Tuesday, November 14, 2017

ENGLISH GRAMMAR & CORRECT USAGE - 1

ENGLISH : GRAMMAR AND CORRECT  USAGE

1. When a noun does not end in s, fom the singular and sometimes the plural possessive by adding an apostrope s (‘s).

          Examples:
          the boy = the boy’s hat                the children = the children’s toys

2. When a noun already ends in s, form the singular possessive by adding an apostrophe s (‘s) and form the plural possessive by adding only an apostrophe (‘).

          Examples
          the boss = the boss’s car             the boys = the boys’ hats
          Charles = Charles’s pen               the ladies = the ladies’ umbrellas

3. This indicates that something is near us: that indicates that it is  at a distance.
          This pencil is in my hand. That book is over there on the table.
          The plural of this is these; the plural of that is those.

          Examples
          These pencils are in my hand.      Those books are over there on the table.

4. Adjectives modify nouns.
          Examples:     a big animal            an open window      a red apple  

5. Adverbs modify verbs. They tell us how we do something.
          Examples:     John speaks slowly.         The birds sing beautifully.

6. We can form many adverbs by adding ly to an adjective.
          Examples:     soft     =        softly           easy   =        easily     
     
7. We can use a few words like fast, hard, late, and low as either adjectives or adverbs without any changes in form.

          Examples:     Marie is a hard worker. ( as  an adjective)
                              Marie works hard. (as an adverb)

8. Good is an adjective and must modify a noun.
          Example:      James is a good singer.

9. Well is usually used as an adverb.
          Example:      Tom speaks well.

  Well is occasionally used as an adjective only when it means to be in good health.
          Example:      Amanda was ill, but now she is well.

10. Who refers to PEOPLE. Which refers to SPECIFIC animals or things. That refers to animals, things as a CLASS. The object (direct or indirect) form of who is whom. Which and that both have the same form whether subject or object.

          Examples:    
          a. Was it Gino who said that?
          b. This is the report that the president wanted.
          c. The motorcycle which Harry used belongs to her brother.
          d. To whom did you give the pizza?
          e. The native inhabitants that lived in Batanes were called Ivatans.
          f. It is the little things in life that count.

11. A and an are indefinite articles. They refer to objects that have not been specifically identified. A or an is used only with singular nouns.

          Examples:
          a. A magazine is on the chair.
          b. Do you have a cigarette?
          c. Irma bought an umbrella.

12. The is a definite article. It refers to a PARTICULAR object. It is used with both singular and plural nouns.

          Examples:
          a. The book which gave me the greatest pleasure was Huckleberry Finn.
          b. The new books which I bought yesterday in National Book Store arrived this morning.

13. Much is used with nouns that cannot be counted and do not add s to show plurality.
          Examples:     much sugar            much rain               much coffee

14. Many is used with plural countable nouns.
          Examples:     many balloons        many cups of tea    many students

15. A lot of is the most commonly used term of these three.
          a lot of sugar                    a lot of books                   a lot of love

16. Also and too change to EITHER in NEGATIVE sentences.
          I want to dance too. I don’t want to dance either.
          We also want this pencil.   We don’t want this pencil either.

17. Use any in NEGATIVE sentences; use some in AFFIRMATIVE sentences.
          Maribel took some vegetables home with her.
          Manolo does not take any books home with him.

18. Use anybody, anyone, anything, and anywhere in NEGATIVE sentences.
          There isn’t anyone at the door.    Bobby didn’t go anywhere with his boss last night.
          They did not hear anything in the dark.

19. Use somebody, someone, something, and somewhere in AFFIRMATIVE sentences.
          She knows something about the plan.   Tim lost his watch somewhere downtown.
          There is someone at the kitchen.

20. For shows the LENGTH of TIME of the action.
          Mary has worked in SM for five months. Joan has not eaten anything for two days.

21. Since shows the TIME that the action BEGAN.
          Nancy has been absent since Monday.  It has been raining since last night.

22. Yet means so far; it is used in NEGATIVES and questions.
          Sean hasn’t arrived yet.     Are we there yet?

23. Already means by this time or previously; it is used in AFFIRMATIVE statements and questions.
          The plane has already left the airport.    Has John gotten his new suit already?

24. If the MAIN VERB of a sentence is in the PAST TENSE, ALL other dependent verbs are usually in the PAST TENSE too.

          The students say they will bring their projects tomorrow.
          The students said they would bring their projects tomorrow.
         
          The meteorologist predicts that it may snow on Monday.
          The meteorologist predicted that it might snow on Monday.

Note the irregular past tense forms of the following auxiliaries:
          will      =        would                      can     =        could
          may    =        might                      have   =        had

25. Have to and must express necessity or strong obligations. Have to is the more commonly used term.

          You must study your lesson.        You have to study your lesson.
          Rolly must work tonight.              Rolly has to work tonight.

26. Must has no past or future tense forms. Use have to to expess obligation or necessity in the past, future, and present perfect tenses.

          I have to attend the meeting.
          I had to attend the meeting.
          I will have to attend the meeting tomorrow.
          I have had to attend the meeting  every day this week.

27. Would rather followed by the simple form of the verb means to prefer. Note the position and use of than.

          I would rather drive a small car than a big one.
          I would rather live in a small town.
          Edgard would rather read a book than see a movie.

28. Had better with the simple form of the verb means it would be better or it would be advisable. Note that this term expresses a FUTURE thought even though it is in a PAST FORM.
          You had better rest a while.                  They had better come back later.

29. Place adverbs of time (yesterday, last week, next month, etc.) at the BEGINNING  or END of a sentence.
         
          We saw Mr. Santos yesterday.              On Thursday you are due in court.

30. Place adverbs of frequency (often, usually, generally, rarely, ever, etc.) BEFORE the MAIN VERB except when the main verb is a form of TO BE.

          She always comes to class early.                    Does he always come to class late?
          They are never late for class.      He has always prepared his lessons.

31. Word order is very important in English sentences. The normal word order for an English statement is SUBJECT, VERB, INDIRECT OBJECT, DIRECT OBJECT, ADVERBIAL MODIFIERS.

          Be careful not to separate a verb and its direct object with an adverbial modifier.

          Wrong:         I saw yesterday my friend.
          Correct:        I saw my friend yesterday.

          Wrong;         He is studying now Spanish at Madrid University.
          Correct:        He is now studying Spanish at Madrid University.

          Wrong:         She said that he had had already three drinks.
          Correct:        She said that he had already had three drinks.

32. Still means even up to the present time. It indicates some continuing action. Still usually comes BEFORE the MAIN verb.

          They are still working in that company.
          He still attends the same church.

33. Anymore indicates that an action that went on in the past has been discontinued. We usually place anymore at the END of a NEGATIVE sentence.

          He isn’t working in that agency anymore.
          We never see you at the school dances anymore.

34. Form the PAST tense of should and ought to with have and the past participle of the main verb.

          Present:        You should study more.
          Past:            You should have studied more.

          Present:        They ought to finish their projects.
          Past:            They ought to have finished their projects.

35. A conditional sentence has two clauses, a DEPENDENT CLAUSE beginning with IF and a MAIN CLAUSE.
         
          In a FUTURE possible conditional sentence, the dependent clause is in the PRESENT TENSE and the MAIN CLAUSE is in the FUTURE tense.

          If I have enough money, I will fly to Boracay.

          If you don’t hurry, we will be late for class.

Monday, November 13, 2017

ALS A&E MATH REVIEWER with SOLUTIONS

MATH REVIEWER

1. Find the median of the given data: 13, 16, 12, 14, 19, 12, 14, 13, 14.
          A. 19            B. 14            C. 12            D. 14.5

Ano ba ang MEDIAN? Ito ay katumbas ng AVERAGE. Just MULTIPLY all the data (numbers) and DIVIDE the sum by the NUMBER of the DATA.

SUM = 13+16+12+14+19+12+14+13+14 = 127
Ilan ang bilang ng data = 9
MEDIAN = 127/9 = 14.11
May dalawang choices na may 14 ang sagot. Isang 14 at isang 14.5
Ang tamang sagot ay B. 14 dahil may malapit ang 14.11 dito kaya sa 14.5
         

2. Simplify: {36 ÷ (-9)} ÷ {(-24) ÷ 6}

Sa ganitong mga problem, gamitin lang natin ang Rule on Order of Operation = kung anong operation ang dapat unahing gawin. Tandaan ang P E M D A S.
Una munang gawin ang mga numerong nasa P = Parenthesis.
Pangalawa: Gawin ang      E = Exponent
Pangatlo:      M = Multiplication
Pang-apat:    D = Division
Panlima:       A = Addition
Pang-anim:   S = Subtraction

Gawin ang susunod ng operation kung wala naman ang mga nauna rito.

Sa ating problem, merong mga numerong nakakulong sa Parenthesis, kaya iyon muna ang ating gagawin.

{36 ÷ (-9)} ÷ {(-24) ÷ 6}

(-4) ÷ (-4) = 1

Tandaan ang Rules on SIGN.
In dividing a negative and positive number, the sign of the quotient is NEGATIVE.
In dividing numbers with the SAME sign, either positive & positive  or negative & negative, the SIGN of the quotient is ALWAYS POSITIVE.


3. What should be added to 53/7 to get 12?
Bottom of Form

Pinahahanap tayo ng numbero na kapag ini-ADD natin sa 53/7 ang magiging sagot ay 12.
Ipagpalagay natin na ang ating hinahanap na bilang ay kinakatawan ng titik A.
Kaya,  A +  5 3/7 = 12

I-convert muna natin ang mixed number ( bilang na may whole number at praksyon) na
5 3/7 sa fraction. Paano ito gagawin? Just MULTIPLY the DENOMINATOR of the fraction part to the WHOLE number and then ADD the NUMERATOR of the fraction part and copy the DENOMINATOR of the fraction part.
Kaya,  (7 x 5 + 3)/7 = 38/7
Ang ating equation ay magiging:  A + 38/7 = 12
Para mapadali ang computation, i-MULTIPLY natin ang BUONG EQUATION sa 7 para mawala ang DENOMINATOR na 7. Tandaan, HINDI NAGBABAGO ang VALUE ng isang EQUATION kapag ang ginawa nating OPERATION sa LEFT TERMS ay GINAWA RIN natin sa RIGHT TERMS.

Ganito na ang mangyayari: 
7 x ( A + 38/7 = 12)
7A + 38 = 84
7A = 84 – 38
7A = 46
A = 46/7

Nakuha na natin ang value ng A. Ito ay 46/7.

Subukan natin itong ipalit sa ating equation na A + 38/7 = 12

46/7 + 38/7 = 12

(46 + 38)/ 7 = 12
84/7 = 12
12 = 12
Tama ang ating sagot.
Kung kailangang i-convert ang ating sagot sa MIXED number, gawin ito. PAANO?

I-DIVIDE lamang ang NUMERATOR sa DENOMINATOR ay idikit ang FRACTION

46/7  = 6 4/7

Para malaman kung tama ang conversion natin, gawin natin na FRACTION ang ating MIXED number na 6 4/7 …. (7 x 6 + 4)/7 = 46/7


4. Each side of a square is 62/3 m long. Find its Area.

          A. 444/9 m2                     B. 123/2 m2                C. 65 1/2 m2                   D. None of these.

Ano ba ang dapat nating malaman dito para makuha natin ang sagot?

1. Dapat alam natin kung ano ang HUGIS na isang SQUARE.
          Ang isang SQUARE o PARISUKAT (PARE-PAREHO ang SUKAT) ay may APAT na GILID (o SIDE) kung saan PARE-PAREHO ang kanilang SUKAT.

Ibig sabihin, ang SIDE 1 = SIDE 2 = SIDE 3 = SIDE 4

Sa ating problem, ang sukat ng mga SIDE ay 6 2/3 m.

2. Ano ba ang AREA?
          Ang isang AREA o LAWAK ng isang SQUARE ay ang SUKAT ng ISANG SIDE MULTIPLY by the OTHER SIDE. Dahil pare-pareho naman sila ng value, hindi na natin kailangan pang hanapin ang sukat ng isang side.

Kung A ay kumakatawan sa ating AREA, ang ating magiging EQUATION ay”

A = 6 2/3 m  MULTIPLY by 6 2/3 m.

Dahil mahirap magmultiply ng mga MIXED numbers, kailangang i-convert natin sila sa FRACTION. Katulad ng ating nagawa na sa Number 3, ang ating 6 2/3 sa FRACTION ay magiging   (3 x 6 + 2)/3 = 20/3

Ang ating bagong equation ay:

A = 20/3 times 20/3
A = 20/3  x  20/3

Paano ba mag-MULTIPLY ng FRACTIONS?

Madali lamang, I-MULTIPLY lamang natin ang NUMERATOR (yong numerong nasa ITAAS ng fraction) sa KAPWA niya NUMERATOR at I-MULTIPLY din natin ang DENOMINATOR (ang bilang sa IBABA ng fraction) sa KAPWA niya DENOMINATOR.

Kung gayon,  A =  ( 20 x 20) / (3 x 3) =  400 / 9
A = 400/9
Gawin natin ang ating sagot sa MIXED number. I-DIVIDE lamang ang NUMERATOR sa DENOMINATOR, kunin ang REMAINDER at ilagay ang Denominator.

400/9 = 44 4/9 m2

aNG atin sagot ay letter A.


5. Fill in the blanks:  5/-7 = ..../35

          A. 5              B. 25            C. -25           D. 30

Ano ba ang pinapahanap sa atin?

Pinapahanap sa atin ang NUMERATOR ng 35 upang ang magiging FRACTION ay KATUMBAS ng 5/-7

Paano ito gagawin?

Ipaghalimbawa na ang A ang hinahanap nating NUMERATOR.
Kung gayon,  5/-7 = A/35
Sa mga ganitong PORMA ng EQUATION, magagamit natin ang CROSS MULTIPLICATION kung saan i-MUMULTIPLY natin ang NUMERATOR ng LEFT TERM sa DENOMINATOR ng RIGHT TERM at ANG DENOMINATOR ng LEFT TERM sa NUMERATOR ng RIGHT TERM.( Pwede rin namang D1 x N2 = N1 x D2, dahil pareho rin ang kalalabasan)

5/-7 = A/35
(-7 x A) = (5 x 35)
-7A = 175
A = 175/-7
A = -25

Maging mapagmatyag sa SIGN ng ating sagot. Dahil NEGATIVE-POSITIVE sila, NEGATIVE ang SIGN ng ating sagot.

Ang ating sagot ay -25 , Letter C.

6. Simplify: 0 x 102

               A. 10            B. 10.2         C. 102                    D. None of these

Kahit hindi tayo mag-compute ay dapat alam na natin na ZERO ang sagot. BAKIT?
ANY NUMBER multiplied by ZERO is ZERO.

Letter D ang ating sagot.

7. Subtract – 8a from  - 3a.

          A. 2a            B. 5a            C. -11a         D. 11a

                                                

Tingnan at unawain ang problem. Paano ba natin isusulat ang ating equation?

          -8a – 3a = ?
          -3a – 8a =?
          -8a – (-3a) = ?
          -3a – (-8a) = ?

Ang sabi ay IBAWAS natin ang NEGATIVE 8a MULA sa NEGATIVE 3. Kaya ang tamang equation ay:
(-3a) – (-8a) = ?

Tandaan, kapag nagbabawas tayo ng NEGATIVE number, sa halip ng SUBTRACTION ay nagiging ADDITION ang operation.

Kaya,  (-3a) + 8a = 5a

Letter B ang ating sagot.

8. Solve:   x – 3 = 5

          A. -8             B. -5             C. -9             D. 8

Madali lamang ang pagsagot nito.

          x – 3 = 5

Ililipat lang natin sa right side ang whole number sa kabila.
Mag-ADD lang tayo ng numerong ililipat natin sa kanan.

Dahil -3 ang ating ililipat sa kanan, magdadagdaga tayo ng POSITIVE 3 sa magkabilang panig.

          x – 3 = 5
          x – 3 + 3 = 5 + 3
          x = 8

Letter D ang ating sagot.

Bottom of Form


 9. Two numbers are in ratio 4 : 5. If the sum of the numbers is 135, find the numbers.

          A, 60 and 75
          B. 50 and 56
          C. 70 and 95
          D. 65 and 75

Medyo may kahirapang sagutin ang tanong na ito sa unang tingin subali’t ito ay simple lamang. Maraming paraan at shortcut sa pagsagot nito. Doon muna tayo sa pinakamaikli.

Ang pinakamadali ay i-ADD natin ang mga BILANG na pagpipilian.
Ang A ay 60 + 75 = 135
Ang B ay 50 + 56 = 106
Ang C ay 70 + 95 = 165
Ang D ay 65 + 75 = 140
Dito pa lamang ay alam na natin na Letter A ang ating sagot dahil ang SUM ng ating hinahanap ng mga numero ay 135.

PAANO kung pare-parehong 135 ang pagpipilian? Ano ang ating gagawin?

SOLUTION 1.

Let x = multiplier so that we get the ratio of the two numbers and equate them to 135.
Kaya, 4x + 5x = 135
          9x = 135
          x = 135/9
          x = 15
Let’s substitute the value of x to our first equation.
          (4 x 15) + (5 x 15) = 135
          60 + 75 = 135
          135 = 135
Ang ating mga numbers ay 60 and 75, letter A.

SOLUTION 2
Ang ratio ng ating 2 numbers ay 4: 5
Kung ating unang number ay X at ang ating pangalawang number ay Y, ibig sabihin

X/Y = 4/5
Alam din natin na ang X + Y = 135

Narito ang ating 2 Equations

X/Y = 4/5  (Equation 1)
X + Y = 135 (Equation 2)

From Equation 1,    X/Y = 4/5    X = 4/5Y
Substitute the value of X into Equation 2.
  4/5Y + Y = 135
9/5Y = 135
9Y = 675
Y = 675/9
Y = 75

Subsitute the value of Y into Equation 1 to get the value of X

X/Y = 4/5
X/75 = 4/5
5X = 75 x 4
5X = 300
X = 300/5
X = 60

So our 2 numbers are 60 and 75, Letter A.

10. A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 liters of petrol?

          A. 213 km     B. 223 km     C. 203 km     D. 302 km

Sa unang tingin ay tila napakahirap ang ganitong problem subali’t simple lang ang pagkula nito. Gamitin lang natin ang proportion.

Kung ang 36 liters ay makakatakbo ng 522 km,
         Ang 14 liter s ay makakatakbo ng ____ km  or X km.

Kaya,  36/522 = 14/X
           36X = 14 x 522
          36X = 7308
          X = 7308/36
          X = 203 km
Letter C ang ating sagot.


SANA AY NAUNAWAAN!