Warning: Possible readers who can appreciate this post are engineering and math majors who need calculator techniques for the board exams. Numbers and equations are involved.

A few days ago, I got an email from a civil engineering student in Pangasinan. He asked me this question:

“I’ve read in your website that you are sharing tips for engineering board exam.. I’m so grateful to see people who share their knowledge and experiences to other people. I’m very interested to know some calculator techniques in solving problems in engineering mathematics like calculus using fx-991 es.. can you share some to me? thank you so much!”

Thanks so much for this emailed question! Keep the questions coming, board exam related or not, because I really accommodate what you guys want to read here next.

I already made a post on calculators as part of my series of board exam tips in this blog. But the techniques were not posted because I was too lazy at the time. LOL. I am not really much of an expert in maximizing this calculator model, but there were some tricks that I found useful.

One of the best advantages of using Casio ES 991 is the **Natural Display**. It looks exactly as one would write the equation on paper:

**I strongly advise you to read the Casio ES 991 manual before you experiment with the techniques**. I know, it’s like I am asking you to drink acid with this tip, but trust me, it works! For one, I learned from that long manual that you cannot use the derivative and integral function button in certain equations.

So many calculator users may rely too much on the results produced by the integral and derivative buttons of this calculator. But you know what? The algorithm used on the ES 991 calculator for derivatives and integrals is heavily based on a fair mathematical approximation (according to the manual!), and bound to fail in certain types of equations. Be careful. When I took the board exam last year, the only difference between me and the top 1 of our board exam was roughly around five questions. Every item counts.

Also, be consistent with the angle usage. **Check if the mode of your calculator is properly set to degrees or radians. **I heard of a tale of one board exam taker who was computing in degrees but her calculator was set to radians the whole time. She panicked during the exam because her answers were not found in the multiple choices given. She got to fix this minor error about 30 minutes before time was up. She still passed, because she is very intelligent, but that is truly a source of additional stress, if you ask me.

I already said something about the** SHIFT + SOLVE** function in the previous post on calculators, so I will not repeat them anymore.

I frequently used the** CALC** button, especially when I am forced to repeat an equation over and over again for different values. This is very common in long engineering problems.

For example, you need to find y for 5 values of x, and the equation is y = x + 5. I am using basic equations here just so you get the principle. For example, the given values for x are 1,15,25,30, and 16.

Manually, you will have to type in “1+5″, “15+5″, “25+5″, “30+5″, and “16+5″ separately to get the 5 y values you need. That’s just too mechanical, and a complete waste of board exam time.

Using CALC, you can just use any of the variables in the calculator (A,B,C,D,X and Y are all usable for this purpose). Just type in “X+5″ and press the CALC button and the equal sign. You will be prompted by the calculator to give the X values without having to type the formula over and over again. And since you can all use A, B, C, D, X, and Y, you can get values with as much as 6 variables without having to hurt your fingers.

Just be careful not to store important constant values in A, B, C, D, X, and Y when you are using it for CALC. Chances are, the values you stored will be deleted as you use the CALC button.

There are 8 modes in Casio ES 991.

Mode 1 COMPUTATION

This mode is the default mode for calculations and this is where most of your computations will occur.

Mode 2 COMPLEX

The complex mode is hardly used in my major, geodetic engineering. But we did have need to convert Polar to Rectangular coordinates in computing for lot data. I got this technique from Engr. Machele Felicen, who was our Top 1.

We just enter A<B + CALC

It will ask for the values of A and B (A is the r, B is the theta).

Then the answer it will produce is something like this:

1.45365444 + 3.4567**i**

The first term and second term are the rectangular coordinates (x,y) already.

That saves you helluva lot of time than when you use the one given by the Casio manual for converting (r, theta) into (x,y).

Mode 3 STAT

I did not get to use this much during my exam because we geodetic engineers are more inclined to geometry and calculus. But based on what I have seen so far, you can do so many things for Statistics with ES 991. And the natural display will easily show you the list of the values. It was unlike my old calculator where you have to scroll down a lot and punch a lot of buttons before you get to each n value.

Mode 4 BASE-N

BASE-N…I did not get to use it at all. LOL. Sorry.

Mode 5 EQUATION

Mode 5 was one of my favorites during the board exam. It allows you to get the values for **2 equations, 2 unknowns** and **3 equations, 3 unknowns**. It also will help you get the **quadratic and cubic roots of an equation**. They are most useful. All you have left to do during the exam is to reduce all the complex equations into any of these four forms and then you are super done with it.

During our review class, there was one challenging math problem with 9 equations and three unknowns. That’s hell if you do it manually. Simplification was vital. I just reduced it to three equations and used Mode 5 and I got X, Y, and Z in less than 5 minutes.

Mode 6 MATRIX

Matrix operations were pretty common, too. Too bad it can only handle 3 by 3 matrices at the most. But you can store up to three matrices and work with them without having to type the matrices over and over again.

Mode 7 TABLE

In my initial example for CALC, I used different X values which are far from each other in the number line. But what if the x values are within an interval and is equally spaced? For example, the X values are 1,2,3,4, and 5. The Table mode is ideal for values like these.

This TABLE mode will instantly prompt you to give an expression for f(X).

It will ask you where the X values will start (“Start?”) and end (“End?”). It will also ask the interval between the values (“Step?”). In the example’s case, Start is 1, End is 5 and Step is 1 unit.

For its output, the calculator will yield a table containing all the values that you need, showing both X and F(X) as you would see it tabulated on paper, thanks to natural display.

(Note: I tried using variables A, B, C, D, and Y for Table mode, but I believe it only works when you use the X variable.)

**I also use the Table Mode when I have a hard time visualizing a certain function. I just choose a reasonable interval of values, plug the equation and I sketch the table of values on a scratch paper so that I have a better vision of the equation’s physical properties. **

Mode 8 VECTOR

If you need dot products and dim, you can use this mode. It can hold three-dimensional data (X,Y,Z), even. I have not used it too much. I think it will be more useful for Physics classes than in Math board exams. I leave the physicists to enlighten you on the matter.

My reader explicitly asked about Calculus techniques. For this, I believe ES 991 poses you with a tiny limitation. It will only get you derivatives and integrals for those with absolute numerical values. This means, you ought to have upper and lower limit values for the integration function. **In college, this function may be a bit useless because you will need to solve calculus problems by hand if you really want to master the theorems and get a good grade in your class. Don’t do too much shortcuts in college at the expense of learning the principles. But during board exams, where there are application-focused problems likes Maxima-Minima and Related Rates, you can definitely take advantage of the derivative and integral buttons. **

**Do use the calculator everyday, even for small things like your shopping list.** It allows you to get used to the calculator buttons. This, in turn, improves your manual dexterity and speed in using the calculator. Make sure you have enough batteries. At the time of my exam, I replaced the batteries 2-3 days before the actual exam and I had a spare calculator of the same model in case my original calculator breaks down somewhere during the board exam.

**It takes a lot of practice to learn shortcuts. And it saves time in getting you from point A to B during an exam. **

**But do make sure that you know the long methods before you play around with the shortcuts. I am totally not encouraging that you rely purely on shortcuts to pass the exam. The complete comprehension of the concepts is very, very important. **

If you have other calculator tips for our dear readers, this post is open for discussion and comments.

Did you find this post useful? You can click any of the share buttons below (Facebook, Twitter etc.). I have shared my techniques freely to you, so pay it forward and let’s help some more people get their licenses.

(You can also show me some love by subscribing via email for updates at the right side bar of this page. However, I blog about many things, so my posts are not just limited to board exam posts. This brain likes variety so much. :-P)

i haven’t used Vector much either. My favorite function, SHIFT+SOLVE!

Solve ka na in Algebra, Trigo, Analytic Geom and other basic mathematics with SHIFT+SOLVE!

yessss! shift solve is the best!!!! i am still using it at work. lol.

what’s the difference between CASIO ES991 and CASIO ES991PLUS when it comes to its functions???

Hi Jepoy! Based on my experience, the 991 plus is much faster during Shift+Solve computations… But other than that, nothing new really.

Hi Helen,

For Mode 8 VECTOR, dag-dag mo na lang when using the vector function pwede mo kunin yung resultant vector kahit binigyan ka ng X number of vectors through simple vector addition. Simple lang yung operation ibibigay mo lang yung values x,y at z and start mo lang iadd yung mga equations. Pwede rin nyang masimplify yung pagamit sa right hand rule (marami kasing hindi agad nakakagets nito hehehehe) kasi kaya nya rin magvector multiplication through this mode. Ok?

Hope this helps.

boy GPSSSS! hahahahah salamat naman sa pagdalaw at pagdagdag ng pampataba ng utak ng mga engineering majors. LOL. oo nga ano, nalimutan ko na pwede pala yung Mode 8 sa Statics at Dynamics problems. hahaha.

Hi ate Helen!

Ako po yung ng-email po sa inyo.. Thank you very much for sharing some tips using this calculator and in board exam. I will share it to my friends..

hi darius! You are very welcome. I hesitated to include your name kasi you might want to stay anonymous or something… I am glad to be of assistance. Go tell your friends. Good luck and thanks for visiting and commenting.

me too..tnk so much girl..hope to see u soon…

yes! see you very soon ciding!

I keep on telling my students to read their calculator’s manual. I feel like Cassandra sometimes especially when I learn that my students (almost all of them!) do not even bother to read the manual nor keep their copy of it.

One of the techniques I use is to do the algebra first before using my calculator. Often enough, it’s a time-saver, and it’s very useful when studying. Doing the algebra, checking limiting cases, doing dimensional analysis, are all important techniques that are too seldom learned.

Learning the ideas that underlie the methods used by a calculator before using it is spot-on; it is, however seldom learned.

Cassandra? Ay oo nga, the dimensional analysis part is very important to deal with before doing anything else. Nothing sucks more than making lengthy computations only to find out at the end that you used the wrong unit. haha. Thanks Mike. Sobrang expert mo na dito… Would you have additional techniques for Vector mode as a physicist?

I don’t use vector mode; there are a lot of procedures I have not explored in the manual because I haven’t needed them. The ones that do get used frequently are the regression mode, scientific constants and conversions. I’ve looked at the manual for SOLVE, and VECTORS, and found it interesting, but I prefer to do the algebra myself.

The manual contains information about the numerical methods used; Newton’s method is used by SOLVE; there are cases when it fails spectacularly (multiple roots, steep functions, discontinuous functions) so it takes some thinking to decide on whether you can trust the result you get.

On dimensional analysis: the failure to check units can have catastrophic consequences. My favorite story is the crash of the Mars Climate Orbiter mission. Because of the failure to convert units from English to metric, the orbiter crashed into Mars. The link is: http://mars.jpl.nasa.gov/msp98/news/mco990930.html

hi helen gud night po.. allergic ako sa scientific calculator hehehe ok lang sa akin ang mga ordinary calculator kung money money ang cocomputin hehehe joke!!!

good morning na nung nabasa ko csseyah! hahaha. may allergy pala sa calculators? hahahaha… ay oo naman, pag money money nga minsan kahit mental math uubra na sakin. lol.

gud evening po saan po pedeng makakuha mg example…kasi po hindi ko po alam kung saan po ako mag uumpisa..sana matulungan nyu po ako…maraming salamat po.,.,.,

Hi Brecky, so sorry sa late reply. Medyo busy rin kasi ako sa work ngayon. Subukan mo sa mga reviewers. Kasi ang ginawa ko lang talaga noon, sagot lang ako ng sagot ng sagot ng mga problems sa Math tapos talagang gamit na gamit yung calculator ko. Kahit nga wala kang shortcuts basta gamit na gamit yung calculator.

nice post, i remember my college days with this. nakaktuwa it brings back the memories nung nakukulta ang isipan ko sa math.. pero at the same time nakakaenjoy nmn..

hahaha! hi event lover, salamat sa pagdalaw. personally, mas gusto ko ang Math, dahil malinaw na may solution lagi ang problema.

tama..mabuti pa ang math my solution,,kya ma solv ang problem..huhu

hahaha hmm bakit kaya huhu?

hi helen! thanks for sharing ur knowledge about calcu techniques and some board exam tips… it’s been a long time since a took my 1st board exam but i failed.. now,i’m starting to review again (self review) and i really want to pass the board exam. hope u could give me more inspiring thoughts and tips about passing the board exam. i salute u engr.! thanks and more power!

Hi Eymal,

Are you GE too? I’m planning on taking this year’s exam and when I read Helen’s post, it inspires me and scares me at the same time. It’s been ages since my first take and I got too scared to go get the next one but I don’t care, I’m taking it this year. Tumatanda na ako, parang di na bagay na patagalan ko pa. LOL!!

Its glad knowing I’m not alone in feeling like this but I’ll go for it headstrong and determined.

Cheers to us retakers! The industry needs us.

hello there eymal! thank you so much for leaving a comment. Go for the gold this year and get that license!

(I will be making another post that you might find useful. But I am sorry that it is taking a while. I am quite busy with my job right now.)

hello jen,

i’m CE..gaya mo rin na tumatanda na, di na dapat natin to patagalin pa..i’m planning to take up the exam by next yr coz i’m still here in kuwait ryt now. gud luck sau jen and hope to hear u soon engr. jen!

Hi Eymal,

Whether CE or GE basta the passion is there. We should aim diba? Hope to hear from you soon too Engr. Eymal.

Cheers!

THANKS A LOT…

:)Nice!

hi helen,

i have been using a 991ES calculator from past two years. But now some problem has occured with that. I am not able to change any mode. That function is just not responding. I hope you can help me out in this matter.

thanks

Hello Nupur! What particular problem are you encountering? Maybe it will help to reset your calculator? I believe there is a tiny button at the back of the calculator that you can gently poke with a pointed object. Or maybe a battery replacement is in order.

enroll kayo sa POWER HOUSE review center .. may seminar sila para sa CALCULATOR TECHNIQUE . all ENgineering MAth problems . may shortcuts ! enroll and amaze