K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
Grade: 11
Core Subject Title: Pre-Calculus
Semester: First Semester
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
Analytic
Geometry
CONTENT
STANDARDS
The learners
demonstrate an
understanding
of...
key concepts of
conic sections and
systems of
nonlinear
equations
PERFORMANCE
STANDARDS
LEARNING COMPETENCIES
The learners shall be able
to...
The learners...
1.
model situations
appropriately and solve
problems accurately using
conic sections and systems
of nonlinear equations
CODE
2.
3.
determine the standard form of equation of a circle
STEM_PC11AG-Ia-3
4.
graph a circle in a rectangular coordinate system
STEM_PC11AG-Ia-4
define a parabola
determine the standard form of equation of a parabola
graph a parabola in a rectangular coordinate system
define an ellipse
determine the standard form of equation of an ellipse
graph an ellipse in a rectangular coordinate system
define a hyperbola
determine the standard form of equation of a hyperbola
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STEM_PC11AG-Ib-1
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STEM_PC11AG-Ic-2
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5.
6.
7.
8.
9.
10.
11.
12.
K to 12 Senior High School STEM Specialized Subject Pre-Calculus May 2016
STEM_PC11AG-Ia-1
illustrate the different types of conic sections: parabola, ellipse,
circle, hyperbola, and degenerate cases.***
define a circle.
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K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
CONTENT
CONTENT
STANDARDS
PERFORMANCE
STANDARDS
LEARNING COMPETENCIES
13.
graph a hyperbola in a rectangular coordinate system
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14.
recognize the equation and important characteristics of the
different types of conic sections
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15.
solves situational problems involving conic sections
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16.
illustrate systems of nonlinear equations
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17.
determine the solutions of systems of nonlinear equations using
techniques such as substitution, elimination, and graphing***
solve situational problems involving systems
of nonlinear equations
18.
Series and
Mathematical
Induction
key concepts of
series and
mathematical
induction and the
Binomial
Theorem.
CODE
keenly observe and
investigate patterns, and
formulate appropriate
mathematical statements
and prove them using
mathematical induction
and/or Binomial Theorem.
1.
illustrate a series
2.
3.
4.
5.
6.
differentiate a series from a sequence
use the sigma notation to represent a series
illustrate the Principle of Mathematical Induction
apply mathematical induction in proving identities
illustrate Pascals Triangle in the expansion of
for small
positive integral values of
prove the Binomial Theorem
determine any term of
, where is a positive integer,
without expanding
solve problems using mathematical induction and the Binomial
Theorem
7.
8.
9.
K to 12 Senior High School STEM Specialized Subject Pre-Calculus May 2016
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STEM_PC11SMI-Ih-4
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STEM_PC11SMI-Ii-2
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K to 12 BASIC EDUCATION CURRICULUM
SENIOR HIGH SCHOOL SCIENCE, TECHNOLOGY, ENGINEERING AND MATHEMATICS (STEM) SPECIALIZED SUBJECT
CONTENT
Trigonometry
CONTENT
STANDARDS
key concepts of
circular functions,
trigonometric
identities, inverse
trigonometric
functions, and
the polar
coordinate
system
PERFORMANCE
STANDARDS
1. formulate and solve
accurately situational
problems involving
circular functions
2. apply appropriate
trigonometric identities in
solving situational
problems
3. formulate and solve
accurately situational
problems involving
appropriate trigonometric
functions
4. formulate and solve
accurately situational
problems involving the
polar coordinate system
LEARNING COMPETENCIES
1.
CODE
2.
illustrate the unit circle and the relationship between the linear
and angular measures of a central angle in a unit circle
convert degree measure to radian measure and vice versa
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3.
illustrate angles in standard position and coterminal angles
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4.
illustrate the different circular functions
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5.
6.
7.
uses reference angles to find exact values of circular functions
determine the domain and range of the different circular functions
graph the six circular functions (a) amplitude, (b) period, and (c)
phase shift
solve problems involving circular functions
determine whether an equation is an identity or a conditional
equation
derive the fundamental trigonometric identities
derive trigonometric identities involving sum and difference of
angles
derive the double and half-angle formulas
simplify trigonometric expressions
prove other trigonometric identities
solve situational problems involving trigonometric identities
illustrate the domain and range of the inverse trigonometric
functions.
evaluate an inverse trigonometric expression.
solve trigonometric equations.
solve situational problems involving inverse trigonometric
functions and trigonometric equations
locate points in polar coordinate system
convert the coordinates of a point from rectangular to polar
systems and vice versa
solve situational problems involving polar coordinate system
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8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
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***Suggestion for ICT-enhanced lesson when available and where appropriate
K to 12 Senior High School STEM Specialized Subject Pre-Calculus May 2016
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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
DOMAIN/ COMPONENT
SAMPLE
Learning Area and
Strand/ Subject or
Specialization
Science, Technology,
Engineering and Mathematics
Pre-Calculus
Grade Level
Grade 11
Domain/Content/
Component/ Topic
Analytic Geometry
CODE
Analytic Geometry
AG
Series and Mathematical Induction
SMI
First Entry
Uppercase
Letter/s
STEM_PC11AG
Trigonometry
Roman Numeral
*Zero if no specific
quarter
Quarter
First Quarter
Week
Week one
Lowercase
Letter/s
*Put a hyphen (-) in
between letters to
indicate more than a
specific week
Arabic Number
Competency
illustrate the different types
of conic sections: parabola,
ellipse, circle, hyperbola,
and degenerate cases
K to 12 Senior High School STEM Specialized Subject Pre-Calculus May 2016
1
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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
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