K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
Grade: 11 Semester: First Semester
Core Subject Title: Pre-Calculus No. of Hours/ Semester: 80 hours/ semester
Pre-requisite (if needed):
Subject Description: At the end of the course, the students must be able to apply concepts and solve problems involving conic sections, systems of nonlinear equations,
series and mathematical induction, circular and trigonometric functions, trigonometric identities, and polar coordinate system.
CONTENT PERFORMANCE
CONTENT LEARNING COMPETENCIES CODE
STANDARDS STANDARDS
Analytic The learners The learners shall be able The learners...
Geometry demonstrate an to...
understanding STEM_PC11AG-Ia-1
1. illustrate the different types of conic sections: parabola, ellipse,
of...
circle, hyperbola, and degenerate cases.***
model situations 2. define a circle. STEM_PC11AG-Ia-2
appropriately and solve 3. determine the standard form of equation of a circle STEM_PC11AG-Ia-3
key concepts of problems accurately using
conic sections and conic sections and systems 4. graph a circle in a rectangular coordinate system STEM_PC11AG-Ia-4
systems of of nonlinear equations 5. define a parabola STEM_PC11AG-Ia-5
nonlinear 6. determine the standard form of equation of a parabola STEM_PC11AG-Ib-1
equations 7. graph a parabola in a rectangular coordinate system STEM_PC11AG-Ib-2
8. define an ellipse STEM_PC11AG-Ic-1
9. determine the standard form of equation of an ellipse STEM_PC11AG-Ic-2
10. graph an ellipse in a rectangular coordinate system STEM_PC11AG-Ic-3
11. define a hyperbola STEM_PC11AG-Id-1
12. determine the standard form of equation of a hyperbola STEM_PC11AG-Id-2
K to 12 Senior High School STEM Specialized Subject – Pre-Calculus May 2016 Page 1 of 5
K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
CONTENT PERFORMANCE
CONTENT LEARNING COMPETENCIES CODE
STANDARDS STANDARDS
13. graph a hyperbola in a rectangular coordinate system STEM_PC11AG-Id-3
14. recognize the equation and important characteristics of the
STEM_PC11AG-Ie-1
different types of conic sections
15. solves situational problems involving conic sections STEM_PC11AG-Ie-2
16. illustrate systems of nonlinear equations STEM_PC11AG-If-1
17. determine the solutions of systems of nonlinear equations using
STEM_PC11AG-If-g-1
techniques such as substitution, elimination, and graphing***
18. solve situational problems involving systems
STEM_PC11AG-Ig-2
of nonlinear equations
Series and key concepts of keenly observe and STEM_PC11SMI-Ih-1
1. illustrate a series
Mathematical series and investigate patterns, and
Induction mathematical formulate appropriate 2. differentiate a series from a sequence STEM_PC11SMI-Ih-2
induction and the mathematical statements 3. use the sigma notation to represent a series STEM_PC11SMI-Ih-3
Binomial and prove them using 4. illustrate the Principle of Mathematical Induction STEM_PC11SMI-Ih-4
Theorem. mathematical induction 5. apply mathematical induction in proving identities STEM_PC11SMI-Ih-i-1
and/or Binomial Theorem. 6. illustrate Pascal’s Triangle in the expansion of for small
STEM_PC11SMI-Ii-2
positive integral values of
7. prove the Binomial Theorem STEM_PC11SMI-Ii-3
8. determine any term of , where is a positive integer,
STEM_PC11SMI-Ij-1
without expanding
9. solve problems using mathematical induction and the Binomial
STEM_PC11SMI-Ij-2
Theorem
K to 12 Senior High School STEM Specialized Subject – Pre-Calculus May 2016 Page 2 of 5
K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
CONTENT PERFORMANCE
CONTENT LEARNING COMPETENCIES CODE
STANDARDS STANDARDS
Trigonometry key concepts of 1. formulate and solve 1. illustrate the unit circle and the relationship between the linear
circular functions, accurately situational and angular measures of a central angle in a unit circle STEM_PC11T-IIa-1
trigonometric problems involving 2. convert degree measure to radian measure and vice versa STEM_PC11T-IIa-2
identities, inverse circular functions
3. illustrate angles in standard position and coterminal angles STEM_PC11T-IIa-3
trigonometric
functions, and 4. illustrate the different circular functions STEM_PC11T-IIb-1
the polar
coordinate 5. uses reference angles to find exact values of circular functions STEM_PC11T-IIb-2
system 6. determine the domain and range of the different circular functions STEM_PC11T-IIc-1
7. graph the six circular functions (a) amplitude, (b) period, and (c)
STEM_PC11T-IIc-d-1
phase shift
8. solve problems involving circular functions STEM_PC11T-IId-2
2. apply appropriate 9. determine whether an equation is an identity or a conditional
trigonometric identities in STEM_PC11T-IIe-1
equation
solving situational 10. derive the fundamental trigonometric identities STEM_PC11T-IIe-2
problems 11. derive trigonometric identities involving sum and difference of
STEM_PC11T-IIe-3
angles
12. derive the double and half-angle formulas STEM_PC11T-IIf-1
13. simplify trigonometric expressions STEM_PC11T-IIf-2
14. prove other trigonometric identities STEM_PC11T-IIf-g-1
15. solve situational problems involving trigonometric identities STEM_PC11T-IIg-2
3. formulate and solve 16. illustrate the domain and range of the inverse trigonometric
STEM_PC11T-IIh-1
accurately situational functions.
problems involving 17. evaluate an inverse trigonometric expression. STEM_PC11T-IIh-2
appropriate trigonometric 18. solve trigonometric equations. STEM_PC11T-IIh-i-1
functions 19. solve situational problems involving inverse trigonometric
STEM_PC11T-IIi-2
functions and trigonometric equations
4. formulate and solve 20. locate points in polar coordinate system STEM_PC11T-IIj-1
accurately situational 21. convert the coordinates of a point from rectangular to polar
STEM_PC11T-IIj-2
problems involving the systems and vice versa
polar coordinate system 22. solve situational problems involving polar coordinate system STEM_PC11T-IIj-3
***Suggestion for ICT-enhanced lesson when available and where appropriate
K to 12 Senior High School STEM Specialized Subject – Pre-Calculus May 2016 Page 3 of 5
K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
Code Book Legend
Sample: STEM_PC11AG-Ia-1
LEGEND SAMPLE DOMAIN/ COMPONENT CODE
Learning Area and Science, Technology,
Strand/ Subject or Engineering and Mathematics Analytic Geometry AG
Specialization Pre-Calculus
First Entry
STEM_PC11AG Series and Mathematical Induction SMI
Grade Level Grade 11
Uppercase Domain/Content/ Trigonometry T
Analytic Geometry
Letter/s Component/ Topic
-
Roman Numeral
*Zero if no specific Quarter First Quarter I
quarter
Lowercase
Letter/s
*Put a hyphen (-) in
between letters to
Week Week one a
indicate more than a
specific week
-
illustrate the different types
of conic sections: parabola,
Arabic Number Competency
ellipse, circle, hyperbola,
1
and degenerate cases
K to 12 Senior High School STEM Specialized Subject – Pre-Calculus May 2016 Page 4 of 5
K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL – SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
References:
Aufmann, Richard N., Barker, Vernon C. and Nation, Richard D. College Trigonometry. Boston: Houghton Mifflin Company, 2008.
Cabral, Emmanuel A., De Las Penas, Ma. Louise Antonnet .N., De Lara-Tuprio, Elvira P., Francisco, Flordeliza F., Garces, Ian June L., Marcelo, Reginald M. and Sarmiento,
Jumela F., Precalculus. Q.C.: Ateneo de Manila University Press, 2010.
Larson, Ron. Precalculus with Limits. Kentucky: Brooks/Cole, Cengage Learning, 2014.
Leithold, Louis, College Algebra and Trigonometry. Singapore: Pearson Education Asia Pte. Ltd., 2002.
Margaret L., Hornsby, John and Schneider, David I. College Algebra and Trigonometry and Precalculus. Boston: Addison-Wesley Educational Publisher, Inc., 2001.
Stewart, James, Redlin, Lothar, and Watson, Saleem, Precalculus: Mathematics for Calculus. Boston: Brooks/Cole, Cengage Learning, 2012.
Sullivan,Michael, Algebra & Trigonometry. Singapore: Pearson Education, Inc., 2012.
Young, Cynthia, Algebra and Trigonometry. New Jersey: John Wiley & Sons, Inc., 2013.
K to 12 Senior High School STEM Specialized Subject – Pre-Calculus May 2016 Page 5 of 5
