深入理解，快速备考：《精算考试速通策略》

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"深入理解，快速计算——《考试P洞察与快捷策略：第10版》郭手册详解" 《Deeper Understanding, Faster Calculation -- Exam P Insights & Shortcuts》是Yufeng郭博士专为美国精算师协会（SOA）的 Exam P/Computerized Assessment System (CAS) 考试准备的一本电子书籍。这本书旨在帮助考生高效地掌握考试技巧和知识，提升在实际考试中的准确率和速度。作者强调了对于精算考试者来说，理解和运用正确的策略、选择合适的计算器以及掌握高效计算方法的重要性。本书共分为五个核心章节： 1. 考试策略与学习方法：首章介绍了考试策略，区分了"Top Horse"（核心概念掌握者）、"Middle Horse"（需要进一步巩固者）和"Weak Horse"（需要重点攻克者），帮助考生明确学习的优先级。此外，作者揭示了优秀考生失败的一些原因，以便考生自我反思和避免常见问题。 2. 精确计算的艺术：第二章详细讨论了如何在考试中做到100%的正确率，包括推荐使用的计算器类型、关键的计算器使用技巧，以及对市面上三款最佳计算器的比较分析。这章内容对于提高计算效率至关重要。 3. 概率模型与集合理论：第三章深入探讨了概率的基本概念，如集合、样本空间和概率模型，这对于理解和解答与随机事件相关的考题至关重要。 4. 乘法法则与计数问题：第四章涵盖了乘法原理和加法原理的应用，以及如何通过巧妙的方法解决计数问题，这对于处理组合数学和排列问题的学生尤其有帮助。 5. 其他核心主题：第五章可能包括统计学基础、随机变量、期望值等其他精算考试的核心内容，确保考生对整个考试范围有全面的理解。《Deeper Understanding, Faster Calculation》不仅提供了丰富的理论知识，还提供了实用的备考技巧和策略，旨在帮助考生在有限的时间内提升解题速度和准确性，从而提高通过 Exam P或CAS考试的成功率。由于版权原因，该书不得用于商业销售或分享，并且未经作者Yufeng Guo许可，禁止任何形式的复制或分发。备考者可以访问郭博士的官方网站 <http://guo.coursehost.com> 获取更多资源和支持。

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©Yufeng Guo, Deeper Understanding: Exam P

With the online display feature, you can also reuse formulas. For example, a problem

requires you to calculate



y = 21

e for

== =

12 3

5, 6, and 7.

xx x There is no

need to do three separate calculations from scratch. You enter





2(5)1

e into the

calculator to calculate y when x=5. Then you modify the formula to calculate y when

and

This redo calculation feature of TI-30X IIS is extremely useful for solving stock option

pricing problems in Course 6 and Course 8V (8V means Course 8 for investment). Such

problems require a candidate to use similar formulas to calculate a series of present

values of a stock, with the calculated present value as the input for calculating the next

present value. Such calculations are too time-consuming using the BA II Plus under exam

conditions when you have about 3 minutes to solve a problem. However, these

calculations are a simple matter for the TI-30X IIS.

Please note that BA II Plus can let you see the data you entered into the calculator, but

only when you are using BA II Plus’s built-in worksheets such as TVM (time value of

money), Statistics Worksheet,



Worksheet, and all other worksheets. However, the

BA II Plus does not display data if you are NOT using its built-in worksheets. Unlike the

TI-30X IIS, BA II Plus never displays any formulas, whether you are using its built-in

worksheets or not.

So which calculator should I use for Exam P, BA II Plus or TI-30X IIS?

Different people have different preferences. You might want to use both calculators when

doing practice problems to find out which calculator is better for you.

These are my suggestions:

Statistics calculations --- If you need to calculate the mean and variance of a discrete

random variable, use (1) BA II Plus Statistics Worksheet, or (2) TI-30X IIS for its ability

to allow you to redo calculations with different formulas. When using TI-30X IIS, you

can take advantage of the fact that the formula for the mean and the formula for the

variance are very similar:

22 22

() (), ( ) (), () ( ) ()

EX xfx EX x fx VarX EX E X

== =



So you first calculate

() ()

EX xfx



, then modify the mean formula to

() ()

EX x fx



, and calculate the variance

() ( ) ()

Var X E X E X

=  .

Don’t use the TI-30X IIS statistics function to calculate the mean and variance because

the TI-30X IIS statistics function is inferior to the BA II Plus Statistics Worksheet. Later

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©Yufeng Guo, Deeper Understanding: Exam P

in this book, I will give some examples on how to calculate the mean and variance of a

discrete random variable using both calculators.

Other calculations – Most likely, either BA II Plus or TI-30X IIS can do the calculations

for you. BA II Plus lets you quickly calculate the results with fewer calculator key

strokes, but it doesn’t leave an audit trail for you to double check your data entry and

formulas (assuming you are not using the BA II Plus built-in worksheets). If you are not

sure about the result given by BA II Plus, you have to reenter data and calculate the result

a second time. In contrast, TI-30X IIS lets you see and modify your data and formulas,

but you have more calculator key strokes and sometimes you have to wait several

seconds for the result. I recommend that you try both calculators and find out which

calculator is right for you for which calculation tasks.

Critical calculator tips

You might want to read the guidebook to learn how to use both calculators. I’ll just

highlight some of the most important points.

BA II Plus – always choose AOS. BA II Plus has two calculation methods: the chain

method and the algebraic operating system method. Simply put, under the chain method,

BA II Plus calculates numbers in the order that you enter them. For example, if you enter

23100

+×

, BA II Plus first calculates 2+3=5. It then calculates

5 100 500

×=

as the

final result. Under AOS, the calculator follows the standard rules of algebraic hierarchy

in its calculation. Under AOS, if you enter

23100

+×

, BA II Plus first calculates

3100 300

×=

. And then it calculates

2 300 302

as the final result.

AOS is more powerful than the chain method. For example, if you want to find

12 45

e++, under AOS, you need to enter

1 + 2× 3 2

+ 4× 5

(the result is about 50.1153)

Under the chain method, to find

12 45

e++, you have to enter:

1+(2×3 2

)+(4×5

)

You can see that AOS is better because the calculation sequence under AOS is the same

as the calculation sequence in the formula. In contrast, the calculation sequence in the

chain method is cumbersome.

BA II Plus and TI-30X IIS – always set the calculator to display at least four decimal

places. This way, you’ll be able to see the final result of your calculation to at least four

decimal places.

BA II Plus can display eight decimal places; TI-30X IIS can display nine decimal places.

I recommend that you set both calculators to display, at minimum, four decimal places.

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©Yufeng Guo, Deeper Understanding: Exam P

Please note that the internal calculations done in BA II Plus or TI-30X IIS are NOT

affected by the number of decimal places you set the calculator to display. Your choice of

decimal places only affects what you can see on the calculator screen.

BA II Plus and TI-30X IIS—be careful about storing and retrieving intermediate values.

If a calculation has several steps, you will need to store the intermediate values

somewhere – either on scrap paper (which will be the exam paper in the actual exam) or

in the calculator’s memories. Both methods have pros and cons.

If you like to copy intermediate values onto scrap paper (the simpler approach of the

two), writing down all the decimal places will be too time-consuming for some heavy-

duty calculations and your calculation may lose some precision. If you like to store

intermediate values in the calculator’s memory, you do not have to transfer intermediate

values back and forth between the scrap paper and your calculator. However, you have

the extra burden of keeping track of which memory stores which intermediate values.

Mistakes associated with using calculator’s memories are prevalent. One common

mistake is thinking you stored an intermediate value in your calculator’s memory but you

didn’t, in which case your intermediate value is lost and you have to recalculate. Another

common mistake is to store an intermediate value in one memory (such as Memory M0

in BA II Plus or in Memory A in TI-30 IIS) but to retrieve it from another memory (such

as Memory M1 in BA II Plus or Memory B in TI-30X IIS).

Watch out for the distinction between the minus sign and the negative sign. Both BA II

Plus and TI-30X IIS have a minus sign “



” and a negative sign “ - .” They look similar,

but are completely different. If you look closely, the minus sign is longer and the

negative sign is shorter. The real difference is that the minus sign is for subtraction (such

as 5



3=2) and the negative sign is to indicate that a number is negative (such as



=0.36787944). Using the subtraction sign mistakenly for the negative sign will cause a

calculation error.

Be careful using % on the BA II Plus. For example, if you type 100 – 5% in BA II Plus,

you might expect to get 99.95. However, after pressing the [Enter] key, you get 95

instead. BA II Plus calculates

%(1%)

AX A X

±=±

. So if you type 100+5%, you’ll get

105. If your intention is to calculate 100 – 0.05, you can enter 100 -1

5% (i.e. 100 minus

1 times 5%).

Learn how to reset your calculator. According to exam rules, when you use BA II Plus or

TI-30X IIS for an SOA or CAS exam, exam proctors on site will need to clear the

memories of your BA II Plus or TI-30X IIS. Typically, a proctor will clear your

calculator’s memories by resetting the calculator to its default setting. This is done by

pressing “2

” “Reset” “Enter” for BA II Plus and by simultaneously pressing “On” and

“Clear” for TI-30X IIS and TI-30X IIB. You will need to know how to adjust the settings

of BA II Plus and TI-30X IIS to your best advantage for the exam.

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In its default settings, BA II Plus, among other things, uses the chain calculation method,

displays only two decimal places, and sets its Statistics Worksheet to the LIN (standard

linear regression) mode. After the proctor resets your BA II Plus and before the exam

begins, you need to change the settings of your BA II Plus to the AOS calculation

method, at least a four decimal place display, and the 1-V (one variable) as the mode for

its Statistics Worksheet. Refer to the guidebook on how to change the settings of your BA

II Plus.

You need change only one item on your TI-30X IIS once the proctor resets it. In its

default settings, TI-30X IIS displays two decimal places. Instead set your TI-30X IIS to

display at least four decimal places.

When you study for Exam P, practice how to reset your BA II Plus and TI-30X IIS and

how to change their default settings to the settings most beneficial for taking the exam.

Finally … practice, practice, practice until you are perfectly comfortable with the BA II

Plus and TI-30X IIS. Work through all the examples in the guidebook relevant to Exam

Calculator Exercise 1

A group of 23 highly-talented actuary students in a large insurance company are taking

SOA Exam FM at the next exam sitting. The probability for each candidate to pass

Course 2 is 0.73, independent of other students passing or failing the exam. The company

promises to give each actuary student who passes Course 2 a raise of $2,500. What’s the

probability that the insurance company will spend at least $50,000 on raises associated

with passing Exam FM?

Solution

If the company spends at least $50,000 on exam-related raises, then the number of

students who will pass FM must be at least 50,000/2,500=20. So we need to find the

probability of having at least 20 students pass FM.

Let

= the number of students who will pass FM. The problem does not specify the

distribution of

. So possibly

has a binomial distribution. Let’s check the conditions

for a binominal distribution:

• There are only two outcomes for each student taking the exam – either Pass or

Fail.

• The probability of Pass (0.73) or Not Pass (0.27) remains constant from one

student to another.

• The exam result of one student does not affect that of another student.

satisfies the requirements of a binomial random variable with parameters

=23 and

=0.73. We also need to find the probability of



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深入理解，快速备考：《精算考试速通策略》

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