PDF- -CALIFORNIA INSTITUTE OF TECHNOLOGY - calc tech

Description

Session 1

- Part 1

Getting familiar with the functions 1

What are the roots of the polynomial: A

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

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

when substituted to the variable(ie x),

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

Trial and error,

Use the CALCU function

Pag nagtanong ang calculator X

And you will get the answer

repeat the step until you get an output of 0

What are the roots of the polynomial: A

1,2,3 B

1,2,5 C

1,2,4 D

And you will get the answer

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

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

-7 = 1 4 =

Set calculator to equation mode: MODE>5>1 for two-variable equation

And you will get the answer

Input the coefficients of a,b and constant c'of the first equation: 2=3=6=

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

And you will get the answer

The equation has two rational roots,

Find the larger of these two roots

We will be using CALCU function

The calculator should display 0

And you will get the answer

What is the remainder of the polynomial when divided by A

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

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

And you will get the answer

Solve for the value of A

Solve for the value of A

And you will get the answer

Solve for the value of x in the equation: A

To get the SOLVED function,

SHIFT>CALCU>= It should display,

X= answer L-R= 0 (important,

must be 0) And you will get the answer

Additional Exercises

- PART 2

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

Then press =

And you will get the answer

Find x,

Code: Set calculator to computation mode

Type the equation as is

Use the "SOLVE" function and press =

And you will get the answer

Factor A

Evaluate A

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"

Second,

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

Start with the first choice until you get the value of "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

Set the calculator to STAT mode

MODE 3>2 2: A+BX is for Arithmetic Progression( A

May makikita kayo X and Y column

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,

Which mean the 1st term of the A

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

Therefore,

Ang Y-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>5(Yhat)

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

Then press =

And you will get the answer

Kung may tanong kayo dito at di niyo makuha pakipost na lang

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

59,049 B

177,147 C

531,141 D

Set the calculator to STAT mode

MODE 3>5 or MODE3>6 (it's the same for Geometric Progression,

) May makikita kayo X and Y column

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

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

3rd term)

Sa Y column naman,

Which mean the 1st term of the G

After niyo mainput,

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,

Then press =

And you will get the answer

Kung may tanong kayo dito at di niyo makuha pakipost na lang

What is the sum of the first 20 terms of the sequence: 1,

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

In the X column,

In the Y column,

After you input the data,

Don't worry your data will not be deleted (unless you change your mode) 4

Press SHIFT>LOG(found below the ON KEY)

we will use the SUMMATION function

(SUMMATION symbol is like E) 5

Press ALPHA>)(for X)>SHIFT>1>7>5(for Y-hat)>SHIFT>)(for comma)>1>SHIFT>)(for comma)>21>) 6

You will noticed that our summation is from 1 to 21

Why 21 and not 20

Because we start our progression in 1

If we start the progression from 0,

then that's the time we use 0 to 20

And it will be like this

And you will get the answer

What is the sum of the infinite series: 1,

Set the calculator to Computation Mode

MODE>1 Since this is an infinite series,

with a common ratio of less than 1,

then the sum is a finite number

(NOTE: For an infinite series with a common ratio of greater than 1,

Input the equation under SUMMATION function and get the sum from 0 to a large value,

So it will be like this

Then press =

What is the sum of 6+9+12+

Set the Calculator to STAT mode

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

In the X column,

In the Y column,

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

So let's determine how many terms it has

Earlier in this tutorial I said X is for nth term and Y is for progression

Therefore,

Since 171 is our last term

And the calculator will display "56" 4

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

What is the 6th term of the infinite series: 1,

1/3125 B

1/15625 C

-1/3125 D

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 =

Rationalize the given equation: A

Set the calculator to COMPLEX mode

Input the equation as it is in the calculator

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

Then press =

And you will get the answer in gal

And you will get the answer

The function discontinous at x=

SESSION 2 PART 1 1

Subtract A

Code: Pag sinabing discontinous,

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,

Siguro naman kayang kaya niyo na ito

Set the calculator to COMP MODE

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

During a rain,

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

21,381 B

25,381 C

27,381 D

Alternative solution

Type the equation as it is and press = START

? (your number depends on the choices

we start from the lowest which is

So enter

? (the largest in the choices)

So enter 2 and press = STEP

? (The variation in the choices)

Important po ito

kailangan madaanan nung function yung mga choices

In this case 2 and

So enter 2 and press =

Kung saan may error yun na yun

Conversion only

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

It will give an answer 40468

Then multiply it to

Convert this to Liters

And it will display 80937

12 in L

Finally convert this to gal

Press CONV#14 L>gal(US)

Find the possible factors of A

all of the above Code: Para masabing factor siya,

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

We use CALC function

Set the calculator to MODE 1

Type the equation as it is and press CALC

Get the root of the choices and substitute

Try the next one

Try the last one

Therefore you know the answer

Determine the area of the triangle bounded by the straight lines x+2y-7=0,

3x-4y-1=0,

units Code: First get the point of intersection

MODE 5>1 For the first two equation,

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

Then try the next equation

and y=-4 try the last combination of equation

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

Set the calculator to MATRIX

MODE 6 and press AC

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

So press SHIFT>4>1>1>1 and enter 321

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

Then press =

Remember the area of a triangle given the vertices is 0

Therefore multiply it to 0

Then you will get the final answer

Find the center of the circle that is circumscribed about the triangle whose vertices are (-3,1),

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

In the first point you will get the equation

Therefore we have 3 equations,

3 unknown

Use the EQN 2 and enter

-10 3 1 1

-10 5 3 1

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

Ito ang shortcut para makuha ang center

CENTER OF CIRCLE,

ELLIPSE or PARABOLA:

In the x column enter 1,2 In the y column enter 2,5 then press AC

Use the SUMMATION FUNCTION

And you will get the answer

Therefore our center (h,k) is at (-3,9)

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

In the x column enter

-1,5 and 1

In the y column enter 0,0,

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

Find the sum of a G

) Then use the SUMMATION function to get the sum

And you will get the answer

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

We use the COMBINATION function

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

SESSION 2 PART 2 Starting in this Part,

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

Kung may tanong kayo at di niyo makuha,

Code: Type niyo lang sa calcu

Wag kalimutan base 8 and base 10 yan

Press HEX for the final answer

Evaluate A x B

Find the decimal equivalent of A

32677 B

36277 C

23677 D

Set to BIN then type the number

Press DEC and you got the answer

Additional TIP: Kung hindi na kasya sa calculator at sobrang haba ng BIN mo,

Set to OCT and type the OCT equivalent,

Find the hexadecimal equivalent of

Code: MODE 6>AC

Tandaan daanan lagi si DIM

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

You got the answer

Additional TIP: If A/B,

DON'T use divide,

instead use the reverse function

And it will be like this

Find dy/dx if

To get the slope,

simply get the first derivative of the equation

And you will get the answer

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-type sa calcu like this

Then we must come up with Using Pythagorean theorem:

If y = 4tanh x + sinh 2x,

what is the slope of the curve when x = 2

And derive with respect to theta

Substituting the given and using the d/dx function of the calcu,

Next we must get From the figure,

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

Dividing the results and you got the answer

Find the equation of the nomal line of the curve at (1,2) A

4x-y=2 B

4x-y=-2 C

Determine the current at the end of 2 seconds

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

According to Torricelli's law,

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

Code: When you are getting the slope of the line using the first derivative,

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)

And getting the negative reciprocal of this we have

Then get the equation using STAT 2

And press AC

Get A and B

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

the equation of STAT 2 is y=a+bx

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

The charge in coulombs that passes through a wire after t seconds is given by the function

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

-40 gpm B

-30 gpm C

-20 gpm D

And you will get the answer in gpm

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

Lagyan ng limits from 0 to 1 then press = Makakakuha ka ng sagot

I-note ito

i-substitute ang limits sa choices

Wag intindihin ang constant "C"

lets say for example sa choice A

Pag pumarehas ang sagot mo kanina(yung ni-note mo) yun ang sagot

Happy integrating

0 e 1 1/e

Kung anu sa choices ang nag equal to 0,

SESSION 2 PART 3

Find the centroid of the area bounded by the parabolas and A

1) Code:

Find the A

Code: Remember,

in solving Trigonometric or inverse trigonometric,

Shorcuts lang ang ibibigay ko since ito ay calculator technique

Pag nakita niyo na parehas yan,

Find the area of the region bounded by ,

and the vertical lines x=0 and x=4

16/3 sq

17/3 sq

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

Use EQN 3

X=3 and X=2

Pasensiya na po kayo sa drawing ko

Ayun bale alternating po yan

Then integrate using the limits

Ang you will get the answer

Find the lenght of arc of the curve y = ln cosx from x=0 to x=pi/4

88 Code:

Kaya po negative yung isa kasi dumaan po sa negative half cycle

And you will get the answer

Determine the area of the region bounded by the curve and the x-axis,

37/12 sq

units Code: Get the limits from the equation

Use EQN 4

Kung alam niyo formula gamit ang long method,

Di ko na siya ibibigay

Shortcuts lang lahat ito

Ang shortcut dito ay distance formula(two points)

First get the functions of y=f(x) When x=0,

And you will get the answer

The speed of the particle is given by

What distance does it travel while its speed increases from 7 to 99 ft/s

90 ft C

Code: Get the limits from the equation when d=7

Use EQN 4

Get the limits from the equation when d=99

Use EQN 4

Then integrate the equation using your lower and 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

Solve for the general solution of the differential equation:

If yes,

then your choice is the right answer

Solve for the general solution of the differential equation y'-y = 2

Code: Get the roots

Use EQN 4

KEY: Pag real root = Pag complex root = sin and cos

Solved for the particular solution of the differential equation: x + y dy/dx = 2 when x=1 and y=1 A

Code: Choose one in the choices

Choose your favorite number for C and x and substitute it to your choice

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

Will be posted soon

SESSION 2 PART 4 31

A radioactive substance decreases from 10 grams to 9 grams in two hours

Find its half life

19 hr B

49 hr C

89 hr D

nagiincrease ito exponentially

Which means kung exponentially ito,

Code: Pag temperature ang pinaguusapan use STAT 5

Sa x column natin is the time(min) and in y column it's either "Ts-T" or "TTs" (temperature)

It depends kung sino malaki kung si T or si Ts

T = Object temperature Ts = surrounding/environment temperature gets

Let's proceed

Since malaki ang Ts natin which is Ts-T

therefore ang gagamitin natin ay

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

Since ang kinukuha natin dito ay equation,

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

Ang x column natin ay ang time(hr) and y column natin ay quantity

X-----|-----Y 0-----|-----10 2-----|-----9

After makuha ang A and B,

alam natin na ang equation sa STAT 5 ay

since time in its half life ang hinahanap,

How fast does light travel in glass of refractive index 1

A thermometer reading is brought into a room where the temperature is

Find the temperature equation as a function of time

I-substitute ang A and B,

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

Refractive index formula

At the surface of the earth,

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

BUT F=mg,

41 Code:

Use STAT 1 and follow the formula,

Find the value of A

8 + 8i C

Pwede pong ganito:

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

Y column = Resistance

---x--- |

---30 |

I-type lang po natin sa calcu yung given then press = Convert po natin sa polar form then booomm

I've reached the image limit

Sa next part na

Marami pa naman ito

The resistance of a wire is 126

Determine the temperature when the resistance is

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,

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

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

So unahin natin si 3rd year

STAT 5 or 6 X column = mt(ito yung naka-raised sa formula) Y column =

----- X

----- |

----- Y

--------12

----- | 1

? 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

Mag-isip po ng number na malapit sa 0

For example 0

Then press '='

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

And you will get the answer

SESSION 3 PART 1 Differential Calculus

infinity Code: Same method lang po sa #1

napaisip ka ngayon kung paano infinity

Ano po ba ang infinity

? Ito ay isang malaking number

So press CALC

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

And you will get the answer

Pero wag kalimutan na ilagay sa rad mode ang calcu

Code: Same method as #4

infinity Code: Same method lang din as #4

Palitan ang x ng malapit sa 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

Gamitin ang d/dx function

SHIFT>INTEGRAL then i-type ang equation

At maglagay ng value ng x

Youre favorite number

I preferred 5

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

Find the derivative of y if A

Find the derivative of y if tan y = x

Ang technique lang lagi dito guys is that you must convert the equation into y into a function of x

That is,

Code: Same lang sa #7

I hope you get it

That's what you called reverse engineering

Then yun,

SESSION 3 PART 2

Find the derivative of y if A

Find the first derivative of y if A

Quote: Same lang ito sa mga nakaraang examples ko sa differential calculus

Kung hindi niyo alam ito,

basa muna kayo sa mga naunang example

NOTE: Pag parehas ang sagot,

HUWAG GAMITIN ANG 1

USE 2 or 3

Find the second derivative of y if A

Quote: So,

mano-mano ito since walang shortcut pag second derivative

Sa board exam may ganyan

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

Find the third derivative of y = x ln x

-1/(x^2) C

-1/(x^3) D

mano-mano ito since walang shortcut pag third derivative

Sa board exam may ganyan

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

Find the derivative of y if A

change to function of x then use d/dx function

Kayo na bahala kung anong value ng x gusto niyo

Then compare

Actually same lang ito sa #7

Find the first derivative of y if A

Find the partial derivatives with respect to x of the function A

For example,

Substitute 4 in the equation

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

Then use (d/dx)(16x-4)

Ang x natin dito ay always 1

So kung anong nakuha niyo answer diyan,

kailangan mag equal siya dun sa answer

For example ang answer ay 16

Letter B and tamang sagot kasi y = 4 and y^2 = 16

The function A

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

Isubstitute ang lahat ng choices at kung saan nagerror,

Find the slope of the tangent line to the graph of the function at the point where x=3

Quote: same with #18

Find C so that the line y = 4x + 3 is tangent to the curve y = x^2 + C

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

Use d/dx with x=1,

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

Then get the value of y from y=4x+3 y = 11

Therefore,

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

Quote: Radian mode

Use d/dx function with x=3 Slope tangent is equal to the first derivative(y')

If y=4cos x + sin 2x,

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

share ko lang din ng CALCU TECHNIQUE sa Laplace Transformation:

Examples:

Find the laplace transform of f(t) = cosh 5t a

- 25) b

- 25) c

Sana po nakatulong sa nyo kahit paano

Sana makapasa tayong lahat sa board exam

God Bless "Knowledge are meant to be shared,

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

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

Type mo (e^-9x) (cosh 5x) c

Then yung limit po,

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,

Like for this example,

letter d'yung may kaparehas na sagot

Find the inverse laplace of [3(s^2-2)^2] / 2s^5 a

- (3/2)

From this example,

reverse process po ang gagawin

Just input sa calculator yung inverse laplace equation

Ang sagot po dapat sa equation na [3(s^2-2)^2] / 2s^5 ay

158537 b

From the given choices,

trial and error po uli ang gagawin

Sa question,

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

Type mo (e^-9x) ([3(s^2-2)^2] / 2s^5)

Limit is the same from 0 to 9,

Medjo matagal nga lang po lumabas yung sagot

Ang sagot po dapat ay

Last edited by robgab