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PRECALCULUS
PRECALCULUS
DAILY
DAILY
LESSON LOG
LESSON LOG
School
School
CALAYOG CI!Y NA!IONAL "IG"
CALAYOG CI!Y NA!IONAL "IG"
SC"OOL #
SC"OOL #
SENIOR "IG" SC"OOL DEPAR!$EN!
SENIOR "IG" SC"OOL DEPAR!$EN!
G%&
G%&de
de le'
le'el
el GRA
GRADE
DE 11 (
11 ( S!E
S!E$ A
$ A
!
!e&che%
e&che% ENGR
ENGR. CES
. CESAR $.
AR $. DEL R
DEL ROSAR
OSARIO )
IO )R.
R.
Le&%*+*g
Le&%*+*g
A%e&
A%e&
PRECALCULUS # 21
PRECALCULUS # 21S!
S!
 CEN!URY $
 CEN!URY $
!e&ch+*g D&tes &*d
!e&ch+*g D&tes &*d
!+me
!+me
SEP!E$ER 2,(-/ 21,/ -0-(0-
SEP!E$ER 2,(-/ 21,/ -0-(0-
P$
P$
$o*d&3!4esd&35ed*esd&3!h4%sd
$o*d&3!4esd&35ed*esd&3!h4%sd
&
&
6
64&
4&%t
%te%
e% 7I
7IRS
RS!
!
I. OBJECTIVES
I. OBJECTIVES $
$O
ON
ND
DA
AY
Y !
!U
UE
ES
SD
DA
AY
Y 5
5E
ED
DN
NE
ES
SD
DA
AY
Y !
!"
"U
UR
RS
SD
DA
AY  
Y  
A. Co*te*t St&*d&%ds
A. Co*te*t St&*d&%ds !he le&%*e%s demo*st%&te &* 4*de%st&*d+*g o8 9e co*cepts o8
!he le&%*e%s demo*st%&te &* 4*de%st&*d+*g o8 9e co*cepts o8 se%+es &*d m&them&t+c&l +*d4ct+o* &*d the +*om+&l !heo%em.
se%+es &*d m&them&t+c&l +*d4ct+o* &*d the +*om+&l !heo%em.
. Pe%8o%m&*ce
. Pe%8o%m&*ce
St&*d&%ds
St&*d&%ds
!he le&%*e%s sh&ll be &ble to 9ee*l obse%'e &*d +*'est+g&te p&tte%*s/ &*d
!he le&%*e%s sh&ll be &ble to 9ee*l obse%'e &*d +*'est+g&te p&tte%*s/ &*d 8o%m4l&te &pp%op%+&te m&them&t+c&l st&teme*ts &*d
8o%m4l&te &pp%op%+&te m&them&t+c&l st&teme*ts &*d
C. Le&%*+*g
C. Le&%*+*g
Compete*c+es3 Ob:ect+'es
Compete*c+es3 Ob:ect+'es
;5%+te the LC Code 8o%
;5%+te the LC Code 8o%
e&ch<
e&ch<
At the e*d o8 the
At the e*d o8 the
lesso*/ the le&%*e%s
lesso*/ the le&%*e%s
=+ll sol'e p%oblems
=+ll sol'e p%oblems
4s+*g m&them&t+c&l
4s+*g m&them&t+c&l
+*d4ct+o* &*d the
+*d4ct+o* &*d the
+*om+&l !heo%em.
+*om+&l !heo%em.
S!E$>PC11S$I(I:(2
S!E$>PC11S$I(I:(2
At the e*d o8 the
At the e*d o8 the lesso*/
lesso*/
the st4de*t +s &ble to0
the st4de*t +s &ble to0
;1< +ll4st%&te the 4*+t
;1< +ll4st%&te the 4*+t
c+%cle &*d the
c+%cle &*d the
%el&t+o*sh+p bet=ee* the
%el&t+o*sh+p bet=ee* the
l+*e&% &*d &*g4l&%
l+*e&% &*d &*g4l&%
me&s4%es o8 &%cs +* &
me&s4%es o8 &%cs +* &
4*+t c+%cle/ &*d
4*+t c+%cle/ &*d
;2< co*'e%t deg%ee
;2< co*'e%t deg%ee
me&s4%e to
me&s4%e to
%&d+&* me&s4%e/ &*d '+ce
%&d+&* me&s4%e/ &*d '+ce
'e%s&.
'e%s&.
S!E$>PC11!(II&(1 &*d
S!E$>PC11!(II&(1 &*d
II&(2
II&(2
II. CONTENT 
II. CONTENT 
Se%+es &*d
Se%+es &*d
$&them&t+c&l
$&them&t+c&l
I*d4ct+o*
I*d4ct+o*
A*gles +* & U*+t C+%cle
A*gles +* & U*+t C+%cle
III. LEARNING
III. LEARNING
RESOURCES
RESOURCES
A. Re8e%e*ces
A. Re8e%e*ces
1.
1. T
Teacher’s Guide
eacher’s Guide pages
pages Precalculus,
Precalculus,
Teacher’s Guide,
Teacher’s Guide,
 paes !!" # !$
 paes !!" # !$!
!
Precalculus, Teacher’s
Precalculus, Teacher’s
Guide, paes !$% & !$
Guide, paes !$% & !$
DepedK12.blogspot.com
2. Learner’s Materials
pages
Precalculus,
Lear'er’s (a)erial,
 paes !!*#!$!
Precalculus, Lear'er’s
(a)erial, paes !$% #
!$
3. Textbook pages
4. Additional Materials fro
Learning !esource "L!#
portal
+++.
a'al-ea)h.c/
+++.ale0ra.c/
+++.
a'al-ea)h.c/
+++.ale0ra.c/
. Othe% Le&%*+*g
Reso4%ces
IV. PROCE1URES
A. Re'+e=+*g p%e'+o4s
lesso* o% p%ese*t+*g the
*e= lesso*
!e$ie% the concepts
discussed last eeting
. Est&bl+sh+*g & p4%pose
8o% the lesso*
&'ind the nth ter of
"x()#*n’
&'ind the linear and
angular easure of arcs+
&,on$ert degree
easure to radian- and
$ice $ersa+
C. P%ese*t+*g e?&mples3
+*st&*ces
Co*'e%t deg/ m+*/ sec
to deg0
Co*'e%t deg to deg/
m+*/ sec.0
D. D+sc4ss+*g *e=
co*cepts &*d p%&ct+c+*g
Co*cept0 Co*cept0
DepedK12.blogspot.com
*e= s9+lls @1  The ascal’s T
riangle
does not allo% us to
%rite the general
expansion of the nth
po%er of a binoial.
/e need a %a) of
expressing the
coe0cients in
algebraic s)bols.
/e can obtain the
forula for expansion
using cobinations.
'or exaple- %e can
get the forula for
"x()#* b) using the
forula for the r
cobination of n
obects.
1* ( x*4 ) (
1x*3 )*2 ( 1x*2
)*3 ( x)*4 ( 1 )*
Angles in trigonoetr)
di5er
fro angles in 6uclidean
geoetr) in the sense of
otion.
An angle in geoetr) is
dened
as a union of ra)s "that
is- static# and has
easure
bet%een  and 17.
An angle in trigonoetr)
is a rotation of a ra)-
and- therefore- has no
liit. 8t has positi$e and
negati$e directions and
easures.
(easuree')s
2c/'3ersi/'45
A central angle of a circle
easures one degree-
%ritten 19- if it intercepts
1:3; of the
circuference of the
circle. <ne minute-
%ritten 1’- is
1:; of 19- %hile one
second- %ritten 1’’- is
1:; of 1’.
179 = > radian
1 radian = ?.39
E. D+sc4ss+*g *e=
co*cepts &*d p%&ct+c+*g
Co*cept0
Using the formula of
Co*cept0
DepedK12.blogspot.com
*e= s9+lls @2 combination C(n, r)
where n=5 because we
have 5,4,3,2,1
,"-# = 1
,"-2# = 1
,"-4# = 
,"-1# = 
,"-3# = 1
,"-# = 1
7o%m4l&0 C ;*/ %< 
*B 3 % B ;*(%<B
 n angle is said to be
 !ositive if the ra" (terminal
side) rotates in a
countercloc#wise direction
from the initial side, and the
angle is negative if it
rotates in a cloc#wise
direction$
a)
b)
c)
7. De'elop+*g m&ste%
;Le&ds to 7o%m&t+'e
Assessme*t 2<
P%oblem0
'ind the fourth ter of
"2x@)#*;.
2 "2x#*3  "@)#*3 =
= 2 "7x*3# "@)*3#
= @1; x*3 )*3
"A*s=e%<
P%oblem0
8n the follo%ing Bgure-
identif) the terinal side
of an angle in
standard position %ith
gi$en easure.
DepedK12.blogspot.com
G. 7+*d+*g p%&ct+c&l
&ppl+c&t+o*s o8 co*cepts
&*d s9+lls +* d&+l l+'+*g
". $&9+*g ge*e%&l+&t+o*s
&*d &bst%&ct+o*s &bo4t
the lesso*
%im!lif" the discussed
conce!ts
%im!lif" the discussed
conce!ts
I. E'&l4&t+*g le&%*+*g
 ). Add+t+o*&l &ct+'+t+es 8o%
&ppl+c&t+o* Se&t=o%9 &t pp. 11 to
12
Se&t=o%9 &t pp. 12 to
12
V. RE(AR6S INDUC!ION INDUC!ION3$A!" 6UIF INDUC!IO
VI. RE7LECTION
A. No. o8 le&%*e%s =ho
e&%*ed  +* the
e'&l4&t+o*.
. No. o8 le&%*e%s =ho
%eH4+%e &dd+t+o*&l
&ct+'+t+es 8o% %emed+&t+o*
=ho sco%ed belo=
C. D+d the %emed+&l
lesso*s =o%9 No. o8
le&%*e%s =ho h&'e c&4ght
4p =+th the lesso*.
D. No. o8 le&%*e%s =ho
co*t+*4e to %eH4+%e
%emed+&t+o*.
DepedK12.blogspot.com
E. 5h+ch o8 m te&ch+*g
st%&teg+es =o%9ed =ell
5h d+d these =o%9
7. 5h&t d+Jc4lt+es d+d I
e*co4*te% =h+ch m
p%+*c+p&l o% s4pe%'+so%
c&* help me sol'e
G. 5h&t +**o'&t+o* o%
loc&l+ed m&te%+&ls d+d I
4se3d+sco'e% =h+ch I =+sh
to sh&%e =+th othe%
te&che%s
repared b)C ,hecked b)C
Ces&% $. del Ros&%+o/ CE C&l+c9 D. A%%+et&/ PhD
%&% '1 %chool rinci!al *

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document.pdf

  • 1. DepedK12.blogspot.com DepedK12.blogspot.com PRECALCULUS PRECALCULUS DAILY DAILY LESSON LOG LESSON LOG School School CALAYOG CI!Y NA!IONAL "IG" CALAYOG CI!Y NA!IONAL "IG" SC"OOL # SC"OOL # SENIOR "IG" SC"OOL DEPAR!$EN! SENIOR "IG" SC"OOL DEPAR!$EN! G%& G%&de de le' le'el el GRA GRADE DE 11 ( 11 ( S!E S!E$ A $ A ! !e&che% e&che% ENGR ENGR. CES . CESAR $. AR $. DEL R DEL ROSAR OSARIO ) IO )R. R. Le&%*+*g Le&%*+*g A%e& A%e& PRECALCULUS # 21 PRECALCULUS # 21S! S!  CEN!URY $  CEN!URY $ !e&ch+*g D&tes &*d !e&ch+*g D&tes &*d !+me !+me SEP!E$ER 2,(-/ 21,/ -0-(0- SEP!E$ER 2,(-/ 21,/ -0-(0- P$ P$ $o*d&3!4esd&35ed*esd&3!h4%sd $o*d&3!4esd&35ed*esd&3!h4%sd & & 6 64& 4&%t %te% e% 7I 7IRS RS! ! I. OBJECTIVES I. OBJECTIVES $ $O ON ND DA AY Y ! !U UE ES SD DA AY Y 5 5E ED DN NE ES SD DA AY Y ! !" "U UR RS SD DA AY   Y   A. Co*te*t St&*d&%ds A. Co*te*t St&*d&%ds !he le&%*e%s demo*st%&te &* 4*de%st&*d+*g o8 9e co*cepts o8 !he le&%*e%s demo*st%&te &* 4*de%st&*d+*g o8 9e co*cepts o8 se%+es &*d m&them&t+c&l +*d4ct+o* &*d the +*om+&l !heo%em. se%+es &*d m&them&t+c&l +*d4ct+o* &*d the +*om+&l !heo%em. . Pe%8o%m&*ce . Pe%8o%m&*ce St&*d&%ds St&*d&%ds !he le&%*e%s sh&ll be &ble to 9ee*l obse%'e &*d +*'est+g&te p&tte%*s/ &*d !he le&%*e%s sh&ll be &ble to 9ee*l obse%'e &*d +*'est+g&te p&tte%*s/ &*d 8o%m4l&te &pp%op%+&te m&them&t+c&l st&teme*ts &*d 8o%m4l&te &pp%op%+&te m&them&t+c&l st&teme*ts &*d C. Le&%*+*g C. Le&%*+*g Compete*c+es3 Ob:ect+'es Compete*c+es3 Ob:ect+'es ;5%+te the LC Code 8o% ;5%+te the LC Code 8o% e&ch< e&ch< At the e*d o8 the At the e*d o8 the lesso*/ the le&%*e%s lesso*/ the le&%*e%s =+ll sol'e p%oblems =+ll sol'e p%oblems 4s+*g m&them&t+c&l 4s+*g m&them&t+c&l +*d4ct+o* &*d the +*d4ct+o* &*d the +*om+&l !heo%em. +*om+&l !heo%em. S!E$>PC11S$I(I:(2 S!E$>PC11S$I(I:(2 At the e*d o8 the At the e*d o8 the lesso*/ lesso*/ the st4de*t +s &ble to0 the st4de*t +s &ble to0 ;1< +ll4st%&te the 4*+t ;1< +ll4st%&te the 4*+t c+%cle &*d the c+%cle &*d the %el&t+o*sh+p bet=ee* the %el&t+o*sh+p bet=ee* the l+*e&% &*d &*g4l&% l+*e&% &*d &*g4l&% me&s4%es o8 &%cs +* & me&s4%es o8 &%cs +* & 4*+t c+%cle/ &*d 4*+t c+%cle/ &*d ;2< co*'e%t deg%ee ;2< co*'e%t deg%ee me&s4%e to me&s4%e to %&d+&* me&s4%e/ &*d '+ce %&d+&* me&s4%e/ &*d '+ce 'e%s&. 'e%s&. S!E$>PC11!(II&(1 &*d S!E$>PC11!(II&(1 &*d II&(2 II&(2 II. CONTENT  II. CONTENT  Se%+es &*d Se%+es &*d $&them&t+c&l $&them&t+c&l I*d4ct+o* I*d4ct+o* A*gles +* & U*+t C+%cle A*gles +* & U*+t C+%cle III. LEARNING III. LEARNING RESOURCES RESOURCES A. Re8e%e*ces A. Re8e%e*ces 1. 1. T Teacher’s Guide eacher’s Guide pages pages Precalculus, Precalculus, Teacher’s Guide, Teacher’s Guide,  paes !!" # !$  paes !!" # !$! ! Precalculus, Teacher’s Precalculus, Teacher’s Guide, paes !$% & !$ Guide, paes !$% & !$
  • 2. DepedK12.blogspot.com 2. Learner’s Materials pages Precalculus, Lear'er’s (a)erial,  paes !!*#!$! Precalculus, Lear'er’s (a)erial, paes !$% # !$ 3. Textbook pages 4. Additional Materials fro Learning !esource "L!# portal +++. a'al-ea)h.c/ +++.ale0ra.c/ +++. a'al-ea)h.c/ +++.ale0ra.c/ . Othe% Le&%*+*g Reso4%ces IV. PROCE1URES A. Re'+e=+*g p%e'+o4s lesso* o% p%ese*t+*g the *e= lesso* !e$ie% the concepts discussed last eeting . Est&bl+sh+*g & p4%pose 8o% the lesso* &'ind the nth ter of "x()#*n’ &'ind the linear and angular easure of arcs+ &,on$ert degree easure to radian- and $ice $ersa+ C. P%ese*t+*g e?&mples3 +*st&*ces Co*'e%t deg/ m+*/ sec to deg0 Co*'e%t deg to deg/ m+*/ sec.0 D. D+sc4ss+*g *e= co*cepts &*d p%&ct+c+*g Co*cept0 Co*cept0
  • 3. DepedK12.blogspot.com *e= s9+lls @1  The ascal’s T riangle does not allo% us to %rite the general expansion of the nth po%er of a binoial. /e need a %a) of expressing the coe0cients in algebraic s)bols. /e can obtain the forula for expansion using cobinations. 'or exaple- %e can get the forula for "x()#* b) using the forula for the r cobination of n obects. 1* ( x*4 ) ( 1x*3 )*2 ( 1x*2 )*3 ( x)*4 ( 1 )* Angles in trigonoetr) di5er fro angles in 6uclidean geoetr) in the sense of otion. An angle in geoetr) is dened as a union of ra)s "that is- static# and has easure bet%een  and 17. An angle in trigonoetr) is a rotation of a ra)- and- therefore- has no liit. 8t has positi$e and negati$e directions and easures. (easuree')s 2c/'3ersi/'45 A central angle of a circle easures one degree- %ritten 19- if it intercepts 1:3; of the circuference of the circle. <ne minute- %ritten 1’- is 1:; of 19- %hile one second- %ritten 1’’- is 1:; of 1’. 179 = > radian 1 radian = ?.39 E. D+sc4ss+*g *e= co*cepts &*d p%&ct+c+*g Co*cept0 Using the formula of Co*cept0
  • 4. DepedK12.blogspot.com *e= s9+lls @2 combination C(n, r) where n=5 because we have 5,4,3,2,1 ,"-# = 1 ,"-2# = 1 ,"-4# =  ,"-1# =  ,"-3# = 1 ,"-# = 1 7o%m4l&0 C ;*/ %<  *B 3 % B ;*(%<B  n angle is said to be  !ositive if the ra" (terminal side) rotates in a countercloc#wise direction from the initial side, and the angle is negative if it rotates in a cloc#wise direction$ a) b) c) 7. De'elop+*g m&ste% ;Le&ds to 7o%m&t+'e Assessme*t 2< P%oblem0 'ind the fourth ter of "2x@)#*;. 2 "2x#*3  "@)#*3 = = 2 "7x*3# "@)*3# = @1; x*3 )*3 "A*s=e%< P%oblem0 8n the follo%ing Bgure- identif) the terinal side of an angle in standard position %ith gi$en easure.
  • 5. DepedK12.blogspot.com G. 7+*d+*g p%&ct+c&l &ppl+c&t+o*s o8 co*cepts &*d s9+lls +* d&+l l+'+*g ". $&9+*g ge*e%&l+&t+o*s &*d &bst%&ct+o*s &bo4t the lesso* %im!lif" the discussed conce!ts %im!lif" the discussed conce!ts I. E'&l4&t+*g le&%*+*g  ). Add+t+o*&l &ct+'+t+es 8o% &ppl+c&t+o* Se&t=o%9 &t pp. 11 to 12 Se&t=o%9 &t pp. 12 to 12 V. RE(AR6S INDUC!ION INDUC!ION3$A!" 6UIF INDUC!IO VI. RE7LECTION A. No. o8 le&%*e%s =ho e&%*ed  +* the e'&l4&t+o*. . No. o8 le&%*e%s =ho %eH4+%e &dd+t+o*&l &ct+'+t+es 8o% %emed+&t+o* =ho sco%ed belo= C. D+d the %emed+&l lesso*s =o%9 No. o8 le&%*e%s =ho h&'e c&4ght 4p =+th the lesso*. D. No. o8 le&%*e%s =ho co*t+*4e to %eH4+%e %emed+&t+o*.
  • 6. DepedK12.blogspot.com E. 5h+ch o8 m te&ch+*g st%&teg+es =o%9ed =ell 5h d+d these =o%9 7. 5h&t d+Jc4lt+es d+d I e*co4*te% =h+ch m p%+*c+p&l o% s4pe%'+so% c&* help me sol'e G. 5h&t +**o'&t+o* o% loc&l+ed m&te%+&ls d+d I 4se3d+sco'e% =h+ch I =+sh to sh&%e =+th othe% te&che%s repared b)C ,hecked b)C Ces&% $. del Ros&%+o/ CE C&l+c9 D. A%%+et&/ PhD %&% '1 %chool rinci!al *