MATH/CHEM/ENGLISH REVIEW

Activity for Adjective/Adverb

2009-07-16T07:06:00.000-07:00

1. Those children play (noisy,noisily)

2. My uncle drives his car very (careful,carefully)

3. Juan feels (sad,sadly) whenever he visits that place.

4. She sang (beautiful,beautifully)just before church.

5. Directions should be given (plain,plainly).

6. The pole bolter cleared the bar (easy,easily).

7. The jump was (easy,easily) for the athlete.

8. The meal tasted (wonderful,wonderfully) to me.

9. The teacher spoke (serious,seriously)to the little boy.

10. Put your clothes away (neat,neatly).

Activity for Modifier 2

2009-07-16T06:28:00.001-07:00

1. The old creaky wagon traveled slowly
2. Many weary children slept soundly
3. A soft comforter provided a warm,snug bed.
4. Two restless babies cried occasionaly.
5. Patient mothers hummed soothing lullabies.
6. The squeaking wheels created a striking contrast.
7. The lonely,desolate trail stretched endlessly.
8. An eagle circled the lumbering wagons ominously.
9. The exhausted travelers heard a startling,unfamiliar sound.
10. Anxious eyes scanned the surrounding rocky hills.

Modifiers 2

2009-07-16T06:25:00.000-07:00

example : The Scout and little boy ate hurriedly

The words stout and little describe the boy and the word hurriedly describes how he ate. These words are called modifiers. If you remove the small word the in the sentence,you would probably find it akward,although it does not add meaning to a sentence. This small word the including a,an,two,all,few,some,etc.,is called a noun marker.

Standard Enthalpy Changes

2009-07-15T23:53:00.000-07:00

Enthalpy of Physical Change
Enthalpy of Chemical Change- the change in enthalpy when the reactants in their standard states change to product in their standard states.

HESS'S LAW - The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.

Standard Enthalpy of Formation - the standard reaction enthalpy for the formation of the compound from its elements in their reference states.

Standard Enthalpy of Combustion - the standard reaction enthalpy for the burning of substance with oxygen normally yielding carbon dioxide and water.

Kirchoff's Law
Joule and Joule Thomson Experiments

Colligative properties

osmotic pressure
Vapor Pressure Lowering
Freezing Point Depression
Boiling Poin Elevation

THERMODYNAMICS

2009-07-15T23:47:00.000-07:00

Zeroth Law of thermodynamics - If A is in thermal equilibrium with B and B is thermal Equilibrium with C then, A and C are in thermal quilibrium.

First Law of thermodynamics - Law of Energy Conservation. Energy cannot be created nor destroyed only be transformed from one form to another.

Second Law of Thermodynamics - The entropy of the Universe increases.

Third law of Thermodynamics - The entropy of all perfect crystal is zero at absolute zero (0 degree Kelvin). It is impossible by any procedure to reduce any system to the absolute zero of temperature in a finite number of idealized steps.

***********recall the four fundamental Laws of Thermodynamics (U or E,H,A,G)*********

Thermochemistry - study of the heat changes accompanying chemical reactions.

Physical Chemistry (Basics)

2009-07-15T22:57:00.000-07:00

Definitions:

Adiabat = The path or lines depicting an adiabatic process
Adiabatic Process = Process in which no heat is transfered into or out of the system.
Boiling Point = The lowest temperature at which a liquid under fixed pressures changes state from liquid to vapor (vapor pressure=pressure on liquid)
Carnot Cycle = A system undergoing a cyclical process involving two reversible isothermal processes and two reversible adiabatic processes.
Carnot Engine = the most efficient heat engine which follows the Carnot Cycle
Chemical Potential = A measure of a chemical system's tendency to change (e.g.undergo a reaction,form a new phase,go into solution)
Critical Point = Temperature at which a liquid and its vapor become identical.
Cyclical Process = A process which repeats a series of changes in the system.
Enthalpy (H): The quantity of heat in a substance per unit mass under constant pressure.
Entropy (S): A measure of the degree of randomness of a system.
Equilibrium State: A state in which macroscopic properties of the system (i.e. temperature,density,chemical composition) are well defined and do not change with time.
Heat (Q): A form of energy;also an energy transfer as a consequence of temperature difference between the system and surroundings.
Heat Capacity (C): Total amount of heat needed to produce a one degree rise in temperature of a given substance.
Heat Engine: A device which converts heat into mechanical energy.
Internal Energy (U or E): The total kinetic and potential energy at the molecular level.
Irreversible Process: A non equilibrium process in which no small change in conditions could make the process goes in reverse.
Isobar: A path or line depicting an isobaric process
Isobaric Process: A process in which the pressure remains constant.
Isochoric Process: A process in which the temperature remain constant.
Mass: Amount of matter in an Object.
Melting point: The lowest temperature at which a solid under a fixed pressure changes state from solid to a liquid.
Pressure (P): The force acting per unit area.
Quantity of Heat: Total kinetic energy of all the molecule of a substance (Note: Not to be confused with the temperature)
Refrigerator: A device which transfer heat from a cold place to a hot place
Reversible process: A process whose direction may be reversed by an infinitesimal change in one of the forces;the system is always near equilibrium.
State Function: Also known as State Variables( A property of a system which has some difinite value for each state,and which does not depend on how the states is reached. (e.g Temperature,pressure,volume)
System: Region of universe being investigated
Temperature (T): the average kinetic energy of the molecules of a substance (Note: Not to be confused with quantity of heat)
Triple Point: A temperatre and pressure at which 3 phases of a substance (i.e solid,liquid,vapor) co-exist in equilibrium.
Work (W): Form of energy transfer that may be represented as a force acting through a distance.

GASES

Three types of system:
Open system- one that exchange of matter and energy with the surroundings
Closed system- one that allows exchange of energy but not matter.
Isolated System- both matter and energy are not communicated with the surroundings.

Definition of simple systems:

Macroscopically homogenous (uniform)
Isotropic (does not depend on direction)
No surface effects (Large enough sample available)
No charged particle (introduces complications,can be dealth with later)
No external fields (gravity,electric,etc) or considered negligible

Properties of Gases

No definite shape and volume
Diffuse very rapidly
Can be compressed very readily
Low density

Gas Laws

Boyle's Law- For a fixed mass of gas at a given temperature and pressures not too high,the volume of a given quantity varies inversely with the pressure of the gas.

Charle's Law- For a given quantity of a gas at constant pressure, the volume is found to increase as the temperature increases.

Gay-Lussac's Law a.k.a Amontons Law- For a fixed amount of a gas at constant volume,the pressur of gas increases with temperature.

Avogadro's Law- One mole of a gas,at a given temperature and pressure occupies the same volume as that of any gas. Equal volume of gases at the same temperature and pressure contain the same number of molecules.

Mixture of Gases:

Dalton's Law of Partial Pressures:

P=P1 + P2 + P3

Average Molecular Weight:

M= X1M1 + X2M2 + X3M3

Barometric Distribution Law:

P = P(Sub o) exp -{(Mgz/RT)}

Real Gases: particularly important at higher pressures and low temperatures

Compressibility Factor, Z

Recall:

Van der Waals (VDW) Equation - the critical parameters (V,P,T)
Berthelot
Dieterici
Redlich-Kwong
Virial (Kammerlingh-Onnes)

Fugacity

Making Verbs Agree with Noun Subjects

2009-04-01T06:23:00.000-07:00

You have heard again and again the basic rule that verb agrees with its subject that is, as singular verb; and a plural subject,a plural verb that general rule,however,has specific subdivisions.

The Rule

RULE 1. Use is,was,has,does,and their contractions with singular subject;use are,were,have,do,and their contractions with a plural subject. (Dont and doesnt cause most difficulty;watch them)

Jane doesnt live here now. The boys arent working.

Do not be confused by (a) words or phrases between verb and subject, (b) an introductory here or there, (c) questions with verb before subject.

a) A list of ten names was read.
b) Here are the papers.
c) Has that little boy been found yet?
d) Ed, as well as the girls,is here
e) There goes Jim.

RULE 2 Do not be influenced by a predicate nominative differing in number from the subject: Our problem is the crowds in the street.

RULE 3 Use a plural verb with compound subjects joined by and except when they form a unit oe when the subjects refer to one or the same person.

Ham and egss is a good dish. Eggs and butter are sold here.

RULE 4 Use a singular verb with singular compound subjects joined by or,noe,either-or,neither-nor;use a plural verb with plural subjects.If they vary,use a verb agreeing with the nearer subject.

Either Dean or Mark helps.
Two boys or man is enough.
Rats or mice are in the loft.
A man or two boys are enough.

RULE 5 If one subjects is affirmative and another negative,make the verb agree with the affirmative subject:

Tom,not his brother,works here.

RULE 6 Use a singular verb with the subjects,either simple or compound,that are limited by each or every: Every boy and girl here is welcome.

RULE 7 Use a singular verb with a collective noun subjects is the group acts as a unit. Use a plural verb if the members act individually.

The audience as has grown. The audience were whispering.

RULE 8 As a rule,use a singular verb after the number;use a plural verb after a number.The number of cases is small. A number are better.

RULE 9 If a fraction or a per cent is the subject and is followed by an "of" phrase,use a verb that agrees with the object in the phrase.

Two third of the pie remains. Ten per cent of the books are new.

RULE 10 Use a dingular verb with words plural in form but singular in meaning:

Essays of Elia is a book by Lamb. Ten dollars is left.

RULE 11 In most cases,use a singular verb with these subjects: civics,economics,mathematics,measles,molasses,mumps,physics,United States;use a plural verb with ashes,athletics,clothes,hysterics,pliers,politics,Scissors,shears,slacks,statistics,suds,thanks,tings,trousers,tweezers

useful information on Chemistry

2009-03-27T21:03:00.000-07:00

Heat= The energy which is manifested by temperature.

Potential Energy= The energy related to position or state of existence.

Kinetic Energy= The energy possessed by a moving body by virtue of its velocity.

Radiant Energy= The energy of electro magnetic radiations.

Chemical Energy= The energy released by substances during chemical reactions.

Nuclear or Atomic Energy= The energy released when atoms are split.

Chemistry= The branch of natural science that deals with the identification of matter and the changes that result as the energy content it transformed from one form to another.

Meter= The fundamental unit of length in the metric system.

Useful information on Chemistry

2009-03-27T08:14:00.000-07:00

Science= A field of study concerned with observing and interpreting facts that are readily reproduced.

Fact= An actual happening,something that is definitely true.

Hypothesis= A statement about something that is yet to be verified through experiments.A declaration based on a few facts and requires further clarification.

Law= A brief but precise statement about a number of related facts.

Theory= A declaration similar to but more formal than a hypothesis and is based on more facts.

Matter= Anything that occupies space and has a mass.

Energy= The capacity to perform work.

Diophantine Equations Problem

2009-03-27T07:43:00.000-07:00

A man bought 20 pcs of assorted calculators for 20 thousand. These calculators are of three types namely:

a. Programmable at P3000/pc
b. Scientific at P1500/pc
c. Household type at P500/pc

How many of each type did he buy?

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

I havent by on this page for quite sometime. I was busy of completing my papers for my upcoming interview. For those who will stop by here on this page. I ask a favor of prayers that i passed every endevour i have now. Thank you everyone. In return i will do my part on encouraging people specially students to embrace Math as one of the things that we have to take more into considerations than anything else today instead of playing computers or psp.

Later on I will post the answer to the Diophantine Equations problem...

Thank you and Mabuhay :D

Mixture Problem

2009-02-28T03:19:00.000-08:00

How much tin and how much lead must be added to 700 kg of an alloy containing 50% tin and 25% lead to make an alloy which is 80% tin and 20% lead?

Solution:

Given:

alloy tin lead resulting alloy

50%tin 100%tin 0%tin 60%tin

25%lead 0%lead 100%lead 20%lead

700kg + x + y = 700+x+y

Consider tin content:

50% (700) + 100%x + 0%y =60% (700+x+y)

350 + x = 420 + 0.6x + 0.6y

.4x-.6y=70 -------> equation 1

Consider lead content:

25%(700) + 0%x + 100%y = 20% (700+x+y)

175 + y = 140+.2 + .2y

0.2x + 0.8y = 35 --------> multiplied by 2

0.4x + 1.6y = 70 subtract equation 1

(-) 0.4x - 0.6 (0) = 70 ------> equation 1

y=0 substitute to equation 1

0.4-0.6(0) = 70

x=70/0.4= 175 kg

Thus:

Add 175 kg of tin and no lead

DIOPHANTINE EQUATIONS

2009-02-27T13:34:00.000-08:00

Properties

1. More unknowns than equations

2. Unknowns are normally a whole numbers and not equal to zero.

3. Solutions is by trial and error

MIXTURE PROBLEM

2009-02-23T07:47:00.000-08:00

Principle:

c------> % concentraton of solute (or any fractional unit)

A------> amount of mixture

cA-----> amout of solute or any fractional part

Quadratic Equation Problem

2009-02-22T06:59:00.000-08:00

One student make a mistake in copying the coefficient of x and got a root of +3 and -2. Another student made a mistake in copying the constant term and got a root of +3 and +2. Find the correct equation and correct roots.

Solution:
Let the correct equation be:

Ax^2 + Bx + c

and the correct roots be:

x1 and x2

Consider the first student's equation. It is wrong in B but correct in A and C. Thus,product of roots is the same as that of the correct equation.

C/A = 3(-2)= -6

Consider the 2nd student's equation. It is wrong in C but correct in A&B.Thus,sum of roots is the same as that of the correct equation.

-B/A = 3 + 2

B/A = -5

Consider the correct equation:

Ax^2 + Bx + c = 0 ------> divide by A

x^2 + B/Ax + C/A =0

thus

x^2-5x-6=0 -------> correct equation

solve for roots by factoring:

x^2-5x-6=0

(x-6)(x+1)=0

x=6 and -1

Therefore,the correct roots are:

6 and -1

the NEGATIVE SIGN on B Quadratic Equation :D

2009-02-22T06:42:00.000-08:00

First of all, i would like to thank my first time visitor under the name Mom for her time and for correcting my previous post. As you can see the first pic i posted lacked of something which is the negative sign,so please take note of it. If you take a close look on the second picture adding the X1 + X2 equals -2B/2A, i thought you might begin wondering considering the first pic with no negative sign, it should just be 2B/2A if you will add it without the sign. You wouldnt even come up with x1 + x2 = -B/A....

Below is the corrected formula with the minus sign...

:D

oh :D did i said take note of the negative sign on my previous post,i should have clearly said take note of the negative sign on the B eh he he thanks ms. mom

Quadratic Equations follow ups...

2009-02-21T07:15:00.000-08:00

Pardon me for not completing up my post on each topic as i have some other things to do at home but i will try to keep this blog updated, i do research online all the time when i need to know something about a certain topic. I feel the pain of searching nonstop and not getting the informations i wanted. This the reason why i set up my own blog and share my knowledge. Okie :D enough with my sentiments and now i would like to begin this with my follow ups on.....

What i am showing you above is the roots of the quadratic equation.You might find it useful for you someday....

While below shows the equation for the Sum of roots,take note of the negative sign.

And then the last thing i am showing you is the Product of Roots...

Take note of all formulas in quadratic equation and later on i will post example problem on Quadratic Equation in which we will appply this formula.Hope this one helps. :D

Quadratic Equation

2009-02-20T00:07:00.000-08:00

How many of you are familiar with Quadratic Equation? or should i say did you ever take time on reading what is quadratic equation is all about? hmmm?

oh well when i was taking this up i was dozing off that i didnt pay attention not until i felt a force that i needed time to study this things or otherwise i will fail in school :D.

this is the quadratic equation.........

WORK PROBLEM 2

2009-02-19T23:52:00.000-08:00

Ding can finish a job in 8 hours. Tito can do it in 5 hrs. If Ding worked for 3 hours and then Tito was asked to help him finish it, how long Tito will help him finish it, how long Tito will have to work with Ding?

Solution:
let t = time Tito worked with Ding to finish the job.

Condition 1:

t for Ding=8

D= 1/t = 1/8

Condition 2:

t for Tito=5

T= 1/t = 1/5

Condition 3:

D(3) + T(t) + D(t) = 1

1/8(3) + 1/5(t) + 1/8(t)=1

t= 1.92 hrs

WORK PROBLEM 1

2009-02-19T22:22:00.000-08:00

A and B can do a piece of work in 20 days, B and C in 30 days, C and A in 40 days. Find:

a) How long will each woeker can do the work alone?
b) If the three work together,how long will they be able to finish the job?

Solution:
a) Let

A= rate of workman "A"
B= rate of workman "B"
C= rate of workman "C"

Condition 1:

A(20) + B(20) = 1 -----> equation 1

Condition 2:

B(30) + C(30) = 1 -----> equation 2

Condition 3:

A(40) + C(40) = 1 -----> equation 3

Solving the three equations simultaneously:

A= 5/240

B= 7/240

C= 1/240

therefore:

time for A is 48 days
time for B is 34.3 days
time for C is 240 days

note: on how we arrived on those answer is through using the equation t=1/rate of the worker which are worker A, worker B and worker C.

b) let t=time for A,B,C to finish the job by working together.

At + Bt + Ct = 1

(A + B + C)t = 1

t = 1/ ( A + B + C )

t = 1/ ( 5/240 + 7/240 + 1/240 )

t = 240/13 days

Moving on to New topic

2009-02-19T05:12:00.000-08:00

The previous post was all about age problem. I usually encounter this problem not only on exams given in school but also when you apply for job. Its a common prodecure where in you are required to take exam such as iq test.The next topic i would like to share is about work problem. Before i give you different examples of work problems i would like first to discuss with the principle which is necessary to begin and for us to easily understand.

PRINCIPLE:

Let:

A= rate of worker "A"
t= time "A" worked
At= amount of work done by "A" to finish the work alone.

Thus:

At = 1 ----> A= 1/t or t = 1/A

Easy :D. As simple as that.

AGE PROBLEM 2

2009-02-19T01:05:00.001-08:00

Mary is 24: Mary is twice as old as Ana was when Mary was as old as Ana is now.
How old is Ana?

Solution:
was is will be
Mary 2x 24
Ana x 2x

Key Equation:

2x-x = 2x
x=8
2x=16
Therefore:
Ana is 16 yrs old

Note: This solution is based on the interpretation that the time condition.
'when Mary was old as Ana is now' refers entirely to the statement 'Mary is twice as old as Ana was and not only to the phrase 'Ana was'

AGE PROBLEM 1

2009-02-18T21:45:00.000-08:00

Two years ago, a boy is 2/3 as old as his sister. In two years, the boy will be ¾ as old as she. How old are they?

Solution:

(2 yrs ago) (now) (2 yrs from now)
was is will be

Boy 2/3 x 2/3x + 2 ¾ y
Sister x x + 2 y

y-x = 4 ------ equation 1

3/4y- 2/3 x = 4 ----------equation 2

Consider time elapsed from was to will be:

9 (y-x =4)

12 (3/4 y- 2/3 x = 4)

9y-8x = 48 eq. 3
9y-9x = 36 eq. 4 note: subtract eq. 4 from eq. 3
x = 12

x + 2 = 14

2/3 x+ 32 = 10

Therefore the boy is 10 yrs. Old and his sister is 14 years old.

AGE PROBLEM

2009-02-18T07:18:00.000-08:00

Principle: Time elapsed for persons concerned are equal

Problem:
A man is three times as old as his son.Five years ago,he was five times as old as his son was at that time.How old is the son.

5 yrs is will be
man 5y 3x
son y x

Key Equation:

5(x-y=5) ---> equation 1
3x-5y=5)---> equation 2
(-)5x-5y=25

note subtracting equation 2 to equation 1 will give us -2x= -20 and y is equal to 10.

Therefore the son is 10 years old.

LoViN Math!LoViN Science

2008-12-06T09:15:00.001-08:00

Mathematics is an academics subjects that 80 percent of students hate to take.Even an average students find it hard to deal with this subject unless you enjoy.It takes some appreciation to deal with this subject no matter how hard it is.It requires patient like anything else on this earth in order to survive.

I created this blog to somehow help our students appreciate and love Math.Also,I am going to try include other informative subjects to feed your mind as well. Anything goes as long as it is something everybody will learn.

As this site grew older,I am hoping that i will able to reach out in my own ways to encourage everyone and support them in dealing with mathematics and sciences.

I would like to extend my gratefulness to everyone who will support my site.