# Eight Secret Tricks to Passing (Exam FM)

1.  Be over-prepared: The syllabus is so extensive, and there are so many twists that may be put on standard material, that there are always going to be questions that look foreign. The more that you are prepared, the more that you will be able to handle some of these. Being over prepared also helps to deal with emotions. There were points during the exam when a little voice in my head said “There is no way that you are going to pass this.” Yet, that same voice was in my head during many sample exams which I passed with flying colors. Experience and over-preparation reveals that you can succeed even when you are not at your best. If you walk into the exam center with worries, or a cold,or the flu, or pain in your back, you know that you can still succeed.

2.  Fill in the tough spots: It can hurt your head to learn new things. Identify the areas with which you struggle, and try to get your head around them. Two weeks before the exam, I still had some head-pain topics. Things like duration matching, convexity, interest rate swaps, and put-call parity. But, they were on my daily study schedule, and I forced myself to confront them each day. It paid off.

3.  Fill in the fundamentals: Once you gain proficiency in a topic, the fundamentals look different. In the month before the test, I went back and reviewed some of the basics of interest theory. At this point, the basics were easy, and I picked up on some of the finer points that I missed the first time around. Amortization schedules, for instance.  After I learned the basic formulas, it was easy to ignore the schedules they are based on. Yet many problems are made much easier by using schedules, rather than relying on formulas.

4.  Memorization is easy: Once you understand things thoroughly, you don’t really need to do much memory work for these exams. After months of working problems, most things will be anchored in your head. And yet suppose that you find yourself trapped in a dark alley by two annuities, one of which is twice as long as the other. Then you will be glad that you memorized $\frac{a_{\overline{2n}\lvert }}{a_{\overline{n}\lvert }}=1-v^n$ I have never encountered this fact in practice, but if I did, recognizing this identity might save me a couple of minutes. Spend a little time on memory work, it is easy.

5.  Test symbolic solutions with numbers: If you have a problem with a purely symbolic solution, and you can narrow it down to a couple of possible solutions, you can frequently replace the variables with reasonable numbers, and see if the result is true. This is my favorite new solution technique I learned while studying for this exam.

6.  Read MacDonald: Actually read it. After you learn the math, go back and read it. If you look at the notes from the sample problems, you will notice that the exam writers have made it pretty clear that the exam will be based on the book. Those non-numeric multiple choice questions can be very challenging. Read the book.

7.  Number your Scrap Paper: I learned this trick when taking practice exams.  If you have time to review problems at the end of the exam, you will need to find the scratch-work easily.

8.  Practice with dull number two pencils: Two weeks before the exam, I put all of my mechanical pencils away, and worked only with old fangled sharpenable pencils. Two hours into the exam, you will be working with dull stubs, so you need to be prepared.

# Only 13 days left

Only thirteen days until the exam. That really crept up on me. I have been taking a full practice exam each day, plus lots of other problems, plus trying to fill in weak areas.
I feel that I am more prepared than I was for the last exam. The practice exams that I am taking and more difficult than the actual test, and are quite humbling. This is good, but in the few days before the exam I am just going to study easy stuff, to get my confidence up.
I promise that I will post regularly until the exam.

# Nirvana

My Study Helper

I’m so excited about studying right now. I still have some derivative markets stuff to take on, but the essentials (calls and puts, purchased and written) are becoming fairly intuitive. A couple of weeks ago, I was feeling more negatively. The basic options material looked like a giant heap of meaningless graphs and formulas. Now, I have formed some associations for all of it.

Normally, I study with a certain amount of distraction. There may be a cat sitting on my lap, or chasing the cursor on the screen. There may be a dog that wants to play, or some issue to discuss with my spouse. I may be distracted by tomorrow’s weather forecast, or by the latest Boing Boing post. These distractions are acceptable: I know how to deal with them, and I am motivated enough to regain my focus. At a certain point, however, there is nothing like a single-minded absolute focus on the work in front of me. And to achieve this, there is nothing comparable to taking a test.

I assume that, among actuary students, I am typical in my love of taking exams (I suspect that I am also typical in having been truly humbled by the actuary examinations  🙂 ). Taking tests, and often out-thinking tests, is what got me through grade school, when I did absolutely no school work or studying. My love of standardized tests, and resulting scores, is what eventually led me to be placed in classrooms appropriate to my ability. So, if you want to get my absolute attention, put an exam in front of me.

With this knowledge in mind, I have registered with Coaching Actuaries again. I took my first exam a couple of evenings ago, and I was immediately transported into test nirvana. For three hours, my mind didn’t blink. The fact that the scores are measured, and that there is a leader board to work myself onto, is extremely motivational to me. I can’t wait to take another test this afternoon.

# The Cards

Cutting them up:

I have owned this paper cutter for 25 years.  At that time, I did not own much but the clothes on my back.  How would I have survived without a paper cutter to make little books and cards and such?

Things that I gained by making these cards:

1. A strengthened knowledge of FM fundamentals.
2. Increased fluency with LaTeX.
3. A creative project which kept me focused on the subject at hand.
4. A nice little pile of finished cards.
5. Time to think about the pluses and minuses of virtual products versus actual.

# Exam FM, Chapter 1 Flashcards

I just posted my nearly final version of the first chapter of flashcards for exam FM.  I added some questions on geometric progressions, and some on force of interest, so now there are 226 cards.  I know that there are still a few holes, but I will worry about that later.  I could probably come up with 300 cards for the first chapter very easily.  But, having put together several sets of study cards, I find that I add fewer cards for subsequent topics.  In almost any subject, the most vital information to commit permanently to memory is at the beginning.

I tried to use a sampling of the different terminologies.  For instance, I used the accumulation function $a(t)$ as well as the FV, PV terminology.  When I look at the solutions for the exam sample questions, I see both types used, so I suppose that it is possible for either to appear in an examination question.

For most formulas, I give several types of numerical examples.  It is important to see the relationships at work.  To see the animals in their native habitat.

In a later post, I will describe how to use these cards to best effect.  I do intend them as a means of permanently learning the material.

# Finite Geometric Progressions

If you look over in the right sidebar, under Memes For You, you will find the expression If not now, when? Here is how I apply this expression to mathematics: During the course of work, if I encounter a mathematical expression, algorithm, or symbol which I don’t fully understand, I take some time and learn it right now. Probably I will run into this mathematical truth again. Perhaps I should have learned this mathematical truth in High School, or College. Plausibly I am missing out on a beautiful gem of mathematics. A few examples: the triangle inequality (simple nearly to the point of triviality, yet beautiful, and vital in certain proofs), the quadratic equation (immensely practical, yet also historical (you can’t use a formula to solve equations of any higher degree), why did I not memorize it in high school?), the definition of real numbers (my favorite definition, centuries in the making).

That leaves us right now with Finite Geometric Progressions. Somehow, they avoided me, or I avoided them, for all of these years. But, here they are, at the root of financial mathematics. I may be able to learn financial mathematics without them, but why should I miss out on an opportunity to become friends with these cute little critters? Here we go.

Starting a month from today, you are going to deposit one dollar each month into an account that pays 0.25 % interest per month. How much money will be in the account in 6 months, at the time of the last payment?

Let’s work backwards. You have made 6 payments.

• The 6th payment has accumulated no interest, so is still worth 1.
• The 5th payment has accumulated one period of interest, so is worth $1 (1.0025)$
• The 4th payment has accumulated two months of interest, so it is worth $1 (1.0025)^2$
• The 3rd payment has accumulated three months of interest, so it is worth $1 (1.0025)^3$
• The 2nd payment has accumulated four months of interest, so it is worth $1 (1.0025)^4$
• The 1st payment has accumulated five months of interest, so it is worth $1 (1.0025)^5$

The sum of all the deposits, plus the interest, is hence $1 + (1.0025) + (1.0025)^2 + (1.0025)^3 + 1.0025)^4 + (1.0025)^5$

We might have written this as $t_1 + t_1 r + t_1 r^2 + t_1 r^3 + t_1 r^4 + t_1 r^5$ or the sum of the first n terms of a geometric progression with common ratio r. In high school, we should have learned that this sum is equal to:

$t_1 \frac{r^n -1}{r-1}$

In our case, r = 1.0025, n = 6.

$1 \frac{1.0025^5 -1}{1.0025-1}= 6.0376$

We might also write this as $\frac {(1+i)^n -1}{(1+i)-1}$

Which clearly equals $\frac {(1+i)^n -1}{i}$

Which mysteriously is also s angle n, or the accumulated value of the annuity immediate.

# Another Update on Exam FM Flashcards

I updated my Financial Mathematics cards again this morning. The link from a couple of days ago reflects the updates. There are now 190 cards.

The cards are in the form of a PDF file, to be printed on letter size paper (8.5 x 11 in). Many printers do not print the front and back of each page in good alignment, so I made sure not to place text too near the borders of the back of the cards.  Simply print the cards out, cut a 1cm border from around the page, then cut the cards out.  Whoops!  I have mixed inches and centimeters.  I will straighten out the unit issue on the next version, with a 1/2 inch border.

I am trying to really fill out most of the fundamentals.  This makes the cards useful not just for someone studying for the actuary exams, but also for anyone learning the basics of finance.

Let me know how the cards work for you, or if you find any errors.

# Nearly done With First Chapter of Cards

I have just updated the first chapter of my Financial Mathematics cards.  (link is on post from a couple of days ago).  The deck is up to about 160 cards.  I am looking at the exam FM syllabus, plus some books, and filling in topics.  Next week the first chapter will be finalized, and I will post a permanent link on the sidebar.

Later, I will post some advice on how these cards are intended to be used.  In essence, these cards reinforce the fundamental pieces that go into solving difficult problems.  They certainly do not replace solving tough problems, or replace learning the concepts.  Often, they may suggest new ways of solving complex problems.  I intend them to be used along with a pencil, paper, and calculator.  Setting up the solution is more important than a numerical answer, however.  The numerical cards are intended more as ways of recognizing and reinforcing the fundamental equations and relationships.

I can’t wait to finally post my Exam P cheat sheet.  LaTeX is great 🙂

I have been working hard today.  Here is a PDF of the first draft of my exam FM flashcards.  So far, they just cover “chapter 1” stuff like Interest Theory and Lump Sums.  I think that there are about 110 cards so far.  I will soon be fleshing out the missing Interest Theory topics, then I will add the Annuity cards that I have made.

I am delighted to have used LaTeX to design the cards.  They are 2 cards by 5 cards on a letter size page.  This is a standard card size, which you can buy paper for at the store.  I will add some cut marks when I figure out how.

More tomorrow.

# Update on Card Formatting

Yesterday, I posted this flash card as an example:

When I did my repetitions this morning, I realized that this card, and several similar ones that I created yesterday, are too complicated.  Cards should only test one very small item of knowledge. (Read SuperMemo 20 Rules of Formatting Knowledge)  The cards from yesterday test not only the function of the “a angle n” function, but also require a calculation with this function.  A much better card is as so:

The wording of the card now makes it obvious that I am not looking for a numeric answer.  The purpose of this card is simply to help the mind to recognize and recall a common relationship that involves the present value of the annuity immediate.