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Saturday, January 2, 2016

TRINAL RESULTS


CONGRATULATIONS



Top  Scorers  of  the  TRINALS

Given last December 16 - 17,  2015



        PHYSICS E 101                Score

1.   Hernandez,  Mary Rose                           84
2.   Jumamil, Catherine H.                              81



        MATH  E  114                   Score
1.  Hernandez,  Mary Rose                           84
2. Cortez,  Dennis                                         80



     F ELECT 3 / MATH 25         Score
1.   Silongan, Datu Mohmmad E.                  84
2.   Cabangisan, Loribee Ann T.                   83




                                        Efren  F. Cadungog, Sr., MIM
                                                  Class adviser



Tuesday, November 17, 2015

INCLINATION, SLOPE AND ANGLE BETWEEN TWO LINES

  
INCLINATION AND SLOPE
               The inclination  of a line is the least counterclockwise angle  q  through which the 
     x axis must be rotated about the point of intersection in order to bring it into coincidence with the line. The inclination of a line parallel to the x axis is by definition zero, that of a vertical line is undefined. The slope of a line inclined upward to the right is positive and that of a line inclined downward to the right is negative.  

               The slope of a line, denoted by m is defined as the tangent of inclination, that is 
        
                                                          m = tan q.

           The slope of the line  L  is

                                                       m  =  tan q   =    y2 – y1        .                                       
                                                                                  x2 – x1

       Ex.  Find the slope of the following lines passing through the given segments.

              1.   ( 2, – 1),   ( 7, – 6 )                6.  (–2 , 4) ,  ( 2, –3 )
              2.   (–2 , 1),   (–7, 6 )                   7.  ( 2 , 3) ,  (–2, –5 )
              3.   ( 0 , – 3),   ( 3, 6 )                  8.  (–3 , –2),  ( 2, 4 )
              4.   ( 2 , – 5),   ( 5, – 1 )               9.  (3, –2) ,  (–1, 4 )
              5.   (– 4 , 1),   ( 2, 6 )                 10.  ( 3 , 2) ,  ( 5, – 3 )


PARALLEL AND PERPENDICULAR LINES


    Theorems :


         1.  Two lines are parallel, if, and only if, their slopes are equal, that is,  m1 = m2.

         2.  Two lines are perpendicular, if, and only if, the slope of one line is the negative
               reciprocal of the slope of the other line, that is,  


                                           m2  =  – 1/m1      or    m1m2  =  – 1.


Example 
       Prove that the points ( 1, 1), ( 4, 5 ), ( 0, 8) and (– 3, 4) are vertices of a square and
       find the area.

Exercises :
  1. Prove that the points (–1, 1), ( 0, – 3), ( 5, 2) and (4, 6) are vertices of a parallelogram.
  2. Prove that the points (–2, 0), (2, 3)  and (5, –1) are vertices of a right triangle. 

  3. Prove that the points (1, 1),  (4, 5),  (0, 8),  and (–3, 4) are vertices of a square.
  4. Show that the points (0, 0), (10, 3), (11, 1) and (1, 2) are vertices of a
       parallelogram.
  5. Show that the points (-1, 1),  (0, -3), (5, 2) and ( 4, 6) are vertices of a parallelogram.



ANGLE  BETWEEN  TWO LINES
         
  The angle from a line of slope m1  to  a line of slope m2  is given by the formula

                                                      tan F =   m2  –  m1  .      
                                                                     1 + m1 m2  


      Examples
       
    I.   The line L1 passes through the first pair of points, line L2 through the second
          pair, find the angle from  L1  to  L2.  

        1.  ( 4, 3),  (6, – 2 ) ;  ( 9, 5 ), (6, – 2 )                                            

        2.  ( 1, 9),  (2, 6) ;  (3, 3),  (– 1, 5)                                                 
  
        3.  ( 2, 0),  (3, 5 ) ;  ( 5, 2 ), (4, 6 )                                               

        4.  (– 5, – 3),  (2, 6) ;  (6, 4),  (8, 2)                                             


    II.  1. Find the interior angles of the triangle with vertices ( 0, 0),  (8, 6) and (9, 2 ).  
        
         2. Find the interior angles of the triangle with vertices ( 2, – 5),  (6, 2) and (4, 1). 

         3. Find the interior angles of the triangle with vertices ( 0, 0),  (– 8, 6) and (9, 0 ). 

         4. Find the interior angles of the triangle with vertices ( 2, 3),  (1, 1) and (–2, –2 ). 

         5. Find the angle between the lines (a)  y = 2x + 4 and  y + 3x =  3,

              (b) x – y = 2 and 2y +  x =  2, and  (c) 3x + 2y = 6  and  2x – 3y = 6.                      






Friday, November 6, 2015

ANALYTIC GEOMETRY ASSIGNMENT NOVEMBER 9, 10, 2015


For  4:00 – 5:00  MWF  class ( due on November 9, 2015  at  4:00 PM ) 

Draw all figures on a graphing paper.

I.   Given points.
  
            A( – 4 ,  2 )                  C(  5 ,  8 )

            B(  7 ,  – 2 )                 D( – 3 , 6 )


    Find the distance between the given points by referring to the
    coordinates above.

      1.   AB                                             4.  BD  

      2.   BC                                             5.  AD

      3.   CD                                             6.  AC

II.  1. Show that the points A(1 , 2 ) ,  B( 3, 5 ) and  C(–3, 9 ) are vertices
         of a right  triangle and find the area.

     2. Show that the points  A( 7, – 1 ), B( 3, 5 ) and  C( 1, – 5 ) are vertices of
          an isosceles triangle.  

     3. The circle with center at C( – 3,  – 4 ) passes through the point  ( 1 , 4 ).
         What is the diameter and area of this circle ?

    4.  Show that the points (– 1, 1 ),  ( 0, – 3 ),  ( 5, 2 ) and ( 4 , 6 ) are vertices
          of a parallelogram.


E N D




For  8:30 AM TTH class ( due on November 10, 2015  at  4:00  PM )

Draw all figures on a graphing paper.

I.   Given points.
  
            A( – 3 ,  5 )                  C( 2 ,  8 )

            B( 7 , – 2 )                   D(– 6 , 4 )

    Find the distance between the given points by referring to the
    coordinates above.

      1.   AB                                             4.  BD  

      2.   BC                                             5.  AD

      3.   CD                                             6.  AC

II.  1. Show that the points A(– 2 , 0 ) ,  B( 2, 3 ) and  C( 5 , –1 ) are vertices
         of a right  triangle and find the area.

     2. Show that the points  A( 5, 4 ), B(– 2, 1 ) and  C( 2, – 3 ) are vertices of
          an isosceles triangle.  

     3. The circle with center at  C( 2,  – 2 ) passes through the point  ( 6, 6 ).
         What is the diameter and area of this circle ?

    4.  Show that the points ( 1, 1 ),  ( 4, 5 ) and ( 0 , 8 ) and  (– 3 , 4 ) are the
          vertices of a square and find its area.


E N D









Friday, October 9, 2015

TOP SCORERS DURING FINALS


CONGRATULATIONS



Top  Scorers  of  the  FINALS

Given on October 7 - 10,  2015



        PHYSICS E 102           Score

             1.   Intes, Emmanuel C.                            96
             2.   Intes, Klyde Paul L.                             92
             3.   Vingno, Lawrence Denver                   85


        PHYSICS 21 E            Score
             1.   Puyod, Nonezza  B.                          96
             Fajota,  Silbert Jr. N.                         96
             2.   Bayogos, Princess Julie Ann            95
             3.   Flores, April Joy  V.                          93
             4.    Labiao,  Keshia Mary D.                   90
             Eugenio,  Ella  B.                             90
             5.   Buraay,  Aika  C.                              89
             6.   Gallego,  Angelica Mia A.                87
            Escote,  Michelle  S.                        87
             7.  Bayog-ang, Michael Neil                  86
            Bisagar,  Edilene  J.                        86
            Canarejo,  Judy Ann B.                   86
             8.  Valdez,  Jessylyn                            82
             9.  Villaruz,  Johnie Rey  P.                  81
            Dubpaleg,  Hadiguia                       81


        PHYSICS 101            Score
             1.   Alad-ad, Jessa Mae  Q.                  85
             2.   Bayona,  Jessie  S.                        84
             3.   Estrellanes, Ana Madel  C.            83
             Ansay,  Norjana  M.                      83    
             4.  Tangaro,  Charry Joyce E.             82
             5.   Gargar, Celmer Marie D.               81
Montalvo,  Ruchel May                81


        MATH 11A                   Score
                1.   Catubig, Christian B.                  95
 Masinapoc,  Jan Marie  P.         95
               2.   Asentista,  Prince Alexis  C.        94
               3.   Dalisay,  Krizza  A.                      93
               4.   Martizano,  Luke S.                     92
              Blanco,  Justine Mark P.             92
              5.   Pancho,  Roxan  S.                     90
              6.   Cabagua,  Dexter  A.                   87
              7.   Glang,  Hannan  K.                      86
Bauzon,  John Mark                    86
Melocotones,  Robert  A.            86
              8.   Diamos,  Melvi  B.                        84
             Cabuguason,  Karen Kate N.       84
              9.   Villamor,  Ivy  Joy  F.                   82
Claudio,  Khrista  Eva  O.           82 
            10.   Alam,  Sharine  D.                        81
            11.  Lakiman,  Guiahada A.                 80    




        MATH  E 13        Score
1.   Campollo,  Jerlyn                      84
2.   Jumamil,  Catherine                  80     






                         Efren  F. Cadungog, Sr., MIM
                                  Class adviser


Sunday, September 13, 2015

TOP SCORERS ON MIDTERM EXAMINATION


Top Scorers on Midterm
given last August 28, 2015


  MATH  E 13 – Plane & Spherical Trigonometry

1.  Jumamil, Catherine                       88 
     Presas, Mark Bryan                       88
2.  Hernandez, Mary Rose                 86


  PHYSICS  E  102  –  College Physics 2

1.  Intes, Emmanuel  C.                      82


  MATH   11 A   –   College  Algebra

1.  Masinapoc, Jan Marie  P.             100
     Catubig,  Christian B.                   100
2.  Martizano, Luke, Janrey S.           94
3.  Pancho, Roxan  S.                         90
4.  Glang, Hannan K.                          83
5.  Dacuscus,  Shenni  S.                   81
     Delgado,  Eric Roy  A.                   81

PHYSICS 21 E – Physics for Health Science Students
 1. Labiao,  Keshia Mary  D.             100
 2.  Escote,  Michelle  S.                    97
 3.  Villaruz,   Johnie Rey  P.             95
      Pabilona,  Liza Mae  L.                95
      Canarejo,  Judy Ann B.               95
 4.  Flores,  April Joy  V.                    93
 5.  Bisagar,  Edilene  J.                     90
 6.  Eugenio,  Ella  B.                          88
      Dubpaleg,  Hadiguia  A.               88 
      Bernardo,  Rica  C.                       88
      Bayog-ang,  Michael Neil             88
 7.  Andol,  Sheila Mae  U.                  85
 8.  Gallego,  Angelica Mia  A.            84
 9.  Valdez,  Jessylyn  S.                     81
      Puyod,  Nonezza  B.                      81 
      Gornez,  Jessabel  E.                    81 
      Fajota,  Silbert Jr.  N.                    81
      Carian,  Ricky John  P.                 81






           Prepared by : Efren F. Cadungog Sr.,  MIM
                             Class adviser





Sunday, July 19, 2015

TRINALS TOP SCORERS


CONGRATULATIONS



Top Scorers of TRINALS 2015

Given on July 15 - 16,  2015



        MATH 11A                    Score

1.  Masinapoc, Jan Marie                              98
2.  Martizano, Luke Janrey                                     96
3.  Dacuscus, Shenni                                             92
Catubig, Christian                                     92
4.  Melocotones,  Robert                               90
Limpioso, Princess Jhuner                        90
5.  Pancho,  Roxan                                         86
6.  Bauzon,  John Mark                                  84
Claudio, Krista Eva                                    84
Cabagua, Dexter                                       84
7.  Cabuguason,  Karen Kate                         82
Blanco,  Justine  Mark                               82
8.  Glang,  Hannan                                         80
Diamos,  Melvi                                          80




        PHYSICS 21 E                   Score

     1.  Puyod,  Nonezza                                            82
       Escote,  Michelle                                           82



                                        Efren  F. Cadungog, Sr., MIM
                                        Class adviser