Tut Math - Calculator Techniques by Sirhoseven -Final 2

[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Foreword: Hi everyone, especially math majors! I compile these tutorials from one forum thread in Symbianize.com which I think can help you to Pass the LET Exam thru mastering (if possible) your best tool that you have during the Exam, that is your scientific calculator. The most common, one of the allowable and the best calculator that you should have is CASIO fx-991 ES PLUS. CASIO fx-991 ES PLUS has a lot of functions which are very helpful to you during exam days. Familiarizing or if possible mastering this kind of Scientific Calculator can be a great asset during LET exam. Somehow, These tutorials used CASIO fx-991 ES which is just a little bit different from CASIO fx-991 ES PLUS. I really hope you will learn a lot from this tutorial and hoping to see your name in LET Passers.. Go TEACHERS!  Note: I maintain its style and content from the original source. To see the original source of this tutorials, please go to this link and give thanks to the author. http://www.symbianize.com/showthread.php?t=761517

--Pulandit

Authored by:

Hello Symbianizers Today, I will teach you the Calculator technique use to solve Math problems. In this tutorial I will be using CASIO fx-991 ES. So don't ask me on how to do it in other calculator. Moreover, I will not cover the CASIO fx-991 ES PLUS although, some of you think its the same, I say to you it's different in someway or in some functions especially in STAT MODE. This is good and very helpful especially in Board Exam and in some school na hindi kinakailangan ng solution(multiple choice lang). Sa una nahirapan ako dahil iniisip ko kung paano ko isusulat ang mga equation. Ayun nagawan ko naman ng paraan.

Requirement in this MATH CALCU tutorial: 1. Basic knowledge in math( You cannot understand it if you don't know the basics..Mostly shorcuts ito kaya you should know the basic..) 2. CASIO FX-991 ES with the manual 3. Read your manual(all the functions and definiton of each will be found in the manual) 4. Brain/Common Sense Fx-991 ES Plus

Ok lets get it on! Edited by: Pulandit

Original Source: http://www.symbianize.com/showthread.php?t=761517

[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 1 - Part 1 Getting familiar with the functions 1. What are the roots of the polynomial: A. -3, -4 B. 6, 2 C. 2, 3 D. 3,4 Code: Set Calculator to equation mode: MODE>5>3 for quadratic equation Mode 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. 1,2,5 C. 1,2,4 D. 2,3,5 Code: Set Calculator to equation mode: MODE>5>4 for cubic equation Mode 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. 0 C. -2 D. 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. Trial and error, Use the CALCU function.. Pag nagtanong ang calculator X? iinput ang mga choices.. X? 3 = output is 240.. repeat the step until you get an output of 0.. And you will get the answer..

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 4. Find the value of x and y in the following equations:

A. -12/19, 16/19 B. -24/19, -22/19 C. 12/19, -16/19 D. 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 first equation: 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.. And you will get the answer..

5. The equation Find the larger of these two roots. A. 1 B. 2 C. 3 D. 4

has two rational roots, both of which are positive.

Code: Same method with number 3..We will be using CALCU function..The calculator should display 0.. And you will get the answer..

6. What is the remainder of the polynomial A. 208 B. 218 C. 283 D. 305

when divided by

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..

7. Solve the values of y in the system of equations:

Code: Set the calculator to equation mode: MODE>5>2 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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.. And you will get the answer..

8. Solve for the value of A. 2 B. 2i C. -2 D. -2i Code: Set the calculator to computation mode: MODE>1 Input the equation in the calculator(as is).. and you will get the answer..

9. Solve for the value of A. 1.91 B. 2.19 C. 1.19 D. 2.91 Code: Set the calculator to computation mode Input the equation in the calculator(as is) And you will get the answer..

10. Solve for the value of x in the equation: A. 1.91 B. 1.19 C. 1.46 D. 2.13 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, SHIFT>CALCU>= It should display, X= answer L-R= 0 (important, must be 0) And you will get the answer..

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Additional Exercises - PART 2 Additional Exercises - PART 2

11. Evaluate A. 9920 B. 2920 C. 9200 D. 2290 Code: 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..

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 =.. And you will get the answer..

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 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. 25 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven B. 27 C. 29 D. 31 Code: 1. Set the calculator to STAT mode..MODE 3>2

2: 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 column naman, 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 ika15th 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 this dahil gagamitin natin ito in the next problems.. 5. Then press =.. And you will get the answer.. Kung may tanong kayo dito at di niyo makuha pakipost na lang..

15. Find the 12th term in the geometric series: 3, 9, 27 . . . A. 59,049 B. 177,147 C. 531,141 D. 1,594,323 Code: 1. Set the calculator to STAT mode..MODE 3>5 or MODE3>6 (it's the same for

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 column naman, 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 ika12th term?..meaning ang hinahanap ang value sa Y column..gets?.. 4. Therefore, type 12Y-hat.. 5. Then press =.. And you will get the answer.. Kung may tanong kayo dito at di niyo makuha pakipost na lang..

16. What is the sum of the first 20 terms of the sequence: 1, 3, 5, 7... A. 361 B. 391 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven C. 400 D. 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 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..walang Y-hat na symbol e..

And you will get the answer..

17. What is the sum of the infinite series: 1, -1/5, 1/25, . . . A. 5/6 B. 4/5 C. 5/7 D. 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 a finite number..(NOTE: For an infinite series with a common ratio of greater than 1, the sum 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. 4956 B. 4389 C. 5198 D. 5462 Code: 1. Set the Calculator to STAT mode..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.. 3. 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 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven is for nth term and Y is for progression..Therefore, our code is 171Xhat..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. 1/15625 C. -1/3125 D. -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)/6 C. 1+2i D. (2+i)/3 Code: 1. Set the calculator to COMPLEX mode..MODE>2

2. 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..

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 2 Part 1 SESSION 2 PART 1 1. Subtract A. B. C. D. Code: Siguro naman kayang kaya niyo na ito..:D

2. During a rain, 2mm of water fell. Find how many gallons of water fell on a level 10 acre park. A. 21,381 B. 25,381 C. 27,381 D. 30,381 Code: Conversion only.. V=10 acre (convert acre to m^2)SHIFT>8(for CONV)>11(for acre>m^2)..It will give an answer 40468.56.. Then multiply it to .002 m(given in the problem) and it will display 80.93712 in m^3.. Convert this to Liters..1 m^3 = 1000L..And it will display 80937.12 in L.. Finally convert this to gal..Press CONV#14 L>gal(US).. And you will get the answer in gal..

3. The function A. 2 B. -2 C. either a or b D. neither a nor b

is discontinous at x=?

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, continous parin yun..dapat mageerror siya..gets?.. 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.. Alternative solution..we use the TABLE function..MODE 7.. Type the equation as it is and press = Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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 madaanan nung 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 and substitute.. 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 2xy+6=0.. A. 10 sq.units B. 15 sq.units C. 20 sq.units D. 25 sq.units Code: First get the point of intersection..use the EQN function..MODE 5>1 For 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=-4 try the last combination of equation.. 1 2 7 2 -1 -6 Then press = =......x=-1, 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 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 3 2 1 -5 -4 1 -1 4 1 then press AC.. 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 0.5 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 whose vertices 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=-10 The 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=-10 And 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. -5 B. 5 C. -6 D. 6 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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 Find the value of y when x = 4.. therefore 4(y-hat) or And you will get the answer..

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..

And you will get the answer..

9. Find the sum of a G.P.: 2,3,4.5,.................where n=10. A. 226.66 B. 235.42 C. 242.52 D. 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. 80 B. 99 C. 105 D. 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:

And you will get the answer.. Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 2 Part 2 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, pakipost na lang.. 11. Find the decimal equivalent of A. 32677 B. 36277 C. 23677 D. 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.

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven

A.

B.

C.

D. 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

14. Find dy/dx if

and

when

A. 0.433 B. 0.866 C. 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? A. -54.9 B. -28.2 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven C. 54.9 D. 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 A. 5.2 B. -5.2 C. 4.2 D. -4.2

when

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 A. 4x-y=2 B. 4x-y=-2 C. x+4y=9 D. x+4y=-9 Edited by: Pulandit

at (1,2)


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Code: When you are getting the slope of the line using what you are getting is the slope of the tangent the Normal Line, you get the negative reciprocal So, get the first derivate(Tangent slope) of the x=1(given in the problem)

the first derivative, line..To get the slope of of this.. given equation with

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>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..

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 A B. 8 A C. 9 A D. 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 gpm B. -30 gpm C. -20 gpm D. -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. 0 B. e C. 1 D. 1/e Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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? x? x? x?

0 e 1 1/e

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

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 2 Part 3 SESSION 2 PART 3

21. Find the A. B. C. D. Code: Remember, in solving Trigonometric or inverse trigonometric, use RADIAN MODE..

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 A. (1.8, 1.8) B. (1.9, 1.9) C. (2,2) D. (2.1, 2.1)

and

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) = answer

23. Find the area of the region bounded by and x=4.. A. 5 sq. units B. 16/3 sq. units Edited by: Pulandit

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


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven C. 17/3 sq. units D. 6sq. 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..hirap e..Ayun bale alternating po yan.. Then integrate using the limits..

Kaya po negative yung isa kasi dumaan po sa negative half cycle.. And you will get the answer..

24. Determine the area of the region bounded by the curve and the x-axis, A. 2.25 sq. units B. 2.5 sq. units C. 3 sq. units D. 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. 0.81 D. 0.88 Code: Kung alam niyo formula gamit ang long method, go..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) Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven When x=0, x=pi/4 Then y=0, -0.34 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 ft B. 90 ft C. 96.7 ft D. 100 ft Code: Get the limits from the equation when d=7..Use EQN 4.. 2 5 0 -7 Get the real number and that is your lower limit.. Get the limits from the equation when d=99..Use EQN 4.. 2 5 0 -99 Get 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..

27. Solve for the general solution of the differential equation: A. B. C. D. Code: Get the roots..Use EQN 4..1 0 0 8 You 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 = 2 when x=1 and y=1 A. B. C. D. Code: Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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... 2=2 If 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 equation y'-y=2......if 2=2 Therefore, napili mo ang tamang answer..

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 2 Part 4 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 hr B. 11.49 hr C. 12.89 hr D. 13. 16 hr Code: Dahil sa ito ay radioactive, nagiincrease ito exponentially. Which means kung exponentially ito, gagamitin natin ang STAT 5.. Ang x column natin ay ang time(hr) and y column natin ay quantity.. X-----|-----Y 0-----|-----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 si Ts.. T = Object temperature Ts = surrounding/environment temperature gets?. Let's proceed.. Since malaki ang Ts natin which is Ts-T. Gets?..

, therefore ang gagamitin natin ay

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 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

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven I-substitute ang A and B, x=t and y=Ts-T since yun ang ginamit natin(y=70T)

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, km, compute the mass of the earth. A. B. C. D.

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

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. A. 1.11 B. 1.24 C. 1.35 D. 1.41

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Code:

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

36. Find the value of A. 8 - 8i B. 8 + 8i C. 4 - 4i D. 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. 27 C. 76.9 D. 159.4 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 C B. 69.65 degrees C C. 71.25 degrees C D. 75.45 degrees C Code: STAT 2 X column = temp. Y column = Resistance ---x--- | ---Y-----100 | ---126.48 ---30 | ---100 Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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, 169 B. P 15, 288 C. P 16, 721 D. P 17, 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, 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 on the 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.

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven Session 3 Part 1 SESSION 3 PART 1 Differential Calculus

1. Find A. 0 B. 0.353 C. indeterminate D. 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. indeterminate D. 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 magMAMATH error. And you will get the answer.

3. Find A. -1 B. 1 C. -2 D. 2 Code: Same method as #1. Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 4. Find A. 0 B. 1/3 C. 1 D. 3 Code: Same method lang din sa #1. Pero wag kalimutan na ilagay sa rad mode ang calcu.

5. Find A. 0 B. 1/3 C. 1 D. 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 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). Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven 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. 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. Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven SESSION 3 PART 2 11. Find the first derivative of y if A. B. C. D. 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.

12. Find the second derivative of y if A. B. C. D. So, mano-mano ito since walang shortcut pag second derivative. Sa board exam may ganyan. So let's test kung marunong pa kayo sa manomano. 13. Find the third derivative of y = x ln x. A. -1/x B. -1/(x^2) C. -1/(x^3) D. -1 So, mano-mano ito since walang shortcut pag third derivative. Sa board exam may ganyan. So let's test kung marunong pa kayo sa manomano. 14. Find the derivative of y if . A. -x/y B. x/y C. y^-3 D. -y^-3 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. 15. Find the first derivative of y if A. y / (x+y) Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven B. -y / (x+y) C. y / (x+2y) D. -y / (x+2y) Same lang sa #14. 16. Find the partial derivatives with respect to x of the function A. y^2 - 5 B. y^2 C. xy-5y D. 2xy Mag-iisip ka ng value ng y and then kapag dinirivative mo, equal siya dun sa value ng y. For example, y = 4. Substitute 4 in the equation. The equation now becomes 16x-20+6 or 16x-14. 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.

17. The function A. -1, 3 B. 1,-3 C. -1,2 D. 1,-2

is discontinous at

Use d/dx function then x=x and press CALC. Isubstitute ang lahat ng choices at kung saan nagerror, yun na. 18. Find the slope of the tangent line to the graph of the function x=3. A. 60 B. 66 C. 72 D. 78

at the point where

Radian mode. Use d/dx function with x=3 Slope tangent is equal to the first derivative(y') 19. If y=4cos x + sin 2x, what is the slope of the curve when x = 2 radians? A. -2.21 B. -4.94

Edited by: Pulandit


[ TUT ] MATH - CALCULATOR TECHNIQUEs by SirhOSEven C. -3.21 D. 2.21 same with #18. 20. Find C so that the line y = 4x + 3 is tangent to the curve y = x^2 + C. A. 4 B. 5 C. 6 D. 7 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. Use d/dx with x=1, therefore the slope is 4. 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.

Edited by: Pulandit


Tut Math - Calculator Techniques by Sirhoseven -Final 2

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