Calcu Teknik

8/11/2019 Calcu Teknik

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SESSION 1 PART 1

GETTING FAMILIAR WITH THE FUNCTIONS

1. What are the roots of the polynomial:

A.

-3, -4B.6, 2C.2, 3D.3,4

Code:

Set Calculator to equation mode: MODE>5>3 for quadratic equationMode 3 because our polynomial is a 2nd degree equation.. Input the equation coefficients a,b,c:1 = -7 = 1 2 = =

And you will get the answer..

2. What are the roots of the polynomial:

A.1,2,3

B.1,2,5C.1,2,4D.2,3,5

Code:

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

Input the equation coefficients a,b,c:

1 = -7 = 1 4 = -8 = =And you will get the answer..3. Which of the following is a possible root of the polynomial:

A.3

B.0C.-2D.4

Code:

NOTE: A root is any value that, when substituted to the variable(ie x), willsatisfy the equation.(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? iinput ang mgachoices.. X? 3 =output is 240..repeat the step until you get an output of

0.. And you will get the answer..


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

A.-12/19, 16/19

B.-24/19, -22/19C.12/19, -16/19D.24/19, 22/19

Code:

Set calculator to equation mode: MODE>5>1 for two-variable equation.Input the coefficients of a,b and constant c of the firstequation: 2 = 3 = 6 =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..


5. The equation

has two rational roots, both of which are positive. Find the larger of these two roots.

A.1B.2C.3D.

4

Code:

Same method with number 3..We will be using CALCU function..Thecalculator should display 0..


6. What is the remainder of the polynomial

when divided by

A.208

B.218C.283D.305

Code:

Set the calculator to computation mode: MODE>1

Input the left side of the equation

Apply the Remainder theoremUse CALCU function and substitutex=5 And you will get the answer..7. Solve the values of y in the system of equations:

Code:


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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 ofy.. And you will get the answer..

8. Solve for the value of

A.2

B.2i

C.

-2D.-2i

Code:


Input the equation in the calculator(as is)..

and you will get the answer..9. Solve for the value of

A.

1.91

B.2.19C.1.19D.2.91

Code:

Set the calculator to computation modeInput the equation in the calculator(as is)


10. Solve for the value of x in the equation:

A.1.91

B.

1.19C.

1.46D.

2.13

Code:

Set the calculator to computation modeInput the equation and use the SOLVED function to get the value of x..

To get the SOLVED function, SHIFT>CALCU>=It should display,

X= answerL-R= 0 (important, must be 0)



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SESSION 1 PART 2

Additional Exercises

11. Evaluate

A.9920

B.

2920C.

9200D.

2290

Code:


Input the equation as is but replace k with X..

Then press =..

And you will get the answer..12. Find x, if

A.

B.

C.

D.

Code:

Set calculator to computation mode..Type the equation as is..Use the "SOLVE" function and press =..


13. Factor

A.

B.

C.

D.

Code:

First, type the equation and assign an arbitrary constant to substitute to x and use the

CALC function..

for example X=8


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

A.25B.27C.

29D.31

Code:

1.Set the calculator to STAT mode..MODE 3>22: A+BX is for Arithmetic Progression( A.P.)..May makikita kayo X and Y column..And X column natin ay ang nth term while sa

Y column natin ay ang A.P..2.Input sa X column ang 1,2,3(1st term,2nd term, 3rd term)..Sa Y columnnaman, iinput ang 1,3,5 (kahit 3 number lang, kahit wag na yung 7)..

Which mean the 1st term of the A.P. is 1, 2nd term is 3 and 3rd term is 7..3.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 ika-15th term?..meaning ang hinahanap ang value sa Y column..gets?..

4. Therefore, type 15Y-hat..

Ang Y-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>5(Y-hat)..while ang X-hat ay makikita when you press SHIFT>1(STAT)>7(Reg)>4(X-hat)..take note of thisdahil gagamitin natin ito in the next problems.. 5. Then press =..


15. Find the 12th term in the geometric series: 3, 9, 27 . . .

A.59,049B.177,147C.531,141D.1,594,323

Code:

1.Set the calculator to STAT mode..MODE 3>5 or MODE3>6 (it's the samefor Geometric Progression, G.P.)May makikita kayo X and Y column..And X column natin ay ang nth term while sa

Y column natin ay ang G.P..2.Input sa X column ang 1,2,3(1st term,2nd term, 3rd term)..Sa Y columnnaman, iinput ang 3,9,27..Which mean the 1st term of the G.P. is 3, 2nd term is 9 and 3rd term is 27..3.

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 ika-12th term?..meaning ang hinahanap ang value sa Y column..gets?..

4.

Therefore, type 12Y-hat..5.Then press =..



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16. What is the sum of the first 20 terms of the sequence: 1, 3, 5, 7... A.361

B.391C.400D.441

Code:

1.

Set the calculator to STAT mode: MODE 3>2 (since it is A.P.)2.In the X column, input 1,2,3..In the Y column, input 1,3,5..3.After you input the data, press AC..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 theSUMMATION function..(SUMMATION symbol is like E)5.Press ALPHA>)(for X)>SHIFT>1>7>5(for Y-hat)>SHIFT>)(forcomma)>1>SHIFT>) (for comma)>21>)6.You will noticed that our summation is from 1 to 21..Why 21 and not20?..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..walang Y-hat na symbol e..


17. What is the sum of the infinite series: 1, -1/5, 1/25, . . . A.5/6B.4/5C.5/7D.6/7

Code:

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 afinite number..(NOTE: For an infinite series with a common ratio of greater than 1, thesum is infinite)..

2. Input the equation under SUMMATION function and get the sum from 0 to a

large value, say, 50.So it will be like this..Then press =

18. What is the sum of 6+9+12+. . .+171?

A.

4956B.4389C.5198D.5462

Code:

1.Set the Calculator to STAT mode..MODE3>2 (I hope you already know why MODE 32)2.In the X column, input 1,2,3....In the Y column, input 6,9,12 then press AC..3.We should get the sum but we don't know how many term does it have..So let's


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determine how many terms it has..Earlier in this tutorial I said X is for nth term and Y

is for progression..Therefore, our code is 171X-hat..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, its 1,56..

19. What is the 6th term of the infinite series: 1, -1/5, 1/25, ...

A.

1/3125

B.

1/15625C.-1/3125D.-1/15625

Code:

1.

Set the calculator to Computation mode..2.

Input the general equation of the infinite series and substitute 5 to x using the

CALC function to display the 6th term..And press =

20. Rationalize the given equation:

A.

2-5i

B.

(5+10i)/6C.

1+2iD.

(2+i)/3

Code:

1.

Set the calculator to COMPLEX mode..MODE>22.

Input the equation as it is in the calculator..(NOTE: The imaginary i is found

by pressing the ENG key..3.

Then press =And you will get the answer..


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Type the equation as it is and press =

START? (your number depends on the choices..we start from the lowest which is -2..So enter -2 then press =END? (the largest in the choices)..So enter 2 and press =

STEP? (The variation in the choices)..Important po ito..kailangan madaanannung function yung mga choices..In this case 2 and -2..So enter 2 and press =Kung saan may error yun na yun..

4. Find the possible factors of

.

A.(x-2)B.(2x-1)C.(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..Set the calculator to MODE 1..

Type the equation as it is and press CALC..Get the root of the choices andsubstitute.. X? enter 2 if y=0, then possible root siya..Try the next one..X? enter 1/2, if y=0, then possible root siya..Try the last one.. X? enter -3/2 if y=0, then possible root siya..Therefore you know the answer..5. Determine the area of the triangle bounded by the straight lines x+2y-7=0, 3x-4y-1= 0, and 2x-y+6=0..

A.10 sq.unitsB.

15 sq.unitsC.

20 sq.unitsD.

25 sq.units

Code:

First get the point of intersection..use the EQN function..MODE 5>1For the first two equation, type:

1 2 7

3 -4 1

then press = =..Therefore the point of intersection of this is x=3, and y=2..

Then try the next equation..

3 -4 1

2 -1 -6

Then press = =......x=-5, and y=-4try the last combination ofequation.. 1 2 72 -1 -6Then press = =......x=-1, and y=4Then we use the determinant function to get the area of thetriangle.. Set the calculator to MATRIX..MODE 6 and press AC..What important in this is kailangan natin madaan yung DIM or dimension ngmatrix..So press SHIFT>4>1>1>1 and enter3 2 1


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-5 -4 1

-1 4 1then press AC..To get the determinant press SHIFT>7(det)>SHIFT>4>3(since we enter our data inMatA..Then press =..Remember the area of a triangle given the vertices is 0.5 times the

determinant..Therefore multiply it to 0.5 and get its Abs value..

Then you will get the final answer..6. Find the center of the circle that is circumscribed about the triangle whosevertices are (-3,1), (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..

In the first point you will get the equation -3D-E+F=-10The second point will give you 3D+E+F=-10

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

Therefore we have 3 equations, 3 unknown..

Use the EQN 2 and enter-3 -1 1 -10

3 1 1 -10 5

3 1 -34

And you will get D=6, E=-18, and F=-10And write it in the general form..

Ito ang shortcut para makuha ang center..

CENTER OF CIRCLE, ELLIPSE or PARABOLA:(h)

(k)

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

7. Find the value of y of the parabola whose axis is vertical and passes through (-

1,0), (5,0), (1,8) and (4,y)

A.-5B.5C.-6D.6

Code:

We use STAT 3( for parabola) in this case..

In the x column enter -1,5 and 1..

In the y column enter 0,0, and 8 then press AC


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Find the value of y when x = 4..

therefore 4(y-hat) or


8. Find the sum of an A.P.: 2,5,8..............where n=25..

A. 900

B. 925

C. 950

D. 975

Code:

Use STAT 2(for A.P.)In the x column enter 1,2

In the y column enter 2,5 then press AC..

Use the SUMMATION FUNCTION..


9. Find the sum of a G.P.: 2,3,4.5,.................where n=10.

A.

226.66B.

235.42C.242.52D.251.84

Code:

Same method with #9 BUT use STAT 6(for G.P.)Then use the SUMMATION function to get the sum..

And you will get the answer..10. In how many ways can a picture be painted by using three(3) or more of

the seven(7) different colors?.

A.80B.99C.105D.120

Code:

Set the calculator to COMP MODE..

We use the COMBINATION function..It will be found by pressing SHIFT > ( nCr )

And type the equation just like this:



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SESSION 2 PART 2

11. Find the decimal equivalent of

A.32677

B.36277

C.

23677D.26377

Code:

Convert niyo lang sa decimal..MODE 4..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, iconvert mo muna sa

OCT..

101=5

110=6

001=1

111=7

101=5

Set to OCT and type the OCT equivalent, 56175

And press DEC and you got the answer..

12. Find the hexadecimal equivalent of

x

A.

B.

C.

D.

Code:

Type niyo lang sa calcu..Wag kalimutan base 8 and base 10 yan..Press HEX for the final answer..

13. Evaluate A x B.


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A.

B.

C.

D.

Code:

MODE 6>AC.....Tandaan daanan lagi siDIM.. SHIFT>4>1Itype 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 14. Find dy/dx if

and

when

A.0.433

B.0.866C.1.083

D.

1.732

Code:

Pag Trigonometric/Inverse, i-set ang calcu sa RADIAN MODE..I-type sa calcu like this..

Yung

po natin diyan, pi po yun..

15. If y = 4tanh x + sinh 2x, what is the slope of the curve when x = 2?


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A.-54.9

B.-28.2C.54.9D.28.2

Code:

TANDAAN:

Slope = first derivative =

To get the slope, simply get the first derivative of the equation..

And you will get the answer..16. Find the slope of the equation

when

A.5.2

B.-5.2

C.

4.2D.-4.2

Code:

Gagawa tayo ng equation from the figure, since may given tayo na r and

theta..Then we must come up with

Using Pythagorean theorem:

And derive with respect to theta..

Substituting the given and using the d/dx function of the calcu, it will be like this:

Next we must get

From the figure, we have

and equating it to x, we have:

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

Dividing the results and you got the answer..

17. Find the equation of the nomal line of the curve

at (1,2)

A.4x-y=2B.4x-y=-2C.x+4y=9


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D. x+4y=-9

Code:

When you are getting the slope of the line using the first derivative, what you aregetting is the slope of the tangent line..To get the slope of the Normal Line, you getthe negative reciprocal of this..So, 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 -

1/4.. Then get the equation using STAT 2..

And press AC..Get A and B..SHIFT>1>7> and SHIFT>1>7>2Remember, 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..

18. The charge in coulombs that passes through a wire after t seconds is given by

the function.

Determine the current at the end of 2 seconds..

A.6 AB.8 AC.9 AD.

10 A

Code:

Simple get the first derivative of this with x=2 (2 seconds) and you will get the answer..

19. 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

where

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

A.-40 gpmB.-30 gpmC.

-20 gpmD.-10 gpm

Code:

Simply get the derivative of the equation with x=20 (20 minutes)..

And you will get the answer in gpm..

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

A.

0B.eC.1D.1/e

Code:


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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? 0

x? ex? 1x? 1/e

Kung anu sa choices ang nag equal to 0, yun ang sagot..


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SESSION 2 PART 3

21. Find the

A.

B.

C.

D.

Code:

Remember, in solving Trigonometric or inverse trigonometric, use RADIANMODE..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"..remember,

upper limit minus lower limit..lets say for example sa choice A..

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

sagot.. Happy integrating..;)

22. Find the centroid of the area bounded by the parabolas

and

A.(1.8, 1.8)

B.(1.9, 1.9)C.(2,2)D.

(2.1, 2.1)

Code:

Shorcuts lang ang ibibigay ko since ito ay calculator technique..Given:

Pag nakita niyo na parehas yan, i mean 4x,4x...6x,6y...8x,8y...9x,9y and so on,

ang shortcut niyan is 0.9x(center): therefore,

0.9 x (2,2) = answer23. Find the area of the region bounded by


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, the x-axis, and the vertical lines x=0 and x=4..

A.5 sq. unitsB.16/3 sq. unitsC.

17/3 sq. unitsD.

6sq. units

Code:

First get the limits from the equation it self..Use EQN 3..X=3 and X=2Pasensiya na po kayo sa drawing ko..hirap e..Ayun bale alternating po yan.. Then integrate using the limits..

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


24. Determine the area of the region bounded by the curve

and the x-axis,

A.2.25 sq. units

B.2.5 sq. unitsC.3 sq. unitsD.37/12 sq. units

Code:

Get the limits from the equation..Use EQN 4..

Ang you will get the answer..

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

A.

0.65

B.0.72

C.

0.81D.0.88

Code:

Kung alam niyo formula gamit ang long method, go..Di ko na siyaibibigay..Shortcuts lang lahat ito..

Ang shortcut dito ay distance formula(two points)..First get the functions of y=f(x)When x=0, x=pi/4

Then y=0, -0.34


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Then use the distance formula..

And you will get the answer..26. The speed of the particle is given by

.

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

A.

83.3 ftB.90 ft

C.

96.7 ftD.100 ft

Code:

Get the limits from the equation when d=7..Use EQN4.. 2 5 0 -7Get the real number and that is your lower limit..

Get the limits from the equation when d=99..Use EQN4.. 2 5 0 -99Get the real number and that is your upper limit..

Then integrate the equation using your lower and upperlimit.. And you will get the answer..27. Solve for the general solution of the differential equation:

A.

B.

C.

D.

Code:

Get the roots..Use EQN 4..1 0 0 8You will get one real root and two complex roots..

KEY:Pag real root =

Pag complex root = sin and cos

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

B.

C.

D.


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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 valueof dy/dxSubstitute x, y and dy/dx to the equation in the problem and see if it is equal to 2... 2=2If yes, then your choice is the right answer..29. Solve for the general solution of the differential equation y'-y =

2.. A.

B.

C.

D.

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-note..

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 equationy'-y=2......if2=2Therefore, napili mo ang tamang answer..


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SESSION 2 PART 4

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

its half life.

A.10.19 hrB.11.49 hr

C.

12.89 hrD.13. 16 hr

Code:

Dahil sa ito ay radioactive, nagiincrease ito exponentially. Which meanskung exponentially ito, gagamitin natin ang STAT 5..

Ang x column natin ay ang time(hr) and y column natin ay quantity..X -----|-----Y0-----

|-----

10

2-----|-----9

since time in its half life ang hinahanap, press AC then find

32. A thermometer reading

is brought into a room where the temperature is

; 1 min later, the thermometer reading is

. Find the temperature equation as a function of

time. A.

B.

C.

D.

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 "T-Ts" (temperature). It depends kung sino malaki kung si T or siTs.. T = Object temperature

Ts = surrounding/environment temperaturegets?. Let's proceed..Since malaki ang Ts natin which is

, therefore ang gagamitin natin ay Ts-T. Gets?..X -----|-----Y(Ts-T)

0-----|-----(70-18)

1-----|-----(70-31)After natin ma-input ang data, press AC. Since ang kinukuha natin dito ay equation,

therefore kukunin natin ang value ng A and B. I hope and assume na you know it


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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

I-substitute ang A and B, x=t and y=Ts-T since yun ang ginamit natin(y=70-T)

33. How fast does light travel in glass of refractive index 1.5?

A.

B.

C.

D.

Code:

Refractive index formula

34. At the surface of the earth,

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

earth. A.

B.

C.

D.

Code:

BUT F=mg, assume m =

Therefore,

cancels' out

And you will get the answer.

35. Calculate the form factor of a periodic voltage having the following values for equal

time intervals changing one value to the next: 0, 5, 10, 20, 50, 60, 50, 20, 10, 5, etc.


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A.1.11

B.1.24C.1.35D.1.41Code:

Use STAT 1 and follow the formula, and you will get the

answer. 36. Find the value of

A.8 - 8i

B.8 + 8iC.4 - 4iD.4 + 4i

Code:

Ang pwede lang po sa ating calcu ay cube at square ng complex.

Pwede pong ganito:

Or pwede din ito:

37. Determine the argument of the result of

A.

-72

B.

27C.

76.9D.

159.4


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Code:

I-type lang po natin sa calcu yung given then press =

Convert po natin sa polar form then booomm..Yun na..

39. The resistance of a wire is 126.48 ohms at 100 degrees C and 100 ohms at

30 degrees C. Determine the temperature when the resistance is 115 ohms.

A.65.15 degrees CB.69.65 degrees CC.71.25 degrees CD.75.45 degrees C

Code:

STAT 2X column = temp.

Y column = Resistance

---x--- | ---Y------100 | ---126.48---30 | ---100

40. 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?

A.

P 15, 169B.P 15, 288C.P 16, 721D.P 17, 264

Code:

Ang formula po talaga nito ay

where:


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F = future worth

P = present worthi = interest ratem = number of compounding(quarterl, semi-anually, annuallyetc) t = time(years,month, days, 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. So unahin natin si 3rd year.gets?.. STAT 5 or 6

X column = mt(ito yung naka-raised sa

formula) Y column =

----- X ----- | -----Y ---------12 -----| 10,000

----13 -----| 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 onthe next year.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.


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SESSION 3 PART 1

Differential Calculus

1. Find

.

A.

0B.

0.353C.

indeterminateD.

infinity

Code:

I-type lang ang equation

Press CALC.... . .x?

Wag po natin i-substitute as x=0 dahil magmaMATH error po yan. Mag-isip po ng number na malapit sa 0. For example 0.001. Then press '=' ..

And you will get the answer.2. Find

A.0

B.1.75

C.

indeterminateD.infinity

Code:

Same method lang po sa #1. So, napaisip ka ngayon kung paano infinity?.Ano po ba ang infinity? Ito ay isang malaking number.So press CALC... .x?infinity = 1000 or kahit anong malaking number basta wag lang magMAMATHerror. And you will get the answer.3. Find

A.-1

B.1C.-2D.2

Code:

Same method as #1.

4. Find


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A.

0

B.

1/3C.1D.3

Code:

Same method lang din sa #1. Pero wag kalimutan na ilagay sa rad mode ang calcu.

5. Find

A.0

B.1/3C.1D.3

Code:

Same method as#4. 6. Find

A.

B.

C.0

D.infinity

Code:

Same method lang din as #4.

Palitan ang x ng malapit sa 1. either 1.001 or

.9999 7. Find the derivative of

A.

B.

C.

D.

Code:

This time I assume na marunong na ang lahat at pamilyar na kayo sa mga stepsat function na ginagawa natin.Don't forget: Always use rad mode in trigonometric and inversetrigonometric 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.


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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.8. Find the derivative of y if

A.

B.

C.

D.

Code:

Same lang sa #7. I hope you get it. That's what you called reverse engineering.

9. Find the derivative of y if

A.

B.

C.

1 + cos x

D.

1 - cos x

Code:

Same method with #7.10. Find the derivative of y if tan y = x .

A.

B. sec x tan x

C.

D.


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Code:

Ang technique lang lagi dito guys is that you must convert the equation into y into

a function of x. That is,

Then yun, same method na lang as #7.


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SESSION 3 PART 2

11. Find the first derivative of y if

A.

B.

C.

D.

Quote:

NOTE: Pag parehas ang sagot, HUWAG GAMITIN ANG 1. USE 2 or 3.

12. Find the second derivative of y if

A.

B.

C.

D.

Quote:

13. Find the third derivative of y = x ln x.

A.-1/xB.-1/(x^2)

C.

-1/(x^3)D.-1

Quote:

14. Find the derivative of y if

.


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A.-x/y

B.x/yC.y^-3D.-y^-3Quote:

15. Find the first derivative of y if

A.y / (x+y)

B.

-y / (x+y)C.

y / (x+2y)D.-y / (x+2y)

Quote:

16. Find the partial derivatives with respect to x of the function

A.

y^2 - 5

B.

y^2C.

xy-5yD.

2xy

Quote:

17. The function

is discontinous at

A.-1, 3B.1,-3C.-1,2

D.

1,-2

Quote:

18. Find the slope of the tangent line to the graph of the function

at the point where x=3.

A.

60B.

66


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C.72

D.78

Quote:

19.If y=4cos x + sin 2x, what is the slope of the curve when x = 2

radians? A. -2.21

B. -4.94C. -3.21

D. 2.21

Quote:

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

C. A. 4

B. 5C. 6D. 7

Quote:

Remember:


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f(t) = cosh 5t

d. (s / s^2 - 25)

(e^-9x) (cosh 5x)

0 to 9

.1607

just change "s" to 9

[3(s^2-2)^2] / 2s^5

d. (3/2) - 3t^2 + (t^4/4)

Let t = x & s = 9

[3(s^2-2)^2] / 2s^5 .158537

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

0 to 9

.158537


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ANSWER KEY

SESSION 1

PART 1

1.

D

2.

C

3.

C

4.

D

5.

B

6.

B

7.

D

8.

C

9.

C

10.

A

PART 2

11.

A

12.

B

13.

A

14.

C

15.

C

16.

D

17.

A

18.

A

19.

C

20.

C

SESSION 2

PART 1

1.

A

2.

A

3.

B

4.

D

5.

C

6.

A

7.

B

8.

C9.

A

10.

B

PART 2

11.

C

12.

D

13.

A


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14.

C

15.

C

16.

B

17.

C

18.

C

19.

A

20.

B

PART 3

21.

D

22.

A

23.

C

24.

D

25.

D

26.

A

27.

C

28.

B

29.

B30.

Will be posted soon. . .

PART 4

31.

D

32.

C

33.

A

34.

D

35.

C

36.

A

37.

D

38.

N/A39.

B

40.

A

SESSION 3

PART 1

1.

B

2.

B

3.

A

4.

D

5.

D6.

B

7.

B

8.

A

9.

A

10.

C


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