STEM Pre-Calculus CG

VII. Course Content

CONTENT Analytic Geometry

CONTENT STANDARDS The The lea learn rner ers s demo demons nstr trat ate e an an understanding of...

ey ey conc concept epts s o o conic sections and systems o nonlinear equations

PERFORMANCE LEARNING COMPETENCIES STANDARDS The The lea learn rner ers s sh shall all be be abl able e The lear learne ners rs.. .... to.. to.... illustrate the diferent types o conic sections: parabola, 1. ellipse, circle, hyperbola, and degenerate degenerate cases.*** model situations 2. dene a circle. appropriately and solve 3. determine determine the standar standard d orm o equation equation o a circle circle probl problems ems accura accuratel tely y usin using g conic sections and systems !. graph a circle circle in a rectangu rectangular lar coordinat coordinate e system o nonlinear equations ". dene a parabola #. determine determine the standar standard d orm o equation equation o a parabola parabola $. graph a parabola parabola in a rectan rectangular gular coordin coordinate ate system system %. den dene e an ell ellip ipse se &. determine determine the standar standard d orm o equation equation o an ellipse ellipse 1'. graph an ellipse ellipse in a rectan rectangular gular coordina coordinate te system 11. dene dene a hyperb hyperbola ola 12. determine determine the standar standard d orm o equation equation o a hyperbol hyperbola a

K to 12 Senior High School STEM Specialized Subject – re!"alculus Ma# 2$1%

CODE

STEM_PC11AG-Ia-1 STEM_PC11AG-Ia-2 STEM_PC11AG-Ia- STEM_PC11AG-Ia-! STEM_PC11AG-Ia-" STEM_PC11AG-I#-1 STEM_PC11AG-I#-2 STEM_PC11AG-Ic-1 STEM_PC11AG-Ic-2 STEM_PC11AG-Ic- STEM_PC11AG-I$-1 STEM_PC11AG-I$-2

% to 12 &ASIC ED'CATION C'RRIC'L'M SENIOR (IG( SC(OOL ) SCIENCE* TEC(NOLOG+* ENGINEERING AND MAT(EMATICS ,STEM SPECIALI.ED S'&/ECT

CONTENT

CONTENT STANDARDS

PERFORMANCE STANDARDS

LEARNING COMPETENCIES

graph a hyperbola in a rectangular coordinate 13. system

STEM_PC11AG-I$-

recogni(e the equation and important characteristics o 1!. the diferent types o conic sections solves situational problems involving conic 1". sections illustrate systems o nonlinear 1#. equations

ey concepts o Serie an$ Mat3ematica series and l

eenly observe and

In$4ction

mathematical induction and the

ormulate appropriate

)inomial

and prove them using

-heorem.

CODE

STEM_PC11AG-Ie-1

STEM_PC11AG-Ie-2 STEM_PC11AG-I0-1

determine the solutions o systems o nonlinear equations 1$. using techniques such as substitution, elimination, and graphing*** 1%. solve situational problems involving systems o nonlinear equations 1. illustrate a series

STEM_PC11AG-I0--1

STEM_PC11AG-I-2 STEM_PC11SMI-I3-1

investigate patterns, and

mathematical statements

mathematical induction andor )inomial -heorem.

diferentiate a series rom a 2. sequence

3. use the sigma notation to represent a series illustrate the rinciple o +athematical !. nduction apply mathematical induction in ". proving identities

STEM_PC11SMI-I3-2

STEM_PC11SMI-I3- STEM_PC11SMI-I3-!

#. illustrate ascal/s -riangle in the e0pansion o or small positive integral values o prove the )inomial $. -heorem , %. determine any term o here is a positive integer, ithout e0panding

STEM_PC11SMI-I3-i-1 STEM_PC11SMI-Ii-2 STEM_PC11SMI-Ii- STEM_PC11SMI-I5-1

solve problems using mathematical induction and the &. )inomial -heorem


STEM_PC11SMI-I5-2


CONTENT Trionometry

CONTENT STANDARDS ey concepts o circular unctions, trigonometric identities, inverse trigonometric unctions, and the polar

PERFORMANCE STANDARDS 1. ormulate and solve accurately situational problems involving circular unctions

LEARNING COMPETENCIES 1.

CODE

illustrate the unit circle and the relationship beteen the linear

and angular measures o a central angle in a unit circle 2. convert degree measure to radian measure and vice versa

STEM_PC11T-IIa-1 STEM_PC11T-IIa-2

3. illustrate angles in standard position and coterminal angles STEM_PC11T-IIa- !. illustrate the diferent circular unctions

coordinate

".

system

#. $. %.

uses reerence angles to nd e0act values o circular unctions determine the domain and range o the diferent circular unctions graph the si0 circular unctions a amplitude, b period, and c phase shit solve problems involving circular unctions determine hether an equation is an identity or a conditional

2. apply appropriate &. trigonometric identities in equation solving situational 1'. derive the undamental trigonometric identities problems derive trigonometric identities involving sum and 11. diference o angles 12. derive the double and hal4angle ormulas 13. simpliy trigonometric e0pressions 1!. prove other trigonometric identities solve situational problems involving trigonometric 1". identities illustrate the domain and range o the inverse 3. ormulate and solve 1#. trigonometric accurately situational unctions. problems involving 1$. evaluate an inverse trigonometric e0pression. appropriate trigonometric 1%. solve trigonometric equations. unctions 1&. solve situational problems involving inverse trigonometric unctions and trigonometric equations

STEM_PC11T-II#-1 STEM_PC11T-II#-2 STEM_PC11T-IIc-1 STEM_PC11T-IIc-$-1 STEM_PC11T-II$-2 STEM_PC11T-IIe-1 STEM_PC11T-IIe-2 STEM_PC11T-IIe- STEM_PC11T-II0-1 STEM_PC11T-II0-2 STEM_PC11T-II0--1 STEM_PC11T-II-2 STEM_PC11T-II3-1 STEM_PC11T-II3-2 STEM_PC11T-II3-i-1 STEM_PC11T-IIi-2

2'. locate points in polar coordinate system convert the coordinates o a point rom rectangular to accurately situational 21. polar problems involving the systems and vice versa solve situational problems involving polar coordinate polar coordinate system 22. system

!. ormulate and solve

***5uggestion or 6-4enhanced lesson hen available and here appropriate


STEM_PC11T-II5-1 STEM_PC11T-II5-2 STEM_PC11T-II5-


Co$e &oo6 Leen$ Sam7le8 STEM_PC11AG-Ia-1

Ara#ic N4m#er SAMPL E

LEGEND 7earning 8rea and 5trand. 5ub9ect or 5peciali(ation

5cience, -echnology, :ngineering and +athematics *re46alculus

;rade 7evel

;rade 11

8nalytic ;eometry

Firt Entry

'77ercae Letter9

STEM_PC11AG

Roman N4meral &'ero if no speci(c )uarter Lo:ercae Letter9 &ut a h#phen *!+ in bet,een letters to indicate more than a speci(c ,ee-

=uarter

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a

illustrate the diferent types

6ompetency

o conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases

5eries and +athematical nduction

DOMAIN9 COMPONENT

CODE -rigonometry

8nalytic ;eometry

5+

8;


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Re0erence8 8umann, @ichard A., )arer, Bernon 6. and Aation, @ichard <. "ollege Trigonometr#. )oston: Coughton +iDin 6ompany, 2''%. 6abral, mmanuel 8., rancisco, >lordeli(a >., ;arces, an Eune 7., +arcelo, @eginald +. and 5armiento, Eumela >., recalculus. =.6.: 8teneo de +anila Fniversity ress, 2'1'. 7arson, @on. recalculus ,ith imits. Gentucy: )roos6ole, 6engage 7earning, 2'1!. 7eithold/ 7ouis, "ollege 0lgebra and Trigonometr# . 5ingapore: earson ducation 8sia te. 7td., 2''2. +argaret 7., Cornsby, Eohn and 5chneider,

STEM Pre-Calculus CG

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