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Math 2 Workbook

PHILOSOPHY OF EDUCATION

The course design of this workbook reflects a particular philosophy of education that emphasizespractice. From practice follows understanding, and then remembering. Researchers on theneurobiology of learning have found that the brain makes new neural connections when one is learningsomething new, and then strengthens these connections as we use our new knowledge more often.Thus, in a major way, learning is a biological process. t involves the growth of neural connections andstrengthening their insulating sheaths to avoid leakage. This biological process does not take placeovernight, but occurs gradually, with fre!uent use of new"found knowledge.

#earning re!uires practice, patience, persistence.

#earning math is in many ways like learning to swim, to ride a bicycle, or to play the piano. To learn toswim, you $not the instructor%& must jump into the water and do the e'ercises. #earning to ride occursonly when you, not anyone else, are on a bicycle, actually trying to balance it. (ery few, if any, canlearn to play the piano without doing e'ercises themselves on a keyboard. )ou cannot learn by simplywatching the swimming instructor do it, observing how others ride and control a bicycle, or watching amaster pianist play. #ikewise, you cannot learn math by simply listening to lectures either. )ou canonly do so by working on various math problems.

The course revolves around *++ problems, each problem reflecting one or more concepts that need tobe learned. The more problems you work on, the more familiar the concepts will become. Then, theneural connections in your brain will grow and become stronger. This is a biological process that takes

place gradually. ractice reinforces this process.

#ecturers have no -/0 or R0#-) keys. /o prefer to give lectures in hardcopy. Te't can be readagain and again. )ou can underline material, write side notes, return to the more difficult parts as oftenas you like, until something clicks in your brain $gets ko na%2&, the eureka moment. 3ive yourselftime. t will come. Those neural connections will emerge, and they will grow stronger with practice,and you will soon become aware of your new"found knowledge.

4onsider the course a self"discovery process. -t first, you may not know how to solve a lot of theproblems. The seatwork introduces you to the basic concepts. t is your chance to discover whichconcepts you have grasped and which ones are still elusive. This is part of the self"discovery process.

The homework is your chance to work on every problem and to focus on those problems that are givingyou a hard time. 5ften, solving a hard problem once may not be enough. f you are serious about thecourse, you probably need to do further self"study, on your own time, until you are sure you know theconcepts behind the problem and can use them with confidence to solve similar problems. The reviewerand the long e'am itself, will further spur you towards mastery of the subject.

6e will do this one problem, 1+ problems, 7+ problems at a time, for the rest of the course. t8s a lot ofhard work, but you will all learn, 8m sure. erhaps, some faster than others. 9ut you will hopefullydevelop learning habits that will serve you well, not only in college but beyond, not only in math but

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also in your chosen fields.

For many of you, this might the only math subject you8ll take for the rest of your stay in the niversity./o make full use of it. #earn as much math as you can. will try to make the whole process not only

painless but even an enjoyable one for my students.

Roberto /. (erzola

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STANDARD FORMAT

This is the workbook for ;ath * classes conducted by ;ath instructor Roberto (erzola. 6e will adoptsome practices which are specific to this course, to make it easier for the instructor to handle the high

volume of papers from students.

-ll submitted papers $homeworks, seatworks and reviewers& should follow the following standardformat.

#-/T/6>R6>#? age @@ of @@

;ath * /ection @@@ 3roup @@@ Aate /ubmitted

1. Final 4omplete solution here

answer here

(ertical line =orizontal line between numbers

*. Final

answer here 4omplete solution here

The numbering of problems should follow the workbook numbering $for e'ample, B1++"11+&. roblemnumbers should be written on the left column and encircled, so that the number is clearly differentiatedfrom the final answer.

se only one side of the paper.

se only blue or black ink. Ao not write in very small lettersC write legibly.

/ubmissions of two or more pages should be stapled.

6hen you correct your own papers, put your check and cross marks along the vertical line, so that theinstructor can see them in one glance.

apers which do not follow the specified format will be not be counted, and you will be asked to redothem.

6e will use the asterisk2 $D& or the dot2 $E& for the multiplication symbol. 5n many occasions, eventhis symbol will be omitted. Thus, :' means :D'. The letter '2 will always be used as a symbol for a

variable or an unknown, not for multiplication.

The caret2 $sometimes called cap2& character $& will be used for e'ponentiation in printouts,whenever limited typography makes it hard to print out elevated small types. Thus 'G and 'H may alsobe shown as '* and ':.

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Math 2 Workbook: Part 0

MINIMUM PREREQUISITES TO PASS THIS COURSE: 5 SILLS AND 2 HA!ITS

The following five skills should have been ac!uired in high school. They are essential for anymath course. )ou should be familiar J in fact, you should master J these five. 5therwise, it will be ne'tto impossible to pass ;ath *. ;ake sure you understand each of them completely, and that you canapply them to any math problem. The five skills areK

1. Rounding off*. 4onverting units:. /olving for the unknown in an e!uationI. 3raphing e!uations7. 4omputing the perimeter and area of simple figures, and the surface area and volume of simple

solids.

The two habits that students of this course should develop areK1. Ao not omit important steps in your written solution. Ao not do them mentally. nstead, write

down every step, so that your written solution proceeds in a logical, step"by"step manner.*. Aouble"check your final answer. The double"checking should be part of your written solution.

Five bad habitsK1. Rounding off intermediate results*.

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not be taken into account in rounding off rules. They don8t matter, when rounding off.

0'amples of ine'act numbersK" measured numbers such as length, weight, time, temperature, etc. $such as numbers read off from a

dial or some other measuring device&" e'act numbers which have been rounded off $for instance, a school enrollment of *,++1 may be e'act,but the number of students may be rounded off to two thousand and then written down as *,+++&

f you use an ordinary ruler with subdivisions in centimeters $cm& to measure lengths, you might readoff a length as 1*.: cm. This means you are sure about the digits 1 and *, but the : may actually be * orI. f the subdivisions are in +.1 cm $or 1 mm&, then you might read off the length as 1*.:I cm, seeingthat the length is slightly nearer to 1*.: than to 1*.I cm. 5ther measuring devices like calipers andmicrometers are even more precise and may allow you to read of the object8s length as 1*.:IM cm. -measuring instrument8s precision refers to the number of decimal places you can read off its dial.

/uppose a highly precise measuring instrument determines the length as 1*.:I7M cm. This number hasI decimal places $there are I digits after the decimal point&, and M significant digits $* digits before thedecimal point, and I digits after it&. 6e know from the nature of measuring instruments that thenumber8s last digit M is uncertain.

To round off the number to : decimal places $or to 7 significant digits&, we must retain all digits up tothe digit 72 and remove all other digits to its right. f, in addition, the removed digit nearest to 7 was 7J N, we also increase the least significant digit $in this case, 7& by 1. Thus, the number above rounds offto 1*.:IM.

To round off the number to * decimal places $or to I significant digits&, we must retain all digits up tothe digit I2 and remove all other digits to its right. The removed digit nearest to I was 72, which stillcovered by the 7"N rule, so the number rounds off to 1*.:7.

To round off the original number to 1 decimal place $or to : significant digits&, we must retain all digitsup to the digit :2 and remove all other digits to its right. n this case, the removed digit nearest to :was I2 $always look at the original number%&, so the last significant digit is retained as is. Rounded offto : significant digits $or 1 decimal place&, the length is 1*.: cm.

To summarize the rounding off rulesK $understand them, do not memorize&1. f a digit to be rounded off is + to I, just drop it and all other digits to its rightC*. f a digit to be rounded off is 7 to N, do as in B1 above. Then, increase the digit to its left by 1.:. f the digit to be incremented in B* above is a N $thus, it becomes 1+&, follow the usual rules for

carrying over the 1 to the ne't digit to the left.

Aescribing the process probably takes longer than simply giving e'amples. =ere are some e'amplesK

Ro#$% o(( 765.4521to: A$*,r:

1. one decimal place LM7.7

*. two decimal places LM7.I7

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false impression of precision. /o your answer M7.I:7 should be rounded off to M7.I. The same is truefor subtraction.

Thus, for additions and subtractions, the result should be as precise as the least precise decimal place of

the terms involved.

f you are multiplying numbers which have been rounded off, and the least precise among them has 7significant digits $let8s say others may have M, L or more significant digits&, then your answer should berounded to 7 significant digits $not M or L, etc.&

/uppose you are multiplying *.1 and 1*.:, which have * and : significant digits, respectively.

This is how the multiplication goesK

1*.:

' *.1""""""" 1*:

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Thus, we can also write1 ft

12 in.=1 or

12 in.

1 ft=1 because 1 foot and 1* inches are actually the same

length, just e'pressed in different units, and any value divided by itself is always 1.

/o, to convert *: feet to inches, we do the following conversion process, as followsK

23 f t x12in.

1 ft

/ince12 inches

1foot$we can also read it as 1* inches per foot2& is e!ual to 1, we have simply

multiplied *: ft by 1. Therefore, we have not changed its value, because if we multiply any value by 1,we get the same value.

ft. -nd we got*LM inches. /ince we multiplied by 1, we are still describing the same length, but we have changed theunit of length to inches.

6hen doing conversions, alwaysindicate the units of measure involved. Aoing so will help you avoidmistakes like multiplying instead of dividing or forgetting a step in the conversion process.

For a more complicated e'ample, let8s convert km>hr to inches>secK

9asically, we want to convert km into inches and hr in seconds, #et8s do the km"to"inch conversionfirst. 6e can convert km to meters, and then meters to cm, and then cm to inch. To do this, we need todo the following conversionsK

Remember, we are starting withkm

hrand our target is

in.

sec.

To convert km>hr to m>hr, multiply by km>hr by 1+++ m>km, cancelling km out, leaving only m&Kkm

hr

1000 m

km=

m

hr

Thus, you multiply by 1+++.

To convert m>hr to cm>hr, multiply m>hr by 1++ cm>m, cancelling m out, leaving only cmKm

hr100cm

m =

cm

hr

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Thus, you multiply by 1++.

To convert cm>hr to in>hr, multiply cm>hr by in.>*.7I cm, cancelling cm out, leaving only inchKcm

hr

1in.

2.54 cm

=in.

hrThis time, you divide by *.7I.

km, we are multiplying by 1 because 1+++m 1 km. -gain,when we multiply by 1++ cm>m, we are also multiplying by 1 because 1++cm 1 m. -nd again, whenwe multiply by inch>*.7I cm, we are again multiplying by 1 because 1 inch *.7Icm

/ince we keep multiplying by 1, the actual value is not changing, only the units are changingK from km,to m, to cm, and finally to in.

/ince 1 km 1++,+++ cm, we can shortcut the conversion as follows, km>hr D 1++,+++ cm>km cm>hr.

#et8s now do the same thing for the time unit. 6e want to convert in.>hr to in.>sec. =ere8s thecontinuation of the conversion processK

in.

hr=

hr

60 min=

in.

min, cancelling out hr, leaving in.>min. Thus, we divide by M+.

in.

min

min

60sec=

in.

sec, cancelling out min, leaving in.>sec. Thus, we again divide by M+, ending the

conversion process. 6e have converted km>hr to in.>sec.

-gain, since 1 hr M+ min and 1 min M+ secs, we simply multiplied by 1 and didn8t change any value,only the units.

/ince 1hr :,M++ seconds, we can shortcut the conversion as follows, in>hr D hr>:,M++ sec in>sec.Finally, here8s the complete conversion processK

km

hr

1,000 m

km

100cm

m

in.

2.54 cm

hr

60min

min

60 sec=

in.

sec

6hen you are writing the entire conversion procedure, make sure you cancel out the units of measurescarefully $always in pairsK one in the numerator, and another in the denominator&. )ou know you aredone if the only units left the units you are after $inch>sec in the above e'ample&.

To remember the e'planation above better, write out the e'ercise on paper.

The method described above is called dimensional analysis, which involves looking at the units ofmeasure to help you determine the correctness and consistency of e!uations.

#et us review the process once moreK

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To convert a unit of measure in the numerator $such as km in km>hr&, multiply it by a conversion factorwhich has the same unit in the denominator, so that the unit cancels out.

For instance, to convert from inch>hour to centimeter>hour, do we multiply or do we divide by *.7IQ

6e know that 1 inch *.7I cm. /o we can write the conversion factor as1in.

2.54 cmor as

2.54 cm

1in..

f we use the first, we divide by *.7I. f we use the second, we multiply by *.7I. To convert inch in thenumerator to cm, know we should use the conversion factor with the inch in the denominator, so thatinch unit cancels out, leaving cm. Thus, we multiply by *.7I cm>in.

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miles>min km>day feet>hr 4onversion rates

1.IM 1 mile 1.M1 km

7M.O *.7I cm 1 inch:*L

*.4onvert the given water consumption by a family, to three significant digitsK

cu.m.>mo gal>day li>hr 4onversion rates

N*.1 1 cu.m. *MI.* gallons

:O.: 1 gallon :.LO7 liters

*.L7 1 month :+ days

:.4onvert the temperatures on the left. $ 4 P *L:.17&. Round"off to the same number of decimalplaces as the data. )ou can use the formula F :* P N4>7

4 F

1+++

1++

"1+

I.6hat is "NOF in degrees 4elsius and elvinQ $to the nearest tenth of a degree& $ 4 P *L:.17&

7.4onvert I,:N*.L seconds into hrsKminsKsecs $do not round"off&.

4. So+9&$' (or th, #$k$o$: ;&9,$ a$ ,

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end of the see"saw, you must also add e'actly three people at the other end, to keep it in balance.

f you then remove one person at one end $leaving two&, you also need to remove one at the other end,to keep it in balance.

f you triple the number of people at one end $from two to si'&, you must also triple the number at theother end, to keep it in balance.

f you halve the number of people at one end $from si' to three&, you must also halve the number at theother end, to keep it in balance.

Finally, if you s!uare the number of people at one end $: times : is nine&, you must also s!uare thenumber of people at the other end.

n short, whatever you do to one end of the see"saw, you must also do it at the other end, to keep the

see"saw in balance.

t is e'actly the same with an e!uationK whatever you do to the #=/, you must also do to the R=/, topreserve the e!uality, whether it is adding a number, subtracting, multiplying, dividing, or raising to apower.

)ou must remember this very wellK treat both sides e!ually. 9e fair to both sides.

Ea*) ,3a/-+,

6hen you are solving for ' $or any other unknown variable&, your goal is an e!uation where theunknown is alone on one side of the e!uation, and the rest of the numbers>variables are on the otherside. n short, you want to arrive at an e!uation that looks like thisK

' U everything else should be on this side V

/ince ' is alone on the #=/ $it could also be the R=/&, you have already solved for '.

#et8s have an easy e'ampleK given ' P * 7, solve for '.

)ou probably know the answer already, but let8s follow the process in detail.

/ince you want ' to be alone, you want to remove J or strip away J * from the #=/.

To do so, subtract * from bothsides of the e!uation. 9e fair. Treat both sides e!ually.

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A$oth,r ,3a/-+,

/olve for 'K :' P 7 1I

5n the #=/, ' is stuck with two other numbersK : and 7. 6e want to strip away these numbers, leaving' on the #=/.

;ultiplication is more sticky than addition. /o we will undo the addition first and subtract 7 from the#=/. 9ut we have to subtract 7 from boththe #=/ and the R=/. $9e fair%& The e!uation now becomesK

:' P 7 " 7 1I " 7 $on the yellow pad, write "7 under7 and also under1I&.

/ince 7 " 7 +, the above e!uation becomesK :' N

6e are still left with the sticky : together with '. 6e want ' to be aloneC how do we remove :Q /ince :is multiplied to ', we can make it disappear by dividing bothsides $#=/ and R=/& by :. The e!uationnow becomesK

3x

3=

9

3$on the yellow pad, write >: under :' and also under N&.

n the #=/, the : above the division line and the : below it cancel each other out, leaving ' alone.Thus, we haveK

' : and we have solved for '.

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5n the R=/, we will remove the 1 first $addition is less sticky&, and then we will remove the *.

L " 1 *' P 1 " 1 which gives us the simpler M *' $on the yellow pad, write "1 under L and under 1&.

M>* *'>* $on the yellow pad, write >* under M and under *' J this is a habit you must develop%&

The *s in the R=/ cancel each other out, leaving ' alone in the R=/K

: '

Thus we have solved for '.

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/uppose we have two unknowns, ' and y. f we solvefor ', we will have y on the other side of the e!uation,still unknown. f we solve for y, we will have ' on theother side, still unknown.

To determine the actual values of the two unknowns, wewill need two e!uations involving both unknowns. 6ecan solve one of the e!uations for the first unknown, say', in terms of the other unknown, say y. Then we cansubstitute the value of ' into the second e!uation. Thiswill eliminate ' in this e!uation, leaving only y. Finally,we can solve for y.

-fter we solve for y, we can go back to one of theoriginal e!uations, substitute the value of y, and solve

for ' this time.

=ere8s an e'ample of two e!uations with twounknownsKy *D' and y :* P ND'>7

#et us substitute the value of y in the first e!uation, for the y in the second e!uationK*D' :* P ND'>7

7"ND'>7 "ND'>7 $7 J ND'>7 :*'>7 :*D7 D7 $-gain, note how we wrote the termcanceling out >7 below the previous e!uation.&' 1M+

/ubstituting the value of ' into one of the e!uationsKy *D'y *D1M+y :*+. 6e8re done%

6hy do we keep emphasizing that the cancelling termsbe written noton the same line but on a newlineQ9ecause we want to preserve the originale!uation, sothat if we go back and check for errors, the originale!uation will still be there. This is a good habit todevelop when manipulating e!uations.

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

Equation B=2A on the A-B plane

A

B

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

1, 2

2, 4

3, 6

4, 8

5, 10

Table o !alue" on the A-B plane

A

B

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#et us do the other good habit when solving problemsK double"check our answers. 6e got '1M+ andy:*+. f we substitute these numbers into one of the original e!uations, we getK :*+ :* P ND1M+>7C:*+ :* P ND:* :*D$1PN& :*+. 4heck%

-nother important consideration when manipulating e!uations is to know which operations are donefirst. They listed here in the order of decreasing priorityK6hich operations are done firstQ

1. operations inside parenthesisK innermost parentheses first, outermost parentheses last*. special operations $log, e'p, tan, sin, cos, etc.&:. e'ponentiationI. multiplication, division7. addition, subtraction

6hen undoing them to isolate the unknown, reverse the priorityK remove the addition and subtractionterms first, multiplication and division ne't, and so on, until the parentheses.

=ere are additional rules for algebraic operationsK1. commutative ruleK aPb bPaC aDb bDa*. associative ruleK $aPb&Pc aP$bPc&C $aDb&Dc aD$bDc&:. distributive ruleK aD$bPc& aDb P aDc

E3,r.&*,*:

M. -P1* :L. /olve for -.L. 1*D9 NM. /olve for 9.O. :4 P 7 *+. /olve for 4.N. MA P O *A. /olve for A.1+. 0 mcG, where 0 is energy, m is mass and c is the speed of light. /olve for m. /olve for c.11. F ma, where F is force, m is mass and a is acceleration. /olve for m. /olve for a.1*. The body mass inde' 9; 6>=, where 6 is in kg and = in meters. /olve for 6. /olve for =.

1:. / A>T where / is speed, A is distance and T time. /olve for A. /olve for T.1I. 1++ D $- J 9& > 9. /olve for -. /olve for 9.17. F :* P N4>7 $4elsius to Fahrenheit conversion&. /olve for 4.1M. -t what temperature is the Fahrenheit reading e!ual to the 4elsius readingQ1L. -t what temperature is the Fahrenheit reading twice the 4elsius readingQ1O. ;aria is now three times as old as edro. Five years from now, she will be twice as old as him.=ow old are they nowQ

A. ;ra-h&$': ;&9,$ a$ ,

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5ne way to draw a graph is to start with a table of values, for e'ampleK

- 1 * : I 7

9 * I M O 1+

#et us assign - to the horizontal a'is, and 9 to the vertical a'is. Thus, the plane on which we will drawour graph will be called the -"9 plane. The intersection of the -" and 9"a'es is called the origin. Thepoint where -+ and 9+ $right& is called the origin.0ach pair on the table can be drawn as a point on the -"9 plane. #et us consider the first pair of - and9 valuesK $1,*&. =ere, we are following the convention where the value for the horizontal a'is $-& islisted first, and the value for the vertical a'is $9& listed ne't, and the pair is enclosed in parenthesis. Tomap $1,*&, we start from the origin then move horizontally to the right 1 unit and vertically up * units.For the ne't point $*,I&, we move * units to the right on the horizontal a'is then I units up on thevertical a'is. For $:,M&, it is : units to the right on the horizontal and M units up on the vertical. -nd soon. The points are mapped on the graph on the right.

nstead of a table, we can also graph e!uations. 4onsider for instance the e!uation 9 *D-. The firststep is to create a table for values for - and 9. That is, assume a value for -, then use the e!uation tocalculate 9. -ssume another value for -, and get a value for 9. 9y putting various values of - in thee!uation, we get corresponding values for 9. The table we graphed earlier is actually based on thise!uation. n the case of an e!uation, however, - $and correspondingly, 9& can take many values and atable cannot contain all the possibilities. /o, we can only put a few selected pair of values on the table.

f we are graphing the e!uation instead of the table, the variable - can take any value between 1 and *,

between * and :, : and I etc. t can also take values lower than 1 or greater than 7. -nd for each -, wewill have a 9 that is twice -. Thus, the graph of the e!uation 9 *D- will not be just a few points, buta continuous line, as shown on the right.

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*+. 3raph the 4elsius to Fahrenheit conversion formula, taking F as a function of 4, for + W 4 W *++.*1. 3raph A as a linear function of T, given the following $T,A& valuesK $1+,+&C $*+,O&C $I+,*I&.**. -fter the graph above is done, visually estimate A when T1M. (isually estimate T when AI+.

0. Pro-,rt&,* o( *&/-+, ',o/,tr&. (&'#r,* =-,r&/,t,r ar,a> a$% *o+&%* =*#r(a., ar,a 9o+#/,>: )o#*ho#+% b, ab+, to .a+.#+at, th, -,r&/,t,r ar,a or *#r(a., ar,a a$% 9o+#/, o( th, (o++o&$'',o/,tr&. (&'#r,* a$% *o+&%*: tr&a$'+, r,.ta$'+, -ara++,+o'ra/ .&r.+, -r&*/ .#b, .)+&$%,r a$%*-h,r,1

The perimeter of a flat multi"sided figure is the total length of the lines enclosing its area. For figureswith straight sides $polygons&, just add the lengths of every side. For circles, the perimeter is called thecircumference. The circumference is X $pi2& multiplied by the diameter $Xd&, or X times double theradius $4 *Xr&.

F&'#r, P,r&/,t,r Ar,a

aPbPc bh

*$wPh& wh

*$aPb& bh

*Xr Xr

So+&% S#r(a., Ar,a "o+#/,

*- P #$aPbPc&$- bh&

-#$- bh&

*$ab P bc P ac& abc

a

h

b

c h

a

b

h

r

a

a

#

c

b

bc

h

wY

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*XrDh P *$Xr& XrDh

IXr 4

3 r

3

The best way to learn these formulas is to work with them enough number of times. Then, they willetch themselves in your mind and you can remember them easily. For most solids, breakdown thesurface area into components and add the areas of all the components that enclose the space within the

solid.

E3,r.&*,*:

*:. The area of a triangle is one"half its base times its height $- Z DbDh&. - triangle has a heighttwice as long as its base. f its height is 1+ inches, what is the area of the triangleQ*I. The area of a rectangle is its base $or width& times its height $or length&. That is, - bDh lDw.6hat is the area of a rectangle whose base is 1+ cm and who height is 7 inches longer than its baseQ*7. The area of a circle is X times the s!uare of the radius $- X Dr*&. Find the area of a circle whosediameter is 1* inches.*M. -ny polygon can be broken up into triangles. The area of the polygon is then the total area of its

component triangles. 4onsider a rectangle with sides b and h. Araw diagonal lines between theopposite corners of the rectangle, splitting the rectangle into I component triangles. /how that the sumof the areas of the four component triangles is e!ual to the area of the rectangle.

bc

h

r

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PRO!LEM SET 4650

-. Ro#$%&$' o(( r,9&,. 3iven the number ? 7I7I.7I7I7I..., round off ?K1. to the nearest hundred

*. to the nearest ten:. to : significant digitsI. to M significant digits7. to the nearest tenthM. to : decimal placesL. to the nearest hundredthsO. to the nearest centavo $assuming ? is in pesos&

4onvert the following decimals to a fractionKN. +.7I71+. +.7I7I7I.... $=intK 0!uate the decimal to ?, multiple both sides by 1+, subtract ? from 1+?, then

solve for ?.&

9. Co$9,r*&o$ r,9&,1 3iven the following conversion factorsK 1 meter 1++ centimeters1 mile 1.M1 km 1 km 1,+++ meters 1 gallon :.LO7 liters1 inch *.7I cm 1 foot 1* inches 1 cubic meter *MI.* gallons

4onvert the following measurements as indicated, and round off your answers to : significant digitsK11. *L in. @@@ ft1*. *O,LN: in @@@ km1:. 1 million cm @@@ mi.1I. +.++IL mi @@@ cm17. :M1 km>day @@@ ft>sec1M. *1O liters>hr @@@ gals>day1L. 11L mH>min @@@ gals>day1O. 7[>year @@@ [>month1N. I: hrs *1 mins :* secs @@@ hrs $to 7 significant digits&*+. I7,:1* seconds @@@ hrs @@@ mins @@@ secs

4. A+',bra r,9&,: *o+9&$' (or ?*1. ? P :* L7**. LD? OI*:. ?>N J L :*I. I7>? J * L*7. ?>*I P ?>M+ :*M. *? P L 1+? J 1L

*L.I?*

*'M =:

*

*O.X7

X1+=X:

XI

*N. ? :* P N)>7C ? *). /olve for ? and ).

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I7. Find the circumference of the circle on the right.IM. Find the area of the circle on the right.

IL. Find the surface area of the figure on the right.IO. Find the volume of the figure on the right.

IN. Find the surface area of the cylinder on the right.7+. Find the volume of the cylinder on the right.

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