PDF- -CALIFORNIA INSTITUTE OF TECHNOLOGY - calc tech

- Part 1

Getting familiar with the functions 1

What are the roots of the polynomial: A

- 3,4 Code: Set Calculator to equation mode: MODE>5>3 for quadratic equation Mode 3 because our polynomial is a 2nd degree equation

- -7 = 1 2 = =

Which of the following is a possible root of the polynomial: A

- 4 Code: NOTE: A root is any value that,

when substituted to the variable(ie x),

- will satisfy the equation

(In our equation 0=0 ) Set the calculator to computation mode: MODE>1 Input ONLY the left side of the equation

Pag nagtanong ang calculator X

- ? iinput ang mga choices
- ? 3 = output is 240

repeat the step until you get an output of 0

1,2,3 B

1,2,5 C

1,2,4 D

Code: Set Calculator to equation mode: MODE>5>4 for cubic equation Mode 4 because our polynomial is a 3rd degree equation

Find the value of x and y in the following equations:

-12/19,

16/19 B

-24/19,

-22/19 C

-16/19 D

- 22/19 Code:

Input the equation coefficients a,b,c: 1 =

-7 = 1 4 =

And you will get the answer

Solve the values of y in the system of equations: Input the coefficients of a,b and constant c'of the second equation:

- -3 = 5 = 2 = Press the = to get the value of x and press again to get the value of y

And you will get the answer

- both of which are positive

- 4 Code: Same method with number 3

We will be using CALCU function

The calculator should display 0

What is the remainder of the polynomial when divided by A

- 305 Code: Set the calculator to computation mode: MODE>1 Input the left side of the equation Apply the Remainder theorem Use CALCU function and substitute x=5 And you will get the answer

Code: Set the calculator to equation mode: MODE>5>2 Input the coefficients a,b and constant c'of the first,

- second and third equation

Press the equal = button twice to get the value of y

- -2i Code: Set the calculator to computation mode: MODE>1 Input the equation in the calculator(as is)
- and you will get the answer

Solve for the value of A

- 91 Code: Set the calculator to computation mode Input the equation in the calculator(as is)

- 13 Code: Set the calculator to computation mode Input the equation and use the SOLVED function to get the value of x

To get the SOLVED function,

X= answer L-R= 0 (important,

must be 0) And you will get the answer

- PART 2

Set the calculator to computation mode: MODE>1 Input the equation as is but replace k with X

Code: Set calculator to computation mode

2290 Code:

type the equation and assign an arbitrary constant to substitute to x and use the CALC function

for example X=8 The calculator will display "2197"

substitute 8 to the choices and find which one will be equal to "2197"

What we do as well in the previous examples like this is called "REVERSE ENGINEERING"

Find the 15th term in the arithmetic sequence: 1,3,5,7

31 Code: 1

And X column natin ay ang nth term while sa Y column natin ay ang A

Input sa X column ang 1,2,3(1st term,2nd term,

3rd term)

Sa Y column naman,

iinput ang 1,3,5 (kahit 3 number lang,

- kahit wag na yung 7)

- 2nd term is 3 and 3rd term is 7

After niyo mainput,

press AC(don't worry hindi mabubura ang data niyo) Sa problem ang hinahanap ay ang pang 15th term

anu ba ang value ng ika15th term

meaning ang hinahanap ang value sa Y column

- type 15Y-hat

while ang X-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>4(X-hat)

take note of this dahil gagamitin natin ito in the next problems

And you will get the answer

Find the 12th term in the geometric series: 3,

59,049 B

177,147 C

531,141 D

- 1,594,323 Code:

) May makikita kayo X and Y column

And X column natin ay ang nth term while sa Y column natin ay ang G

3rd term)

Sa Y column naman,

- iinput ang 3,9,27

- 2nd term is 9 and 3rd term is 27

press AC(don't worry hindi mabubura ang data niyo) Sa problem ang hinahanap ay ang pang 12th term

anu ba ang value ng ika12th term

meaning ang hinahanap ang value sa Y column

Therefore,

- type 12Y-hat

- 441 Code: 1

Set the calculator to STAT mode: MODE 3>2 (since it is A

- input 1,2,3

In the Y column,

- input 1,3,5

After you input the data,

- press AC

we will use the SUMMATION function

(SUMMATION symbol is like E) 5

then that's the time we use 0 to 20

- walang Y-hat na symbol e

- 6/7 Code: 1

MODE>1 Since this is an infinite series,

with a common ratio of less than 1,

then the sum is a finite number

- the sum is infinite)

So it will be like this

Then press =

- 5462 Code: 1

MODE3>2 (I hope you already know why MODE 3 2) 2

In the X column,

- input 1,2,3

In the Y column,

- input 6,9,12 then press AC

We should get the sum but we don't know how many term does it have

- our code is 171Xhat

Since 171 is our last term

now use the SUMMATION function like in number 26 but this time,

- its 1,56

1/3125 B

1/15625 C

-1/3125 D

- -1/15625 Code: 1

Set the calculator to Computation mode

Input the general equation of the infinite series and substitute 5 to x using the CALC function to display the 6th term

And press =

- (5+10i)/6 C
- (2+i)/3 Code: 1

(NOTE: The imaginary i is found by pressing the ENG key

Then press =

The function discontinous at x=

- either a or b D
- neither a nor b

SESSION 2 PART 1 1

Subtract A

mageerror siya sa value na isusubstitute mo or yung tinatawag na MATH ERROR

Pag may lumalabas parin na value positive or negative or even zero,

- continous parin yun
- dapat mageerror siya

Siguro naman kayang kaya niyo na ito

Set the calculator to COMP MODE

- type na equation as it is

press the CALC function and substitute the numbers in the choices and find which one will get an error

The one error is the answer

- 2mm of water fell

Find how many gallons of water fell on a level 10 acre park

21,381 B

25,381 C

27,381 D

- we use the TABLE function

? (your number depends on the choices

we start from the lowest which is

- -2 then press = END

? (the largest in the choices)

? (The variation in the choices)

kailangan madaanan nung function yung mga choices

So enter 2 and press =

V=10 acre (convert acre to m^2)SHIFT>8(for CONV)>11(for acre>m^2)

- 002 m(given in the problem) and it will display 80
- 93712 in m^3

- 1 m^3 = 1000L

12 in L

Finally convert this to gal

- (x-2) B
- (2x+3) D

all of the above Code: Para masabing factor siya,

kailangan ang y=0 pag isusubstitute natin yung root of x

We use CALC function

Type the equation as it is and press CALC

- ? enter 2 if y=0,
- then possible root siya

- ? enter 1/2,
- if y=0,
- then possible root siya

- ? enter
- -3/2 if y=0,
- then possible root siya

3x-4y-1=0,

- and 2x-y+6=0
- units B
- units C
- units D

units Code: First get the point of intersection

- use the EQN function

- type: 127 3
- -4 1 then press = =

Therefore the point of intersection of this is x=3,

- and y=2

Then try the next equation

- -6 Then press = =

and y=-4 try the last combination of equation

- -6 Then press = =

and y=4 Then we use the determinant function to get the area of the triangle

MODE 6 and press AC

What important in this is kailangan natin madaan yung DIM or dimension ng matrix

- -1 4 1 then press AC

To get the determinant press SHIFT>7(det)>SHIFT>4>3(since we enter our data in MatA

- 5 times the determinant

- 5 and get its Abs value

- (3,1) and (5,3) A
- (-3,9) B
- (3,-9) C
- (-3,-9) D

(3,9) Code: Substitute x and y in the general equation of circle

- -3D-E+F=-10 The second point will give you 3D+E+F=-10 The third point will give you 5D+3E+F=-34

3 unknown

Use the EQN 2 and enter

-10 3 1 1

-10 5 3 1

- -34 And you will get D=6,

and F=-10 And write it in the general form

Ito ang shortcut para makuha ang center

Use the SUMMATION FUNCTION

Find the value of y of the parabola whose axis is vertical and passes through (-1,0),

- (1,8) and (4,y) A
- 6 Code: We use STAT 3( for parabola) in this case

-1,5 and 1

and 8 then press AC Find the value of y when x = 4

therefore 4(y-hat) or And you will get the answer

Find the sum of an A

- : 2,5,8
- where n=25
- 975 Code: Use STAT 2(for A

- : 2,3,4
- where n=10
- 84 Code: Same method with #9 BUT use STAT 6(for G

) Then use the SUMMATION function to get the sum

In how many ways can a picture be painted by using three(3) or more of the seven(7) different colors

- 120 Code: Set the calculator to COMP MODE

It will be found by pressing SHIFT > ÷ ( nCr ) And type the equation just like this: And you will get the answer

di ko na iisa-isahin kung anu pipindutin niyo para madali tayo

Kung may tanong kayo at di niyo makuha,

- pakipost na lang

Evaluate A x B

32677 B

36277 C

23677 D

- 26377 Code: Convert niyo lang sa decimal

- iconvert mo muna sa OCT
- 101=5 110=6 001=1 111=7 101=5

- 56175 And press DEC and you got the answer

SHIFT>4>1 Itype ang matrix and that's it

You got the answer

DON'T use divide,

instead use the reverse function

Find dy/dx if

To get the slope,

simply get the first derivative of the equation

Find the slope of the equation A

Gagawa tayo ng equation from the figure,

since may given tayo na r and Code: Pag Trigonometric/Inverse,

- i-set ang calcu sa RADIAN MODE

- po natin diyan,
- pi po yun

what is the slope of the curve when x = 2

- 2 Code: TANDAAN: Slope = first derivative =

And derive with respect to theta

- it will be like this:

- we have and equating it to x,

we have: Substituting the given and getting the derivative of x with respect to theta,

- we have:

4x-y=2 B

4x-y=-2 C

- x+4y=9 D
- x+4y=-9

- 10 A Code: Simple get the first derivative of this with x=2 (2 seconds) and you will get the answer

A 1800-gallon tank of water drains from the bottm in 30 min

the volume of water remaining in the tant after t minutes is

what you are getting is the slope of the tangent line

To get the slope of the Normal Line,

you get the negative reciprocal of this

get the first derivate(Tangent slope) of the given equation with x=1(given in the problem)

Get A and B

SHIFT>1>7> and SHIFT>1>7>2 Remember,

- in the calculator,

the equation of STAT 2 is y=a+bx

Substitute a and b in the equation and you will get the answer

where How fast is the water draining from the tant after 20 minutes

-40 gpm B

-30 gpm C

-20 gpm D

- -10 gpm Code: Simply get the derivative of the equation with x=20 (20 minutes)

Find the value of x when the function y=lnx/x is at maximum value

Code: For maxima/minima,

the first derivative should be equal to 0

Try or test all the choices using CALC function if dy/dx=0 with x = x to use CALC function while getting the derivative

- and press CALC x

i-substitute ang limits sa choices

Wag intindihin ang constant "C"

- remember,
- upper limit minus lower limit

lets say for example sa choice A

0 e 1 1/e

Kung anu sa choices ang nag equal to 0,

- yun ang sagot

- (2,2) D

1) Code:

in solving Trigonometric or inverse trigonometric,

- use RADIAN MODE

- i mean 4x,4x
- 9x,9y and so on,
- ang shortcut niyan is 0
- 9x(center): therefore,
- 9 x (2,2) = answer

Find the area of the region bounded by ,

- the x-axis,

and the vertical lines x=0 and x=4

- units B

16/3 sq

17/3 sq

- units D

units Code: First get the limits from the equation it self

Use EQN 3

- hirap e

Then integrate using the limits

88 Code:

And you will get the answer

- units B
- units C
- units D

37/12 sq

units Code: Get the limits from the equation

Ang shortcut dito ay distance formula(two points)

- x=pi/4 Then y=0,
- 34 Then use the distance formula

The speed of the particle is given by

90 ft C

Use EQN 4

- -7 Get the real number and that is your lower limit

Use EQN 4

- -99 Get the real number and that is your upper limit

And you will get the answer

Code: Choice one from the choices and Convert the equation to y=f(x)

Differentiate using your calculator with x=1(as given) and you will get the value of dy/dx Substitute x,

y and dy/dx to the equation in the problem and see if it is equal to 2

If yes,

then your choice is the right answer

Use EQN 4

- 1 0 0 8 You will get one real root and two complex roots

And solved for y

i-differentiate ang iyong napiling equation with x=(kung ano ni-substitute mo sa una,

be consistent) You will get the y' Then susbtitute in the given equation y'-y=2

- if 2=2 Therefore,
- napili mo ang tamang answer

Will be posted soon

SESSION 2 PART 4 31

19 hr B

49 hr C

89 hr D

- 16 hr Code: Dahil sa ito ay radioactive,

nagiincrease ito exponentially

- gagamitin natin ang STAT 5

Code: Pag temperature ang pinaguusapan use STAT 5

T = Object temperature Ts = surrounding/environment temperature gets

therefore ang gagamitin natin ay

X-----|-----Y(Ts-T) 0-----|-----(70-18) 1-----|-----(70-31) After natin ma-input ang data,

- press AC

therefore kukunin natin ang value ng A and B

I hope and assume na you know it already kung paano at saan ito kukunin since naturo ko na ito sa naunang session/part

After makuha ang A and B,

alam natin na ang equation sa STAT 5 ay

since time in its half life ang hinahanap,

- press AC then find

- 1 min later,
- the thermometer reading is

x=t and y=Ts-T since yun ang ginamit natin(y=70T)

Assume the earth to be a sphere of radius 6,371 km,

- compute the mass of the earth

BUT F=mg,

- assume m = Therefore,

41 Code:

- and you will get the answer

8 + 8i C

- 4 + 4i Code: Ang pwede lang po sa ating calcu ay cube at square ng complex

cancels' out Or pwede din ito:

And you will get the answer

Calculate the form factor of a periodic voltage having the following values for equal time intervals changing one value to the next: 0,

Determine the argument of the result of A

4 Code:

115 ohms

- 15 degrees C B
- 65 degrees C C
- 25 degrees C D
- 45 degrees C Code: STAT 2 X column = temp

---x--- |

- ---Y-----100 |

---30 |

Marami pa naman ito

The resistance of a wire is 126

- 48 ohms at 100 degrees C and 100 ohms at 30 degrees C

What is the present worth of two 10,000 pesos payment at the end of the 3rd and 4th year if the annual interest is 8% compounded quarterly

264 Code:

Ang formula po talaga nito ay where: F = future worth P = present worth i = interest rate m = number of compounding(quarterl,

- semi-anually,
- annually etc)
- t = time(years,month,

etc) Kung alam niyo kung paano computin sa long method,

- then go

:D Then ito po yung sa CALCU TECHNIQUE: First kukunin natin ang P ng 3rd and 4th year

- indeterminate D
- infinity

----- X

----- |

----- Y

--------12

- ----- | 10,000

----- | 1

- 02(10,000) bakit po 12
- ? kasi mt=(4)(3) bakit po 13
- ? kasi next year
- +1 year gets
- bakit 10,000 lang,
- akala ko yung formula

? ginagamit lang natin yung formula on the next year

I-type lang ang equation Press CALC

? Wag po natin i-substitute as x=0 dahil magmaMATH error po yan

And you will get the answer

Then get the present worth: Second,

kukunin natin ang present worth sa 4th year

Same lang din ito sa 3rd year

Ang pinagkaiba lang yung mt

----- X

----- |

----- Y

- ---------16----- | 10,000
- -----17----- | 1
- 02(10,000) Then get the present worth: Finally get the sum of the present worth in the 3rd year and 4th year

And you will get the answer

- indeterminate D

infinity Code: Same method lang po sa #1

napaisip ka ngayon kung paano infinity

? Ito ay isang malaking number

So press CALC

? infinity = 1000 or kahit anong malaking number basta wag lang magMAMATH error

- 2 Code: Same method as #1
- 3 Code: Same method lang din sa #1

Pero wag kalimutan na ilagay sa rad mode ang calcu

Code: Same method as #4

infinity Code: Same method lang din as #4

- either 1

Find the derivative of A

This time I assume na marunong na ang lahat at pamilyar na kayo sa mga steps at function na ginagawa natin

Don't forget: Always use rad mode in trigonometric and inverse trigonometric equations

Youre favorite number

Set x=5 Makakakuha tayo ng answer

Say A1(answer #1)

Then mula sa choices,

isubstitute lang ang 5 sa x at makakauha tayo ng sagot

Say A2 (answer #2) Kung A1 = A2 then tama ang napili niyo sa choices

- 1 + cos x D
- - cos x Code: Same method with #7

Find the derivative of y if A

Find the derivative of y if tan y = x

- sec x tan x C

I hope you get it

That's what you called reverse engineering

- same method na lang as #7

Find the first derivative of y if A

basa muna kayo sa mga naunang example

Find the second derivative of y if A

Quote: So,

mano-mano ito since walang shortcut pag second derivative

So let's test kung marunong pa kayo sa mano-mano

-1/(x^2) C

-1/(x^3) D

- -1 Quote: So,

mano-mano ito since walang shortcut pag third derivative

change to function of x then use d/dx function

- y / (x+y) B
- -y / (x+y) C
- y / (x+2y) D
- -y / (x+2y) Quote: Same lang sa #14

- xy-5y D
- 2xy Quote: Mag-iisip ka ng value ng y and then kapag dinirivative mo,
- equal siya dun sa value ng y

The equation now becomes 16x-20+6 or 16x14

Ang x natin dito ay always 1

So kung anong nakuha niyo answer diyan,

kailangan mag equal siya dun sa answer

- is discontinous at

Quote: Use d/dx function then x=x and press CALC

Quote: same with #18

- 7 Quote: Remember: m1=m2 (tangent/parallel) m1=
- -1/m2 (normal/perpendicular) And y=4x+3 should be tangent to y=x^2+C First,

get the first derivative or slope of y=4x+3

- therefore the slope is 4

equate y' = y' (y=4x+3) = (y=x^2+C) 4 = 2x and x = 2

our pt is (2,11) Substitute this to Y = x^2 + C to get the value of C

what is the slope of the curve when x = 2 radians

share ko lang din ng CALCU TECHNIQUE sa Laplace Transformation:

Examples:

- (5 / s^2

- 25) b

- (5s / s^2

- 25) c

- (s / s^2 + 25) d
- (s / s^2

Sana po nakatulong sa nyo kahit paano

- not to be kept"

Steps: By calculator technique (FX991ES+): Let t = x a

Press the Integral sign sa calculator (yung nasa baba ng alpha button) b

- ilagay nyo po 0 to 9 d

Answer is

Take note of the answer

Para po malaman mo kung anu yung laplace transform nya sa choices,

trial and error from the choices,

- just change "s" to 9

Like for this example,

letter d'yung may kaparehas na sagot

- (3/2) + 3t^2 + (t^4/4) b
- - (t^4/4) c

- (3/2)

- - 3t^2 + (t^4/4) d
- - 3t^2 + (t^4/4) Steps: By calculator technique (FX991ES+): Let t = x & s'= 9 a

reverse process po ang gagawin

158537 b

trial and error po uli ang gagawin

- letter "d" po yung sagot c

- then press =

Ang sagot po dapat ay

- 11th Aug 2012 Sat at 20:32
- #183 9th Aug 2012 Thu,

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