEORY AMIN WITNO.. w w w. w i t n o. c o m Number Theory Outlines and Problem Sets Amin Witno Preface These notes are mere outlines for the course Math 313 given at Philadelphia
More informationTHE SINUSOIDAL WAVEFORM
Chapter 11 THE SINUSOIDAL WAVEFORM The sinusoidal waveform or sine wave is the fundamental type of alternating current (ac) and alternating voltage. It is also referred to as a sinusoidal wave or, simply,
More informationHonors Algebra 2 Assignment Sheet - Chapter 1
Assignment Sheet - Chapter 1 #01: Read the text and the examples in your book for the following sections: 1.1, 1., and 1.4. Be sure you read and understand the handshake problem. Also make sure you copy
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More informationS56 (5.1) Logs and Exponentials.notebook October 14, 2016
1. Daily Practice 21.9.2016 Exponential Functions Today we will be learning about exponential functions. A function of the form y = a x is called an exponential function with the base 'a' where a 0. y
More informationLogs and Exponentials Higher.notebook February 26, Daily Practice
Daily Practice 2.2.2015 Daily Practice 3.2.2015 Today we will be learning about exponential functions and logs. Homework due! Need to know for Unit Test 2: Expressions and Functions Adding and subtracng
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Trigonometry Final Exam Study Guide Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a polar equation is given. Select the polar
More informationUniversity of North Georgia Department of Mathematics
University of North Georgia Department of Mathematics Instructor: Berhanu Kidane Course: College Algebra Math 1111 Text Book: For this course we use the free e book by Stitz and Zeager with link: http://www.stitz-zeager.com/szca07042013.pdf
More informationDe Anza College Department of Engineering Engr 37-Intorduction to Circuit Analysis
De Anza College Department of Engineering Engr 37-Intorduction to Circuit Analysis Spring 2017 Lec: Mon to Thurs 8:15 am 9:20 am S48 Office Hours: Thursday7:15 am to 8:15 am S48 Manizheh Zand email: zandmanizheh@fhda.edu
More informationTrigonometry. An Overview of Important Topics
Trigonometry An Overview of Important Topics 1 Contents Trigonometry An Overview of Important Topics... 4 UNDERSTAND HOW ANGLES ARE MEASURED... 6 Degrees... 7 Radians... 7 Unit Circle... 9 Practice Problems...
More informationAlex Benn. Math 7 - Outline First Semester ( ) (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days
Math 7 - Outline First Semester (2016-2017) Alex Benn (Numbers in parentheses are the relevant California Math Textbook Sections) Quarter 1 44 days 0.1 Classroom Rules Multiplication Table Unit 1 Measuring
More informationChapter 3 Exponential and Logarithmic Functions
Chapter 3 Exponential and Logarithmic Functions Section 1 Section 2 Section 3 Section 4 Section 5 Exponential Functions and Their Graphs Logarithmic Functions and Their Graphs Properties of Logarithms
More information33. Riemann Summation over Rectangular Regions
. iemann Summation over ectangular egions A rectangular region in the xy-plane can be defined using compound inequalities, where x and y are each bound by constants such that a x a and b y b. Let z = f(x,
More informationNEW Published in June 2018 CATALOGUE 2019
NEW Published in June 2018 CATALOGUE 2019 PASS PUBLICATIONS PRIVATE ACADEMIC AND SCIENTIFIC STUDIES LIMITED passpublications.uk@gmail.com +44(0)20 8857 4752 P A S S PUBLICATIONS PASS is an acronym for
More informationTenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7
EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional
More informationLesson Plan Mr. Baglos Course: Honors Algebra II As of: 4/2/18. After School: 2:30-3:30 Room 2232
Lesson Plan Mr. Baglos Course: Honors Algebra II As of: 4/2/18 After School: 2:30-3:30 Room 2232 HW: Finish all notes for the day, do the assignment from your HMH workbook, Gizmos, your Math Journal, and
More informationAnswer key to select Section 1.2 textbook exercises (If you believe I made a mistake, then please let me know ASAP) x x 50.
Math 60 Textbook : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial Remember : Many homework exercises are used to teach you a concept we did not cover in class. It is important for you to
More informationPractice Test 3 (longer than the actual test will be) 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.
MAT 115 Spring 2015 Practice Test 3 (longer than the actual test will be) Part I: No Calculators. Show work. 1. Solve the following inequalities. Give solutions in interval notation. (Expect 1 or 2.) a.
More informationSECTION 7: FREQUENCY DOMAIN ANALYSIS. MAE 3401 Modeling and Simulation
SECTION 7: FREQUENCY DOMAIN ANALYSIS MAE 3401 Modeling and Simulation 2 Response to Sinusoidal Inputs Frequency Domain Analysis Introduction 3 We ve looked at system impulse and step responses Also interested
More informationMATH 105: Midterm #1 Practice Problems
Name: MATH 105: Midterm #1 Practice Problems 1. TRUE or FALSE, plus explanation. Give a full-word answer TRUE or FALSE. If the statement is true, explain why, using concepts and results from class to justify
More informationPerformance Task. Asteroid Aim. Chapter 8. Instructional Overview
Instructional Overview Performance Task Launch Question Summary Teacher Notes Supplies Mathematical Discourse Writing/Discussion Prompts Apps take a long time to design and program. One app in development
More informationChapter 4/5 Part 2- Trig Identities and Equations
Chapter 4/5 Part 2- Trig Identities and Equations Lesson Package MHF4U Chapter 4/5 Part 2 Outline Unit Goal: By the end of this unit, you will be able to solve trig equations and prove trig identities.
More informationEELE 201 Circuits I. Fall 2013 (4 Credits)
EELE 201 Circuits I Instructor: Fall 2013 (4 Credits) Jim Becker 535 Cobleigh Hall 994-5988 Office hours: Monday 2:30-3:30 pm and Wednesday 3:30-4:30 pm or by appointment EMAIL: For EELE 201-related questions,
More informationExample. h + 8 < -13 and b 4 > -6 Multiplying and dividing inequalities
Unit 2 (continued): Expressions and Equations 2 nd 9 Weeks Suggested Instructional Days: 10 Unit Summary (Learning Target/Goal): Use properties of operations to generate equivalent expressions. CCSS for
More informationS56 (5.3) Logs and Exponentials.notebook March 02, 2016
Daily Practice 22.2.206 Today we will be learning about exponential and logarithmic functions. Homework due tomorrow. Need to know for Unit Test 2: Expressions and Functions Adding and subtracng logs,
More informationPage 1 of 52 Youtube.com/c/StayLearningNewdelhi
Page 1 of 52 www.vijayadarsh.com Youtube.com/c/StayLearningNewdelhi Contact@vijayAdarsh.com +919268373738 About StayLearning StayLearning (a Division of AASS) believes in educating their students with
More informationAlgebra 2 Conic Sections Study Guide
ALGEBRA 2 CONIC SECTIONS STUDY GUIDE PDF - Are you looking for algebra 2 conic sections study guide Books? Now, you will be happy that at this time algebra 2 conic sections study guide PDF is available
More informationCK-12 FOUNDATION. Algebra I Teacher s Edition - Answers to Assessment
CK-12 FOUNDATION Algebra I Teacher s Edition - Answers to Assessment CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the
More information18 Logarithmic Functions
18 Logarithmic Functions Concepts: Logarithms (Section 3.3) Logarithms as Functions Logarithms as Exponent Pickers Inverse Relationship between Logarithmic and Exponential Functions. The Common Logarithm
More informationHigher. Expressions & Functions. Unit 2 Course Contents. Higher Higher Higher Higher Higher. Higher Higher. Higher Higher. Higher Higher.
Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher xpressions & unctions Unit 2 Course Contents Higher
More informationKnow how to represent permutations in the two rowed notation, and how to multiply permutations using this notation.
The third exam will be on Monday, November 21, 2011. It will cover Sections 5.1-5.5. Of course, the material is cumulative, and the listed sections depend on earlier sections, which it is assumed that
More information9/4/2013. Math. Curriculum Council September 5, topics nouns What? rigor verbs How?
Math Curriculum Council September 5, 2013 Cognitive Change rigor verbs How? Content Change topics nouns What? 1 CHANGES TO STUDENT EXPECTATIONS NEW Standard Change of Grade Level Change of Strand Other
More informationExponential And Logarithmic Function Calculator
Exponential And Logarithmic Function Calculator Read Book Online: Exponential And Logarithmic Function Calculator Download or read online ebook exponential and logarithmic function calculator in any format
More informationNu1nber Theory Park Forest Math Team. Meet #1. Self-study Packet. Problem Categories for this Meet:
Park Forest Math Team 2017-18 Meet #1 Nu1nber Theory Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and
More informationSection 7.2 Logarithmic Functions
Math 150 c Lynch 1 of 6 Section 7.2 Logarithmic Functions Definition. Let a be any positive number not equal to 1. The logarithm of x to the base a is y if and only if a y = x. The number y is denoted
More informationBIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals BIG IDEA 1:
BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Decimals Explain the difference between an exact answer and an estimated
More informationContents. How You May Use This Resource Guide
Contents How You May Use This Resource Guide ii 15 An Introduction to Plane Analytic Geometry 1 Worksheet 15.1: Modeling Conics........................ 4 Worksheet 15.2: Program to Graph the Conics..................
More informationDouble-Angle, Half-Angle, and Reduction Formulas
Double-Angle, Half-Angle, and Reduction Formulas By: OpenStaxCollege Bicycle ramps for advanced riders have a steeper incline than those designed for novices. Bicycle ramps made for competition (see [link])
More informationTrigonometric Equations
Chapter Three Trigonometric Equations Solving Simple Trigonometric Equations Algebraically Solving Complicated Trigonometric Equations Algebraically Graphs of Sine and Cosine Functions Solving Trigonometric
More informationUNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet
Name Period Date UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet 5.1 Fractions: Parts and Wholes Identify the whole and its parts. Find and compare areas of different shapes. Identify congruent
More informationYou found trigonometric values using the unit circle. (Lesson 4-3)
You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify
More informationModule 5 Trigonometric Identities I
MAC 1114 Module 5 Trigonometric Identities I Learning Objectives Upon completing this module, you should be able to: 1. Recognize the fundamental identities: reciprocal identities, quotient identities,
More informationMath Exam 1 Review Fall 2009
Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice some kinds of problems. This collection is not necessarily exhaustive.
More informationMA 1032 Review for exam III
MA 10 Review for eam III Name Establish the identit. 1) cot θ sec θ = csc θ 1) ) cscu - cos u sec u= cot u ) ) cos u 1 + tan u - sin u 1 + cot u = cos u - sin u ) ) csc θ + cot θ tan θ + sin θ = csc θ
More informationChino Valley Unified School District High School Course Description #5U01
CONTACTS 1. School Information: School: Chino Valley Unified School District Street Address: 5130 Riverside Dr., Chino, CA 91710 Mailing Address: 5130 Riverside Dr., Chino, CA 91710 Phone: (909) 628-1201
More informationCalculus Second Edition Finney Demana Solutions Manual READ ONLINE
Calculus Second Edition Finney Demana Solutions Manual READ ONLINE Calculus: Graphical, Numerical, Algebraic Student - Calculus: Graphical, Numerical, Algebraic Student Edition 2003c: Ross L. Finney, In
More informationMathematics Success Grade 6
T428 Mathematics Success Grade 6 [OBJECTIVE] The students will plot ordered pairs containing rational values to identify vertical and horizontal lengths between two points in order to solve real-world
More information1 of 5 8/11/2014 8:24 AM Units: Teacher: AdvancedMath, CORE Course: AdvancedMath Year: 2012-13 Ratios s Ratios s Ratio Applications of Ratio What is a ratio? What is a How do I use ratios proportions to
More informationRate of Change and Slope by Paul Alves
Rate of Change and Slope by Paul Alves Activity overview This lesson was designed for the Grade 10 Applied curriculum in Ontario. In that course, students are expected to connect the rate of change of
More informationSiyavula textbooks: Grade 12 Maths. Collection Editor: Free High School Science Texts Project
Siyavula textbooks: Grade 12 Maths Collection Editor: Free High School Science Texts Project Siyavula textbooks: Grade 12 Maths Collection Editor: Free High School Science Texts Project Authors: Free
More informationCOLLEGE OF ARTS AND SCIENCES COMMITTEE ON INSTRUCTION Minutes #9 November 13, Varner Hall MINUTES
Approved on November 20, 2017 COLLEGE OF ARTS AND SCIENCES COMMITTEE ON INSTRUCTION Minutes #9 November 13, 2017 217 Varner Hall MINUTES Present: A. Banes-Berceli, G. Cassano, K. Castoldi, S. Dykstra,
More informationFunctions of several variables
Chapter 6 Functions of several variables 6.1 Limits and continuity Definition 6.1 (Euclidean distance). Given two points P (x 1, y 1 ) and Q(x, y ) on the plane, we define their distance by the formula
More informationAlgebra and Trig. I. The graph of
Algebra and Trig. I 4.5 Graphs of Sine and Cosine Functions The graph of The graph of. The trigonometric functions can be graphed in a rectangular coordinate system by plotting points whose coordinates
More informationMATH STUDENT BOOK. 12th Grade Unit 5
MATH STUDENT BOOK 12th Grade Unit 5 Unit 5 ANALYTIC TRIGONOMETRY MATH 1205 ANALYTIC TRIGONOMETRY INTRODUCTION 3 1. IDENTITIES AND ADDITION FORMULAS 5 FUNDAMENTAL TRIGONOMETRIC IDENTITIES 5 PROVING IDENTITIES
More informationCHAPTER 11 PARTIAL DERIVATIVES
CHAPTER 11 PARTIAL DERIVATIVES 1. FUNCTIONS OF SEVERAL VARIABLES A) Definition: A function of two variables is a rule that assigns to each ordered pair of real numbers (x,y) in a set D a unique real number
More information8.1 Exponential Growth 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations.
8.1 Exponential Growth Objective 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations. Key Terms Exponential Function Asymptote Exponential Growth Function
More informationModular Arithmetic. Kieran Cooney - February 18, 2016
Modular Arithmetic Kieran Cooney - kieran.cooney@hotmail.com February 18, 2016 Sums and products in modular arithmetic Almost all of elementary number theory follows from one very basic theorem: Theorem.
More informationExcel / Education. GCSE Mathematics. Paper 3B (Calculator) Higher Tier. Time: 2 hours. Turn over
Excel / Education GCSE Mathematics Paper 3B (Calculator) Higher Tier Time: 2 hours 3B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil,
More informationPre-Calculus Unit 3 Standards-Based Worksheet
Pre-Calculus Unit 3 Standards-Based Worksheet District of Columbia Public Schools Mathematics STANDARD PCT.P.9. Derive and apply basic trigonometric identities (e.g., sin 2 θ+cos 2 θ= 1,tan 2 θ + 1 = sec
More informationTrigonometric Identities
Trigonometric Identities Scott N. Walck September 1, 010 1 Prerequisites You should know the cosine and sine of 0, π/6, π/4, π/, and π/. Memorize these if you do not already know them. cos 0 = 1 sin 0
More informationChapter 7 Repetitive Change: Cyclic Functions
Chapter 7 Repetitive Change: Cyclic Functions 7.1 Cycles and Sine Functions Data that is periodic may often be modeled by trigonometric functions. This chapter will help you use Excel to deal with periodic
More informationSupplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section 4 Graphing Inequalities
Supplemental Worksheet Problems To Accompan: The Algebra Tutor Please watch Section 4 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item9.cfm Sample
More informationREVIEW SHEET FOR MIDTERM 2: ADVANCED
REVIEW SHEET FOR MIDTERM : ADVANCED MATH 195, SECTION 59 (VIPUL NAIK) To maximize efficiency, please bring a copy (print or readable electronic) of this review sheet to the review session. The document
More informationES 111 Mathematical Methods in the Earth Sciences Lecture Outline 6 - Tues 17th Oct 2017 Functions of Several Variables and Partial Derivatives
ES 111 Mathematical Methods in the Earth Sciences Lecture Outline 6 - Tues 17th Oct 2017 Functions of Several Variables and Partial Derivatives So far we have dealt with functions of the form y = f(x),
More information2.1 BASIC CONCEPTS Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal.
1 2.1 BASIC CONCEPTS 2.1.1 Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal. 2 Time Scaling. Figure 2.4 Time scaling of a signal. 2.1.2 Classification of Signals
More informationMAC 1114 REVIEW FOR EXAM #2 Chapters 3 & 4
MAC 111 REVIEW FOR EXAM # Chapters & This review is intended to aid you in studying for the exam. This should not be the only thing that you do to prepare. Be sure to also look over your notes, textbook,
More informationSpecial Right Triangles and Right Triangle Trigonometry
Special Right Triangles and Right Triangle Trigonometry Reporting Category Topic Triangles Investigating special right triangles and right triangle trigonometry Primary SOL G.8 The student will solve real-world
More informationLab I - Direction fields and solution curves
Lab I - Direction fields and solution curves Richard S. Laugesen September 1, 2009 We consider differential equations having the form In other words, Example 1. a. b. = y, y = f(x, y), = y2 2x + 5. that
More informationHigh School Supply List
High School Supply List 2018-2019 *Some classes may require additional supplies. See teachers on 1 st day. Bible Classes: Jewish History 1 Pens NIV Bible Dividers (optional) 1 folder Marriage & Family
More informationMATH Week 10. Ferenc Balogh Winter. Concordia University
MATH 20 - Week 0 Ferenc Balogh Concordia University 2008 Winter Based on the textbook J. Stuart, L. Redlin, S. Watson, Precalculus - Mathematics for Calculus, 5th Edition, Thomson All figures and videos
More informationGeneral Functions and Graphs
General Functions and Graphs Section 7 Functions Graphs and Symmetry Functions can be represented both as algebraic expressions and as graphs. So far we have concentrated on algebraic operations related
More informationIdeas beyond Number. Activity worksheets
Ideas beyond Number Activity sheet 1 Task 1 Some students started to solve this equation in different ways: For each statement tick True or False: = = = = Task 2: Counter-examples The exception disproves
More informationGeorgia Standards of Excellence Frameworks. Mathematics. Accelerated GSE Pre-Calculus Unit 4: Trigonometric Identities
Georgia Standards of Excellence Frameworks Mathematics Accelerated GSE Pre-Calculus Unit 4: Trigonometric Identities These materials are for nonprofit educational purposes only. Any other use may constitute
More informationCommon Core Math Tutorial and Practice
Common Core Math Tutorial and Practice TABLE OF CONTENTS Chapter One Number and Numerical Operations Number Sense...4 Ratios, Proportions, and Percents...12 Comparing and Ordering...19 Equivalent Numbers,
More informationMATH 1113 Exam 3 Review. Fall 2017
MATH 1113 Exam 3 Review Fall 2017 Topics Covered Section 4.1: Angles and Their Measure Section 4.2: Trigonometric Functions Defined on the Unit Circle Section 4.3: Right Triangle Geometry Section 4.4:
More informationWhat is a Sine Function Graph? U4 L2 Relate Circle to Sine Activity.pdf
Math 3 Unit 6, Trigonometry L04: Amplitude and Period of Sine and Cosine AND Translations of Sine and Cosine Functions WIMD: What I must do: I will find the amplitude and period from a graph of the sine
More information