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SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
Grade: 11 Semester: Second Semester Core Subject Title: Basic Calculus No. of Hours/ Semester: 80 hours/ semester Prerequisite (if needed): Pre-Calculus
Subject Description: At the end of the course, the students must know how to determine the limit of a function, differentiate, and integrate algebraic, exponential, logarithmic, and trigonometric functions in one variable, and to formulate and solve problems involving continuity, extreme values, related rates, population models, and areas of plane regions.
CONTENT
CONTENT STANDARDS
PERFORMANCE
STANDARDS
LEARNING COMPETENCIES CODE
Limits and Continuity
The learners demonstrate an understanding of...
the basic concepts of limit and continuity of a function
The learners shall be able to...
formulate and solve accurately real-life problems involving continuity of functions
The learners…
- illustrate the limit of a function using a table of values and the graph of the function
STEM_BC11LC-IIIa- 1
- distinguish between and STEM_BC11LC-IIIa- 2
- illustrate the limit laws STEM_BC11LC-IIIa- 3
- apply the limit laws in evaluating the limit of algebraic functions (polynomial, rational, and radical)
STEM_BC11LC-IIIa- 4
- compute the limits of exponential, logarithmic, and trigonometric functions using tables of values and graphs of the functions
STEM_BC11LC-IIIb- 1
- evaluate limits involving the expressions ,
and using tables of values
STEM_BC11LC-IIIb- 2
- illustrate continuity of a function at a number STEM_BC11LC-IIIc- 1
- determine whether a function is continuous at a number or not STEM_BC11LC-IIIc- 2
- illustrate continuity of a function on an interval STEM_BC11LC-IIIc- 3
- determine whether a function is continuous on an interval or not. STEM_BC11LC-IIIc- 4
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
CONTENT CONTENT STANDARDS
PERFORMANCE
STANDARDS
LEARNING COMPETENCIES CODE
- illustrate different types of discontinuity (hole/removable, jump/essential, asymptotic/infinite)
STEM_BC11LC-IIId- 1
- illustrate the Intermediate Value and Extreme Value Theorems STEM_BC11LC-IIId- 2
- solves problems involving continuity of a function STEM_BC11LC-IIId- 3
Derivatives basic concepts of derivatives
- formulate and solve accurately situational problems involving extreme values 1. illustrate the tangent line to the graph of a function at a given point
STEM_BC11D-IIIe- 1
- applies the definition of the derivative of a function at a given number STEM_BC11D-IIIe- 2
- relate the derivative of a function to the slope of the tangent line STEM_BC11D-IIIe- 3
- determine the relationship between differentiability and continuity of a function STEM_BC11D - IIIf- 1
- derive the differentiation rules STEM_BC11D-IIIf- 2
- apply the differentiation rules in computing the derivative of an algebraic, exponential, and trigonometric functions
STEM_BC11D-IIIf- 3
- solve optimization problems STEM_BC11D-IIIg- 1
- formulate and solve accurately situational problems involving related rates
- compute higher-order derivatives of functions STEM_BC11D-IIIh- 1
- illustrate the Chain Rule of differentiation STEM_BC11D-IIIh- 2
- solve problems using the Chain Rule STEM_BC11D-IIIh-i- 1
- illustrate implicit differentiation STEM_BC11D-IIIi- 2
- solve problems (including logarithmic, and inverse trigonometric functions) using implicit differentiation
STEM_BC11D-IIIi-j- 1
- solve situational problems involving related rates STEM_BC11D-IIIj- 2
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
Code Book Legend
Sample: STEM_BC11LC-IIIa-
DOMAIN/ COMPONENT CODE
Limits and Continuity LC
Derivatives D
Integration I
LEGEND SAMPLE
First Entry
Learning Area and Strand/ Subject or Specialization
Science, Technology, Engineering and Mathematics Calculus
Grade Level Grade 11^ STEM_BC11LC
Uppercase Letter/s
Domain/Content/ Component/ Topic Limits and Continuity
Roman Numeral *Zero if no specific quarter
Quarter Third Quarter III
Lowercase Letter/s *Put a hyphen (-) in between letters to indicate more than a specific week
Week Week one a
Arabic Number Competency
illustrate the limit of a function using a table of values and the graph of the function
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
References:
Anton, Howard, Bivens, Irl, Davis, Stephen.Calculus: Early Transcendentals. New Jersey: John Wiley and Sons, , 2002.
Barnett, Raymond, Ziegler, Michael, Byleen, Karl.Calculus for Business, Economics, Life Sciences and Social Sciences. Singapore: Pearson Education (Asia), 2003.
Leithold, Louis.College Algebra and Trigonometry. Boston: Addison Wesley Longman Inc., 1989, reprinted-Pearson Education Asia Pte. Ltd, 2002.
Leithold, Louis.The Calculus 7. New York: Harpercollins College Div., 7th edition, 1995.
Math 53 Module Committee,Math 53 Elementary Analysis I Course Module. Q.C.: Institute of Mathematics, UP Diliman, 2012.
Stewart, James.The Calculus: Early Transcendentals. California: Brooks/Cole, 6th Edition, 2008.
Tan, Soo T.,Applied Calculus for the Managerial, Life and Social Sciences. California: Brooks/Cole, Cengage Learning, 9th Edition, 2014.
