TEST OF SYMMETRY
SYMMETRY
X-Axis
Y-axis
Origin
Diagonal
TEST OF SYMMETRY
f(-y)=f(y)
f(-x)=f(x)
-f(x)=f(x)
f(xy)=f(yx)
ROOTS OF MULTIPLICITY
MULTIPLICITY
EVEN
ODD
GRAPH
GRAPH DOES NOT CROSS
GRAPH CROSSES THE AXIS
LIMIT AS IT APPROACHES +∞
CONDITION
DEGREE OF P(x) = Q(x)
DEGREE OF P(x) < Q(x)
DEGREE OF P(x) > Q(x)
LIMIT
IF DEGREE BOTH ARE
POSITIVE: +∞
OTHERWISE, -∞
0
QUOTIENT OF THE
COEFFICIENTS OF THE
HIGHEST DEGREE TERMS
PANGNGALAN
PANGHALIP
PANG-URI
PANG-ABAY
PANDIWA
PANG-UKOL
PANGATNIG





Ng
Sagot sa ano at sino
Bilang pang-ukol
(preposition)
Pag-aari
Sinusundan ng
pangngalan
Sinusundan ng
taggawa ng pandiwa
Pinto
Door
“Buksan mo ang pinto.”
NOUN
PRONOUN
ADJECTIVE
ADVERB
VERB
PREPOSITIONS
CONJUNCTIONS






Nang
Katumbas ng noon,
upang, para, when, in
order/so that
Sinusundan ng pangabay (adverb)
Inuulit na salita
Na+na
Na+ng
Na+ang
Pintuan
Doorway
“Natanggal ang pinto sa
pintuan.”
May
 Sinusundan ng
pangngalan, pandiwa,
pang-uri, panghalip
na paari, mga, sa
Mayroon
 Sinusundan ng
ingklitik/kataga
 Sinusundan ng
panghalip na palagyo
 Pamalit sa
“mayaman”
Hagdan
Stairs
Inakyat niya ang
hagdan.
Hagdanan
Stairway
“Ilagay mo ang hagdanan
sa tapat ng bintana.”
Pahiran/Punasan
To apply (lagyan)
Pahirin/Punasin
Wipe off (tanggalin o
alisin)
Subukan
To see secretly
Subukin
To test/try
Walisin
Specific na bagay
Walisan
lugar
Ooperahin
Specific organ
Iwan
To leave
Bumili
To buy
Ooperahan
general
Iwanan
To leave something to
somebody
Magbili
To sell(magbenta)
Pam-p,b
Hal. pampunas
Pan-d, l, r, s, t
Hal. pantakip
Pang-(patinig, atbp.)
Hal. pang-almusal
Walang gitling kung may 3rd meaning.
Hal. Bahaghari
MOLECULAR GEOMETRY OF MOLECULES:
3
3
4
4
5
5
6
6
LINEAR
BENT
TRIGONAL PLANAR
TRIGONAL PYRAMIDAL
TETRAHEDRAL
SEE-SAW SHAPED
TRIGONAL BIPYRAMIDAL
SQUARE PYRAMIDAL
NONPOLAR
POLAR
NONPOLAR
POLAR
NONPOLAR
POLAR
NONPOLAR
POLAR
HYDROCARBONS ARE USUALLY NONPOLAR.
IF ELECTRONEGATIVITY DIFFERENCE IS >0.4,
THERE EXISTS A POLAR BOND. THEREFORE,
THE MOLUECULE IS A POLAR MOLECULE.
ATOMIC MODELS:
 BILLIARD BALL MODEL (JOHN DALTON)
 PLUM PUDDING MODEL (JJ THOMSON)
 NUCLEAR MODEL (ERNEST RUTHERFORD)
 PLANETARY MODEL (NIELS BOHR)
 QUANTUM MODEL
COHESION (CONVEX)
THE MOLECULES OF THE
LIQUID ARE ATTRACTED
TO ONE ANOTHER AND
AVOID THE TEST TUBE.
ADHESION (CONCAVE)
THE MOLECULES OF THE
LIQUID ARE ATTRACTED
TO THE TEST TUBE THAN
TO ONE ANOTHER.
CONSTANTS:
R=0.0821
G=6.67
N
Avogadro’s number=6.02
(molecules, atoms, electrons,
F.U./mole)
C=3.0
SPEED OF SOUND IN AIR=343m/s
MAGNITUDE – RICHTER SCALE (1-10)
FACTOR OF 10.
INTENSITY – MERCALLI SCALE 1-12.
FORMULAS:
F=
People can hear 1520,000 Hz.
+32
C=
Hz= 1 vibration or
cycle per second.
K=C+273
EM SPECTRUM
F=ma
(DECREASING
WAVELENGTH)
SERIES
(CONSTANT
CURRENT)
V=IR
Radio waves
Microwaves
Infrared
Visible light
UV rays
X-ray
Gamma rays
P=I2R=V2/R
Note: Red light bends
MOMENTUM=mv
the least. Violet light
bends the most.
RT=R1+R2+…+Rn
PARALLEL
VOLTAGE)
(CONSTANT
1/RT=
1/R1+1/R2+…+1/Rn
IMPULSE= CHANGE IN
MOMENTUM
IMPULSE=Ft
F=1/T
CONCAVE
RESULTING IMAGE
 REAL, INVERTED,
REDUCED,
BETWEEN C & F.
 REAL, INVERTED,
SAME SIZE,
PARALLEL TO C.
 REAL, INVERTED,
ENLARGED,
BEFORE C.
 NO IMAGE IS
FORMED IF
OBJECT IS AT
FOCAL POINT.
 VIRTUAL,
UPRIGHT,
ENLARGED.
QUESTION
ANSWER
Concave
vs. Plane mirrors always produce virtual images which are upright and located
behind the mirror; they are always the same size as the object
Plane mirrors
Concave mirrors can produce both real and virtual images; they can be upright (if
virtual) or inverted (if real); they can be behind the mirror (if virtual) or in front
of the mirror (if real); they can also be enlarged, reduced, or the same size as
object.
REAL IMAGE
Only a concave mirror can be used to produce a real image; and this only occurs
if the object is located at a position of more than one focal length from the
concave mirror.
Plane mirrors never produce real images.
VIRTUAL IMAGE A plane mirror will always produce a virtual image. A concave mirror will only
UPRIGHT IMAGE
INVERTED
IMAGE
produce a virtual image if the object is located in front of the focal point.
A plane mirror will always produce an upright image. A concave mirror will only
produce an upright image if the object is located in front of the focal point.
Only a concave mirror can be used to produce an inverted image; and this only
occurs if the object is located at a position of more than one focal length from
the concave mirror.
Plane mirrors never produce inverted images.
Are all real images No. Real images can be larger than the object, smaller than the object, or the
larger than the object? same size as the object.
SHAPES
QUADRILATERAL
PARALLELOGRAM
RECTANGLE
RHOMBUS
SQUARE
PROPERTIES
 4 SIDES, 4 VERTICES, INTERIOR ANGLES=360
 OPPOSITE SIDES AND ANGLES ARE EQUAL
 DIAGONALS BISECT THE ANGLES
 HAS 2 PAIRS OF PARALLEL SIDES
 HAS 4 RIGHT ANGLES
 DIAGONALS ARE EQUAL
 ALL SIDES ARE EQUAL
 HAS
ALL
THE
PROPERTIES
OF
A
PARALLELOGRAM
 DIAGONALS ARE PERPENDICULAR TO EACH
OTHER
 HAS
ALL
THE
PROPERTIES
OF
A
PARALLELOGRAM,
RECTANGLE,
AND
RHOMBUS
 ALL ANGLES ARE EQUAL (90 )
NOTE:
 A PARALLELOGRAM IS SOMETIMES A RECTANGLE.
 A RHOMBUS IS ALWAYS A PARALLELOGRAM.
 A SQUARE IS ALWAYS A RHOMBUS.
 A TRAPEZOID IS NEVER A PARALLELOGRAM.
 A RHOMBUS IS SOMETIMES A SQUARE.
 A SQUARE IS ALWAYS A PARALLELOGRAM.
 A RHOMBUS IS SOMETIMES A RECTANGLE.
 A SQUARE IS ALWAYS A RECTANGLE.
 A TRAPEZOID NEVER HAS TWO PAIRS OF PARALLEL SIDES.
 A TRAPEZIUM SOMETIMES HAS TWO CONGRUENT SIDES.
 A PARALLELOGRAM SOMETIMES HAS FOUR RIGHT ANGLES.
CONIC SECTIONS:
2
2
CIRCLE: (x-h) +(y-k) =r
2
PARABOLA
VERTICAL AXIS:
(x-h)2=4p(y-k)
p>0, opening upward
p<0, opening downward
HORIZONTAL AXIS:
2
(y-k) =4p(x-h)
p>0, opening to the right
p<0, opening to the left
Center: (h,k)
Radius: r
VERTEX (V): (h,k)
Focus point (F): (h, k+p)
Focal length: |p|
Directrix: y=k-p
Length of latus rectum: |4p|
VERTEX (V): (h,k)
Focus point (F): (h+p, k)
Focal length: |p|
Directrix: y=h-p
Length of latus rectum: |4p|
1. If b2-4ac>0, it is a hyperbola.
2
2. If b -4ac<0, it is an ellipse.
3. If b2-4ac=0, it is a circle.
TECHNIQUE: ECCENTRICITY
e= , where c is the distance from the center
to a focus.
a is the distance from the focus to a
vertex.
1.
2.
3.
4.
e=1, parabola
e=0, circle
e<1, ellipse
e>1, hyperbola
MIDSEGMENT OF A TRAPEZOID: ½(b1+b2)
POLYGON INTERIOR ANGLE: (n-2)180
INTEREST=
COMPOUND
INTEREST:
ORDER OF ADJECTIVES:
DOSSACOMPQ.
Determiner
One
Observer
lovely,
Size
small,
Shape
round,
Age
new,
Color
brown,
Origin
Italian,
Material
wooden,
Purpose/Qualifier
wedding ring.
IN vs. ON vs. AT
in
on
at
 enclosed space  surface
 precise &
 large location
 public transport small
location
 nonspecific
 dates & days
time
 names
of  event
 time
 abstract
streets,
(photograph,
avenues
 address
book)
 before
map,
farm,
island,
holiday website
to
into
 +verb of movement &  +verb of movement & a space
 Use for abstract places.
final destination
 an invitation/visit to
Ex. Go to work.
Go to Oxford.
Ex. Go into the garden.
Run into the house.
He entered the data into the
computer.
Note:
Do not use ”to” with the word “home”. = Let’s go home.
Do not use “into” with “enter” for a physical place. = He entered the room.
TOWARD=TOWARDS (INTERCHANGEABLE)
As well as, along with != and