Teaching Guide For Senior High School Basic Calculus-Books Pdf

TEACHING GUIDE FOR SENIOR HIGH SCHOOL Basic Calculus
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Published by the Commission on Higher Education 2016. Chairperson Patricia B Licuanan Ph D, Commission on Higher Education. K to 12 Transition Program Management Unit, Office Address 4th Floor Commission on Higher Education. C P Garcia Ave Diliman Quezon City, Telefax 02 441 1143 E mail Address k12 ched gov ph. DEVELOPMENT TEAM, Team Leader Jose Maria P Balmaceda Ph D. Carlene Perpetua P Arceo Ph D, Richard S Lemence Ph D.
Oreste M Ortega Jr M Sc This Teaching Guide by the. Louie John D Vallejo Ph D Commission on Higher Education. is licensed under a Creative, Technical Editors, Commons Attribution. Jose Ernie C Lope Ph D, NonCommercial ShareAlike, Marian P Roque Ph D 4 0 International License This. Copy Reader Roderick B Lirios means you are free to. Cover Artists Paolo Kurtis N Tan Renan U Ortiz Share copy and redistribute. the material in any medium or, CONSULTANTS format, THIS PROJECT WAS DEVELOPED WITH THE PHILIPPINE NORMAL UNIVERSITY Adapt remix transform and. University President Ester B Ogena Ph D build upon the material. VP for Academics Ma Antoinette C Montealegre Ph D The licensor CHED cannot. VP for University Relations Advancement Rosemarievic V Diaz Ph D revoke these freedoms as long as. Ma Cynthia Rose B Bautista Ph D CHED you follow the license terms. Bienvenido F Nebres S J Ph D Ateneo de Manila University However under the following. Carmela C Oracion Ph D Ateneo de Manila University. Minella C Alarcon Ph D CHED Attribution You must give. Gareth Price Sheffield Hallam University appropriate credit provide a link. Stuart Bevins Ph D Sheffield Hallam University to the license and indicate if. changes were made You may do, SENIOR HIGH SCHOOL SUPPORT TEAM so in any reasonable manner but. CHED K TO 12 TRANSITION PROGRAM MANAGEMENT UNIT not in any way that suggests the. Program Director Karol Mark R Yee licensor endorses you or your use. Lead for Senior High School Support Gerson M Abesamis NonCommercial You may. not use the material for, Lead for Policy Advocacy and Communications Averill M Pizarro commercial purposes.
Course Development Officers ShareAlike If you remix. Danie Son D Gonzalvo John Carlo P Fernando transform or build upon the. material you must distribute, Teacher Training Officers. your contributions under the, Ma Theresa C Carlos Mylene E Dones same license as the original. Monitoring and Evaluation Officer Robert Adrian N Daulat Printed in the Philippines by EC TEC. Commercial No 32 St Louis, Administrative Officers Ma Leana Paula B Bato Compound 7 Baesa Quezon City. Kevin Ross D Nera Allison A Danao Ayhen Loisse B Dalena ectec com yahoo com. Introduction iv, DepEd Basic Calculus Curriculum Guide vii. 1 Limits and Continuity 1, Lesson 1 The Limit of a Function Theorems and Examples 2.
Topic 1 1 The Limit of a Function 3, Topic 1 2 The Limit of a Function at c versus the Value of a Function at c 17. Topic 1 3 Illustration of Limit Theorems 22, Topic 1 4 Limits of Polynomial Rational and Radical Functions 28. Lesson 2 Limits of Some Transcendental Functions and Some Indeterminate Forms 38. Topic 2 1 Limits of Exponential Logarithmic and Trigonometric Functions 39. Topic 2 2 Some Special Limits 46, Lesson 3 Continuity of Functions 52. Topic 3 1 Continuity at a Point 53, Topic 3 2 Continuity on an Interval 58. Lesson 4 More on Continuity 64, Topic 4 1 Different Types of Discontinuities 65.
Topic 4 2 The Intermediate Value and the Extreme Value Theorems 75. Topic 4 3 Problems Involving Continuity 85, 2 Derivatives 89. Lesson 5 The Derivative as the Slope of the Tangent Line 90. Topic 5 1 The Tangent Line to the Graph of a Function at a Point 91. Topic 5 2 The Equation of the Tangent Line 100, Topic 5 3 The Definition of the Derivative 107. Lesson 6 Rules of Differentiation 119, Topic 6 1 Differentiability Implies Continuity 120. Topic 6 2 The Differentiation Rules and Examples Involving Algebraic. Exponential and Trigonometric Functions 126, Lesson 7 Optimization 141. Topic 7 1 Optimization using Calculus 142, Lesson 8 Higher Order Derivatives and the Chain Rule 156.
Topic 8 1 Higher Order Derivatives of Functions 157. Topic 8 2 The Chain Rule 162, Lesson 9 Implicit Differentiation 168. Topic 9 1 What is Implicit Differentiation 169, Lesson 10 Related Rates 180. Topic 10 1 Solutions to Problems Involving Related Rates 181. 3 Integration 191, Lesson 11 Integration 192, Topic 11 1 Illustration of an Antiderivative of a Function 193. Topic 11 2 Antiderivatives of Algebraic Functions 196. Topic 11 3 Antiderivatives of Functions Yielding Exponential Functions and. Logarithmic Functions 199, Topic 11 4 Antiderivatives of Trigonometric Functions 202. Lesson 12 Techniques of Antidifferentiation 204, Topic 12 1 Antidifferentiation by Substitution and by Table of Integrals 205.
Lesson 13 Application of Antidifferentiation to Differential Equations 217. Topic 13 1 Separable Differential Equations 218, Lesson 14 Application of Differential Equations in Life Sciences 224. Topic 14 1 Situational Problems Involving Growth and Decay Problems 225. Lesson 15 Riemann Sums and the Definite Integral 237. Topic 15 1 Approximation of Area using Riemann Sums 238. Topic 15 2 The Formal Definition of the Definite Integral 253. Lesson 16 The Fundamental Theorem of Calculus 268, Topic 16 1 Illustration of the Fundamental Theorem of Calculus 269. Topic 16 2 Computation of Definite Integrals using the Fundamental Theorem. of Calculus 273, Lesson 17 Integration Technique The Substitution Rule for Definite Integrals 280. Topic 17 1 Illustration of the Substitution Rule for Definite Integrals 281. Lesson 18 Application of Definite Integrals in the Computation of Plane Areas 292. Topic 18 1 Areas of Plane Regions Using Definite Integrals 293. Topic 18 2 Application of Definite Integrals Word Problems 304. Biographical Notes 309, Introduction, As the Commission supports DepEd s implementation of Senior High School SHS it upholds the vision. and mission of the K to 12 program stated in Section 2 of Republic Act 10533 or the Enhanced Basic. Education Act of 2013 that every graduate of basic education be an empowered individual through a. program rooted on the competence to engage in work and be productive the ability to coexist in fruitful. harmony with local and global communities the capability to engage in creative and critical thinking. and the capacity and willingness to transform others and oneself. To accomplish this the Commission partnered with the Philippine Normal University PNU the. National Center for Teacher Education to develop Teaching Guides for Courses of SHS Together with. PNU this Teaching Guide was studied and reviewed by education and pedagogy experts and was. enhanced with appropriate methodologies and strategies. Furthermore the Commission believes that teachers are the most important partners in attaining this. goal Incorporated in this Teaching Guide is a framework that will guide them in creating lessons and. assessment tools support them in facilitating activities and questions and assist them towards deeper. content areas and competencies Thus the introduction of the SHS for SHS Framework. The SHS for SHS Framework, The SHS for SHS Framework which stands for Saysay Husay Sarili for Senior High School is at the.
core of this book The lessons which combine high quality content with flexible elements to. accommodate diversity of teachers and environments promote these three fundamental concepts. SAYSAY MEANING HUSAY MASTERY SARILI OWNERSHIP, Why is this important How will I deeply understand this What can I do with this. Through this Teaching Guide Given that developing mastery When teachers empower. teachers will be able to goes beyond memorization learners to take ownership of. facilitate an understanding of teachers should also aim for deep their learning they develop. the value of the lessons for understanding of the subject independence and self. each learner to fully engage in matter where they lead learners direction learning about both. the content on both the to analyze and synthesize the subject matter and. cognitive and affective levels knowledge themselves. The Parts of the Teaching Guide Pedagogical Notes, This Teaching Guide is mapped and aligned to the The teacher should strive to keep a good balance. DepEd SHS Curriculum designed to be highly between conceptual understanding and facility in. usable for teachers It contains classroom activities skills and techniques Teachers are advised to be. and pedagogical notes and integrated with conscious of the content and performance. standards and of the suggested time frame for, innovative pedagogies All of these elements are. each lesson but flexibility in the management of, presented in the following parts. the lessons is possible Interruptions in the class. 1 INTRODUCTION schedule or students poor reception or difficulty. Highlight key concepts and identify the with a particular lesson may require a teacher to. essential questions extend a particular presentation or discussion. Show the big picture Computations in some topics may be facilitated by. Connect and or review prerequisite the use of calculators This is encour aged. knowledge however it is important that the student. understands the concepts and processes involved, Clearly communicate learning.
competencies and objectives in the calculation Exams for the Basic Calculus. course may be designed so that calculators are not. Motivate through applications and, connections to real life. Because senior high school is a transition period, 2 INSTRUCTION DELIVERY for students the latter must also be prepared for. Give a demonstration lecture simulation college level academic rigor Some topics in. hands on activity calculus require much more rigor and precision. Show step by step solutions to sample than topics encountered in previous mathematics. problems courses and treatment of the material may be. Use multimedia and other creative tools different from teaching more elementary courses. Give applications of the theory The teacher is urged to be patient and careful in. presenting and developing the topics To avoid too, Connect to a real life problem if applicable. much technical discussion some ideas can be, 3 PRACTICE introduced intuitively and informally without. Discuss worked out examples sacrificing rigor and correctness. Provide easy medium hard questions The teacher is encouraged to study the guide very. Give time for hands on unguided classroom well work through the examples and solve. work and discovery exercises well in advance of the lesson The. development of calculus is one of humankind s, Use formative assessment to give feedback.
greatest achievements With patience motivation, 4 ENRICHMENT and discipline teaching and learning calculus. Provide additional examples and effectively can be realized by anyone The teaching. applications guide aims to be a valuable resource in this. Introduce extensions or generalisations of objective. Engage in reflection questions, Encourage analysis through higher order. thinking prompts, 5 EVALUATION, Supply a diverse question bank for written. work and exercises, Provide alternative formats for student. work written homework journal portfolio, group individual projects student directed.
research project, On DepEd Functional Skills and CHED s College Readiness Standards. As Higher Education Institutions HEIs welcome the graduates of the Senior High School program it is. of paramount importance to align Functional Skills set by DepEd with the College Readiness Standards. stated by CHED, The DepEd articulated a set of 21st century skills that should be embedded in the SHS curriculum across. various subjects and tracks These skills are desired outcomes that K to 12 graduates should possess in. order to proceed to either higher education employment entrepreneurship or middle level skills. development, On the other hand the Commission declared the College Readiness Standards that consist of the. combination of knowledge skills and reflective thinking necessary to participate and succeed without. remediation in entry level undergraduate courses in college. The alignment of both standards shown below is also presented in this Teaching Guide prepares. Senior High School graduates to the revised college curriculum which will initially be implemented by. AY 2018 2019, College Readiness Standards Foundational Skills DepEd Functional Skills. Produce all forms of texts written oral visual digital based on. 1 Solid grounding on Philippine experience and culture. 2 An understanding of the self community and nation Visual and information literacies. Media literacy, 3 Application of critical and creative thinking and doing processes.
Critical thinking and problem solving skills, 4 Competency in formulating ideas arguments logically scientifically. Creativity, and creatively and Initiative and self direction. 5 Clear appreciation of one s responsibility as a citizen of a multicultural. Philippines and a diverse world, Global awareness, Scientific and economic literacy. Systematically apply knowledge understanding theory and skills Curiosity. for the development of the self local and global communities using Critical thinking and problem solving skills. prior learning inquiry and experimentation Risk taking. TEACHING GUIDE FOR SENIOR HIGH SCHOOL Basic Calculus CORE SUBJECT This Teaching Guide was collaboratively developed and reviewed by educators from public and private schools colleges and universities We encourage teachers and other education stakeholders to email their feedback comments and recommendations to the Commission on Higher Education K to 12 Transition Program Management Unit

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