Calcu Techniques

Today, I will teach you the Calculator technique use to solve Math problems. In this tutorial I will be using CASIO !"##$ %S. So don&t as' me on how to do it in other calculator. Moreover, I will not cover the CASIO !"##$ %S ()*S although, some o you thin' its the same, I say to you it&s dierent in someway or in some unctions especially in STAT MO+%. This is good and very helpul especially in oard %!am and in some school na hindi 'ina'ailangan ng solution-multiple choice lang. Sa una nahirapan a'o dahil iniisip 'o 'ung paano 'o isusulat ang mga equation. Ayun nagawan 'o naman ng paraan. Requirement in this MATH CALCU tutorial: $. asic 'nowledge in math- /ou cannot understand it i you don&t 'now the basics..Mostly shorcuts ito 'aya you should 'now the basic.. 0. CASIO 12"##$ %S with the manual 3. 4ead your manual-all the unctions and deiniton o each will be ound in the manual 5. rain6Common Sense 7etting amiliar with the unctions $. 8hat are the roots o the polynomial9 A. "3, "5 . :, 0 C. 0, 3 +. 3,5 Code9 Set Calculator to equation mode9 MO+%; = $ 5 = "? = = And you will get the answer..

3. 8hich o the ollowing is a possible root o the polynomial9 A. 3 . @ C. "0 +. 5 Code9 OT%9 A root is any value that, when substituted to the variable-ie !, will satisy the equation.-In our equation @=@  Set the calculator to computation mode9 MO+%;$ Input O)/ the let side o the equation. Trial and error, *se the CA)C* unction.. (ag nagtanong ang calculator 2B iinput ang mga choices.. 2B 3 = output is 05@.. repeat the step until you get an output o @.. And you will get the answer.. 5. 1ind the value o ! and y in the ollowing equations9

A. "$06$#, $:6$# . "056$#, "006$# C. $06$#, "$:6$# +. 056$#, 006$# Code9 Set calculator to equation mode9 MO+%;$B A. 5#> . 3:0>> C. 03:>> +. 0:3>> Code9 Convert niyo lang sa decimal.. MO+% 5..Set to I then type the number.. (ress +%C and you got the answer.. Additional TP: Gung hindi na 'asya sa calculator at sobrang haba ng I mo, iconvert mo muna sa OCT.. $@$=< $$@=: @@$=$ $$$=> $@$=< Set to OCT and type the OCT equivalent, < And press +%C and you got the answer..

$0. 1ind the he!adecimal equivalent o

!

A. . C. +. Code9 Type niyo lang sa calcu..8ag 'alimutan base ? and base $@ yan.. (ress D%2 or the inal answer.. $3. %valuate A ! .

A.

.

C.

+. Code9 MO+% :;AC.....Tandaan daanan lagi si +IM.. SDI1T;5;$ Itype ang matri! and that&s it.. /ou got the answer.. Additional TP: I A6, +O&T use divide, instead use the reverse unction..And it will be li'e this

$5. 1ind dy6d! i A. @.533

and

when

. @.?:: C. $.@?3 +. $.>30 Code9 (ag Trigonometric6Inverse, i"set ang calcu sa 4A+IA MO+%.. I"type sa calcu li'e this..

/ung

po natin diyan, pi po yun..

$ to ## t6sB A. ?3.3 t . #@ t C. #:.> t +. $@@ t Code9 7et the limits rom the equation when d=>..*se %K 5.. 0 < @ "> 7et the real number and that is your lower limit.. 7et the limits rom the equation when d=##..*se %K 5.. 0 < @ "## 7et the real number and that is your upper limit..

Then integrate the equation using your lower and upper limit..

And you will get the answer.. 0>. Solve or the general solution o the dierential equation9 A. . C. +. Code9 7et the roots..*se %K 5..$ @ @ ? /ou will get one real root and two comple! roots.. ,E: (ag real root = (ag comple! root = sin and cos 0?. Solved or the particular solution o the dierential equation9 ! F y dy6d! = 0 when !=$ and y=$ A. . C. +. Code9 Choice one rom the choices and Convert the equation to y=-!.. +ierentiate using your calculator with !=$-as given and you will get the value o dy6d! Substitute !, y and dy6d! to the equation in the problem and see i it is equal to 0... 0=0 I yes, then your choice is the right answer.. 0#. Solve or the general solution o the dierential equation y&"y = 0.. A. . C. +. Code9 Choose one in the choices.. Choose your avorite number or C and ! and substitute it to your choice.. And solved or y..i"note.. i"dierentiate ang iyong napiling equation with !=-'ung ano ni"substitute mo sa una, be consistent /ou will get the y& Then susbtitute in the given equation y&"y=0......i

0=0 Thereore, napili mo ang tamang answer.. SESS!" 2 PART . 3$. A radioactive substance decreases rom $@ grams to # grams in two hours. 1ind its hal lie. A. $@.$# hr . $$.5# hr C. $0.?# hr +. $3. $: hr Code9 +ahil sa ito ay radioactive, nagiincrease ito e!ponentially. 8hich means 'ung e!ponentially ito, gagamitin natin ang STAT < C. indeterminate +. ininity Code9

Same method lang po sa J$. So, napaisip 'a ngayon 'ung paano ininityB. Ano po ba ang ininityB Ito ay isang mala'ing number. So press CA)C... .!B ininity = $@@@ or 'ahit anong mala'ing number basta wag lang magMAMATD error. And you will get the answer.

3. 1ind A. "$ . $ C. "0 +. 0 Code9 Same method as J$.

5. 1ind A. @ . $63 C. $ +. 3 Code9 Same method lang din sa J$. (ero wag 'alimutan na ilagay sa rad mode ang calcu.

. 1ind the derivative o A. . C. +. Code9 This time I assume na marunong na ang lahat at pamilyar na 'ayo sa mga steps at unction na ginagawa natin. +on&t orget9 Always use rad mode in trigonometric and inverse trigonometric equations. 7amitin ang d6d! unction. SDI1T;IT%74A) then i"type ang equation. At maglagay ng value ng !. /oure avorite number. I preerred Kuote9 Remem%er: m$=m0 -tangent6parallel m$= "$6m0 -normal6perpendicular And y=5!F3 should be tangent to y=!0FC 1irst, get the irst derivative or slope o y=5!F3. *se d6d! with !=$, thereore the slope is 5. equate y& = y& -y=5!F3 = -y=!0FC 5 = 0! and ! = 0. Then get the value o y rom y=5!F3

at the point where !=3.

y = $$. Thereore, our pt is -0,$$ Substitute this to / = !0 F C to get the value o C. share 'o lang din ng CA)C* T%CDIK*% sa )aplace Transormation9

%!amples9 $. 1ind the laplace transorm o 3t4 5 cosh 6t a. -< 6 s0 " 0