北美精算师(SOA)考试P 2000年 May 真题
北美精算师真题course1
Calculate the percentage of the group that watched none of the three sports during the last year.
(A) (B) (C) (D) (E)
24 36 41 52 60
Course 1
6
Form 03A
2.
c f ( x ) − dg ( x ) . x →0 f ( x ) − g ( x )
(A) (B) (C) (D) (E)
0 cf ′ ( 0 ) − dg ′ ( 0 ) f ′ ( 0) − g′ ( 0)
f ′ ( 0) − g′ ( 0) c−d c+d
Course 1
8
Form 03A
(A) (B) (C) (D) (E)
0.07 0.29 0.38 0.42 0.57
May 2003
9
Course 1
5.
An insurance company examines its pool of auto insurance customers and gathers the following information:
Each of the graphs below contains two curves.
Identify the graph containing a curve representing a function y = f ( x ) and a curve representing its second derivative y = f ′′ ( x ) .
Calculate the rate at which the value of the investment is changing after 8 years.
北美精算师(SOA)考试 FM 2001 May 年真题
1.
Which of the following statements is an implication of the semi-strong form of the Efficient Market Hypothesis?
(A) (B) (C) (D) (E)
Course 2
12
Form 01A
9.
Which of the following statements regarding consumer goods in the marketplace is true?
(A) (B) (C) (D) (E)
The quantity demanded of an inferior good decreases as its price decreases. The intersection of a consumer’s Engel curve and demand curve represents how much the consumer will buy given a specific income level. When the price of a normal good decreases, the increase in quantity due to the income effect cannot be greater than the substitution effect. The compensated demand curve for a normal good will be steeper than the uncompensated demand curve. The income elasticity of demand is equal to the slope of the Engel curve.
2000年真题与解析
2000年真题与解析If a farmer wishes to succeed, he must try to keep a wide gap between his consumption and his production. He must store a large quantity of grain 1 consuming all his grain immediately. He can continue to support himself and his family 2 he produces a surplus. He must use this surplus in three ways: as seed for sowing, as an insurance 3 the unpredictable effects of bad weather and as a commodity which he must sell in order to 4 old agricultural implements and obtain chemical fertilizers to 5 the soil. He may also need money to construct irrigation 6 and improve his farm in other ways. If no surplus is available, a farmer cannot be 7 . He must either sell some of his property or 8 extra funds in the form of loans. Naturally he will try to borrow money at a low 9 of interest, but loans of this kind are not 10 obtainable.1. [A] other than [B] as well as [C] instead of [D] more than2. [A] only if [B] much as [C] long before [D] ever since3. [A] for [B] against [C] of [D] towards4. [A] replace [B] purchase [C] supplement [D] dispose5. [A] enhance [B] mix [C] feed [D] raise6. [A] vessels [B] routes [C] paths [D] channels7. [A] self-confident [B] self-sufficient [C] self-satisfied [D] self-restrained8. [A] search [B] save [C] offer [D] seek9. [A] proportion [B] percentage [C] rate [D] ratio10. [A] genuinely [B] obviously [C] presumably [D] frequently试题解析1. 【答案解析】C考查知识点: 逻辑关系＋短语辨析文章的第一句点明了全文的主题：如果一个农民想成功，他必须保证生产远远大于其消费。
北美精算师(SOA)考试P 2000 November年真题
(A) (B) (C) (D) (E)
208 260 270 312 374
November 2000
1
Course 1
2.
An investor purchases two assets, each having an initial value of 1000 . The value Vn of the first asset after n years can be modeled by the relationship:
0.06 0.16 0.19 0.22 0.25
Course 1
12
Form 00B
13.
An actuary believes that the demand for life insurance, L, and the demand for health insurance, H, can be modeled as functions of time, t:
What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?
(A) (B) (C) (D) (E)
0.68 0.82 0.87 0.95 1.00
Course 1
2
Form 00B
3.
An auto insurance company has 10,000 policyholders. Each policyholder is classified as
(i) (ii) (iii)
young or old; male or female; and married or single.
北美精算学会-SOA-考试制度第2页-精算师考试.doc
财务课程编号名称学分p385财务管理20f580公司财务15f585应用公司财务20f590公司战略和偿付能力管理10团体和健康保险课程编号名称学分g320团体和个人健康保险30的设计和销售g421团体和个人健康保险25的财务管理和法规g422团体和个人健康保险25的定价g522高级品种10g523非养老年金的退休后10和就业前的福利g525灵活的福利计划10g528健康保险专题15个人人寿和年金保险课程编号名称学分l340个人人寿和年金保险30的精算实务调查l343 人寿保险法和税收15n41高级设计和定价25n43估价和财务报告专题25l540个人人寿和年金保险10的营销l545丧失工作能力收入15l550再保险专题15养老金课程编号名称学分p360养老金估价原理15p362退休计划设计15p363养老金筹资工具15p365养老金计划的法律规定25p461养老金估价原理ii和20养老金计划会计标准p560 国际养老金问题20p564作为专家证人的10p567退休收入保障25投资课程编号名称学分v480衍生证券：理论和应用20v485高级资产组合管理15v595资产和负伤管理应用20要取得fsa资格必须通过以上一个方向的所有课程考试，以及再选择以上方向的其他课程，使学分达到150分，即学分总计要达到450分。
此外，当fsa要素的课程考试全部通过后，考生还要参加最后一门课程一一正认可课程(fac)，其内容主要是职业道德和案例，时间为二天半，一般只要自始自终参加，在结束后的晚宴上会获得fsa证书。
到1996年，北美精算学会共有会员16，558名，其中美国11，961名，加拿大3，161名，其他国家1，436名，(除了fsa、asa外，还包括少量的财产和意外险和美国养老金)20，592人，其中美国15，695人，加拿大3，355人，其他国家1，542人。
北美精算学会的考点分布在全世界28个国家和地区，考试每年在春季(五月)和秋季(十一月)举行两次，全世界每年有数干人参加asa一万多门次课程的考试，其中asa的平均通过率为40％。
北美精算师(SOA)考试P 2001 November年真题
is independent of the number of accidents that occur in all other months.
Calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.
(A) (B) (C) (D) (E)
0.0000 0.0004 0.0027 0.0064 0.3679
Course 1, November 2001
9
9.
Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist.
(–1)n n
− an = 1 2n n
Course 1, November 2001
11
11.
A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is
北美精算师考试大纲 2012-May-exam-p
Probability ExamThe Probability Exam is called Exam P by the SOA and Exam 1 by the CAS. This three-hour exam consists of 30 multiple-choice questions. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA).The Probability Exam is administered as a computer-based test. For additional details, Please refer to Exam Rules.The purpose of the syllabus for this examination is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.A table of values for the normal distribution is available below for candidates to download and will be included with the examination. Since the table will be included with the examination, candidates will not be allowed to bring copies of the table into the examination room.Check the Updates section on this exam’s home page for any changes to the exam or syllabus.The ranges of weights shown are intended to apply to the large majority of exams administered. On occasion, the weights of topics on an individual exam may fall outside the published range. Candidates should also recognize that some questions may cover multiple learning outcomes.Each multiple-choice problem includes five answer choices identified by the letters A, B, C, D, and E, only one of which is correct. Candidates must indicate responses to each question on the computer.As part of the computer-based testing process, a few pilot questions will be randomly placed in the exam (paper and pencil and computer-based forms). These pilot questions are included to judge their effectiveness for future exams, but they will not be used in the scoring of this exam. All other questions will be considered in the scoring. All unanswered questions are scored incorrect. Therefore, candidates should answer every question on the exam. There is no set requirement for the distribution of correct answers for the SOA/CAS/CIA multiple-choice preliminary examinations. It is possible that a particular answer choice could appear many times on an examination or not at all. Candidates are advised to answer each question to the best of their ability, independently from how they have answered other questions on the examination.Since the CBT exam will be offered over a period of a few days, each candidate will receive a test form composed of questions selected from a pool of questions. Statistical scaling methods are used to ensure within reasonable and practical limits that, during the same testing period of a few days, all forms of thetest are comparable in content and passing criteria. The methodology that has been adopted is used by many credentialing programs that give multiple forms of an exam.LEARNING OUTCOMESCandidates should be able to use and apply the following concepts in a risk management context:1. General Probability (15-30%)•Set functions including set notation and basic elements of probability•Mutually exclusive events•Addition and multiplication rules•Independence of events•Combinatorial probability•Conditional probability•Bayes Theorem / Law of total probability2. Univariate probability distributions (including binomial, negative binomial, geometric,hypergeometric, Poisson, uniform, exponential, gamma, and normal) (30-50%)•Probability functions and probability density functions•Cumulative distribution functions•Mode, median, percentiles, and moments•Variance and measures of dispersion•Moment generating functions•Transformations3. Multivariate probability distributions (including the bivariate normal) (30-45%)•Joint probability functions and joint probability density functions•Joint cumulative distribution functions•Central Limit Theorem•Conditional and marginal probability distributions•Moments for joint, conditional, and marginal probability distributions•Joint moment generating functions•Variance and measures of dispersion for conditional and marginal probability distributions•Covariance and correlation coefficients•Transformations and order statistics•Probabilities and moments for linear combinations of independent random variablesREFERENCESSuggested TextsThere is no single required text for this exam. The texts listed below may be considered as representative of the many texts available to cover material on which the candidate may be examined. Texts are added and deleted as part of a regular process to keep the list up-to-date. The addition or deletion of a textbook does not change the bank of questions available for examinations. There is no advantage to selecting a text recently added or not using a text recently removed.Not all the topics may be covered adequately by just one text. Candidates may wish to use more than one of the following or other texts of their choosing in their preparation. Earlier or later editions may also be adequate for review.• A First Course in Probability (Eighth Edition), 2009, by Ross, S.M., Chapters 1–8.•Mathematical Statistics with Applications (Seventh Edition), 2008, by Wackerly, D., Mendenhall III, W., Scheaffer, R., Chapters 1-7.•Probability for Risk Management, (Second Edition), 2006, by Hassett, M. and Stewart,D., Chapters 1–11.• Probability and Statistical Inference (Eighth Edition), 2009, by Hogg, R.V. and Tanis,E.A., Chapters 1–5.•Probability and Statistics with Applications: A Problem Solving Text, 2010, by Asimow, L. and Maxwell, M.•Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering 2009, by Bean, M.A., Chapters 1–9.Other ResourcesThe candidate is expected to be familiar with the concepts introduced in “Risk and Insurance”.Tables for Exam P/1Exam P/1 Sample Questions and Solutions (1–153)Risk and Insurance。
北美精算师(SOA)考试 FM 2001 November 年真题和注解
25.
E In order to solve for the price of a call option, first the price of a put option must be determined and then the put-call parity formula is used. Price of put option: [(0.5 x 0) + (0.5 x 10)] / 1.04 = 5/1.04 = 4.81 Price of call option = Price of put option + current stock price – present value of exercise price Price of call option = 4.81 + 45 – 40/1.04 = 11.35
Course 2 Solutions
1
November 2001
5.
A ¬9.2 + 10 ⋅V Present value = 10 ⋅ a5
1+ k 20 = 0.092 − k 0.84 = 21k k = 0.04
5 9.2
(1 + k ) ( 6.44 )(1 + k ) ∑ (1.092) = 38.70 + 0.092 − k = 167.50 t =1
3.
B
∆Y ∆N ∆K − (α N ) − (1 − α N ) = 2.6 − (0.7)(2.0) − (1 − 0.7)(4.0) = 2.6 − 1.4 − 1.2 = 0.0 Y N K
4.
C APV = Base-case NPV + PV tax shield 120, 000 0.35 × 0.08 × 0.54(100, 000) = −100, 000 + + = 0 + 1,400 = 1,400 . 1.2 1.08
Spring 2000 Exam
Probability of involvement in an accident 0.05 0.02 0.03 0.04
An automobile from one of the model years 1997, 1998, and 1999 was involved in an accident.
I
Course 1
2
1.
The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work.
n
X 4.
¦ Xi
i 1
n
denotes the mean of a sample X1,..., Xn .
The Normal Distribution
1 x w2 / 2 e dw for certain values 25 f of x . The integer part of x is given in the top row, and the first decimal place of x is given in the left column. Since the density function of x is symmetric, the value of the cumulative distribution function for negative x can be obtained by subtracting from unity the value of the cumulative distribution function for x . The table below gives the value of )( x ) x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 1 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 2 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 3 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 Selected Points of the Normal Distribution x (x) 0.800 0.842 0.850 1.036 0.900 1.282 0.950 1.645 0.975 1.960 0.990 2.326 0.995 2.576 May 2000
精算师考试试题 (3)
[5]
(iii) Assume now that p ≠ q.
(a) Determine a value θ ≠ 1 such that Yn = θSn is a martingale.
Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
12 September 2001 (pm)
Subject 103 — Stochastic Modelling
Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Write your surname in full, the initials of your other names and your Candidate’s Number on the front of the answer booklet. 2. Mark allocations are shown in brackets. 3. Attempt all 10 questions, beginning your answer to each question on a separate sheet.
applies to this model and verify that the transition matrix P(t) = P(0, t) given below is a solution:
P(t)
=
æ ç ç
1 2 1 4
e−2αt e−2αt
+ −
1 2
e−6αt
1 4
e−6αt
e−2αt − e−6αt
1 2
e−2αt
北美精算考试试题
北美精算考试试题1. The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work.Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.(A) 0.05(B) 0.12(C) 0.18(D) 0.25(E) 0.352. A study of automobile accidents produced the following data:An automobile from one of the model years 1997, 1998, and 1999 was involved in an accident.Determine the probability that the model year of this automobile is 1997 .(A) 0.22(B) 0.30(C) 0.33(D) 0.45(E) 0.503. The lifetime of a printer costing 200 is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100 printers, how much should it expect to pay in refunds?(A) 6,321(B) 7,358(C) 7,869(D) 10,256(E) 12,6424. Let T denote the time in minutes for a customer service representative to respond to 10 telephone inquiries. T is uniformly distributed on the interval with endpoints 8 minutes and 12 minutes. Let R denote the average rate, in customers per minute, at which the representative responds to inquiries.Which of the following is the density function of the random variable R on the interval(A)12/5(B) 3 (C) (D) (E)5. Let T1 and T2 represent the lifetimes in hours of two linked components in an electronic device. The joint density function for T1 and T2 is uniform over the region defined by 0 <= t1<= t2<=L where L is a positive constant.Determine the expected value of the sum of the squares of T1 and T2 .(A)L2/3(B)L2/2(C)2 L2/3(D) 3 L2/4(E) L26. Two instruments are used to measure the height, h, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056h . The error made by the more accurate instrument is normally distributed with mean 0 and standard deviation 0.0044h . Assuming the two measurements are independent random variables, what is the probability that their average value is within 0.005h of the height of the tower?(A) 0.38(B) 0.47(C) 0.68(D) 0.84(E) 0.907. An insurance company’s monthly claims are modeled by a continuous, positive randomvariable X, whose probability density function is proportional to (1 + x)-4 ,where 0 < x Determine the company’s expected monthly claims.(A)1/6(B)1/3(C)1/2(D) 1(E) 38. A probability distribution of the claim sizes for an auto insurance policy is given in thetable below:What percentage of the claims are within one standard deviation of the mean claim size?(A) 45%(B) 55%(C) 68%(D) 85%(E) 100%9. The total claim amount for a health insurance policy follows a distributionwith density function The premium for the policy is set at 100 over the expected total claim amount.If 100 policies are sold, what is the approximate probability that the insurancecompany will have claims exceeding the premiums collected?(A) 0.001(B) 0.159(C) 0.333(D) 0.407(E) 0.46010. An insurance company sells two types of auto insurance policies: Basic and Deluxe. The time until the next Basic Policy claim is an exponential random variable with mean two days. The time until the next Deluxe Policy claim is an independent exponential random variable with mean three days. What is the probability that the next claim will be a Deluxe Policy claim?(A) 0.172(B) 0.223(C) 0.400(D) 0.487(E) 0.50011. A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy. To purchase the supplemental policy, an employee must first purchase the basic policy.Let X denote the proportion of employees who purchase the basic policy, and Y the proportion of employees who purchase the supplemental policy. Let X and Y have the joint density function f(x,y) = 2(x + y) on the region where the density is positive. Given that 10% of the employees buy the basic policy, what is the probability that fewer than 5% buy the supplemental policy?(A) 0.010(B) 0.013(C) 0.108(D) 0.417(E) 0.50012. Let C be the curve defined by x = sin t + t and y = cos t – t,Find an equation of the line tangent to C at (0, 1) .(A) y = 1(B) y = 1 + 2x(C) y = 1 – 2x(D) y = 1 –x(E) y = 1 –0.5x13. For a certain product priced at p per unit, 2000 – 10p units will be sold.Which of the following best represents the graph of revenue, r, as a function of price, p ?(A) (B) (C) (D) (E)14. A virus is spreading through a population in a manner that can be modeled by thefunction where A is the total population, g(t) is the number infected at time t, and B is a constant.What proportion of the population is infected when the virus is spreading the fastest?(A)1/3(B)1/2(C)2/3(D)3/4(E) 115. In a certain town, the rate of deaths at time t due to a particular disease is modeled by What is the total number of deaths from this disease predicted by the model?(A) 243(B) 370(C) 556(D) 1,111(E) 10,00016. The total cost, c, to a company for selling n widgets is c(n) = n2 + 4n + 100 . The price per widget is p(n) = 100 – n .What price per widget will yield the maximum profit for the company?(A) 50(B) 76(C) 96(D) 98(E) 10017. An insurance company has 120,000 to spend on the development and promotion of a new insurance policy for car owners. The company estimates that if x is spent on development and y is spent on promotion, then policies will besold.Based on this estimate, what is the maximum number of policies that the insurance company can sell?(A) 3,897(B) 9,000(C) 11,691(D) 30,000(E) 90,00018. An insurance policy reimburses dental expense, X, up to a maximum benefit of 250 . The probability density function for X is: where c is a constant.Calculate the median benefit for this policy.(A) 161(B) 165(C) 173(D) 182(E) 25019. In an analysis of healthcare data, ages have been rounded to the nearest multiple of 5 years. The difference between the true age and the rounded age is assumed to be uniformly distributed on the interval from _2.5 years to 2.5 years. The healthcare data are based on a random sample of 48 people. What is the approximate probability that the mean of the rounded ages is within 0.25 years of the mean of the true ages?(A) 0.14(B) 0.38(C) 0.57(D) 0.77(E) 0.8820. Let X and Y denote the values of two stocks at the end of a five-year period. X is uniformly distributed on the interval (0,12) . Given X = x, Y is uniformly distributed on the interval (0, x) . Determine Cov(X, Y) according to this model.(A) 0(B) 4(C) 6(D) 12(E) 2421. A ball rolls along the polar curve defined by r = sin . The ball starts at = 0 and ends at Calculate the distance the ball travels.(A) (B) (C) (D) (E)22. An actuary determines that the annual numbers of tornadoes in counties P and Q are jointly distributed as follows:Calculate the conditional variance of the annual number of tornadoes in county Q, giventhat there are no tornadoes in county P .(A) 0.51(B) 0.84(C) 0.88(D) 0.99(E) 1.7623. An insurance policy is written to cover a loss X where X has density function The time (in hours) to processa claim of size x, where 0 _ x _ 2, is uniformly distributed on the interval from x to 2x .Calculate the probability that a randomly chosen claim on this policy is processed in three hours or more.(A) 0.17(B) 0.25(C) 0.32(D) 0.58(E) 0.8324. An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims.If the number of claims filed has a Poisson distribution, what is the variance of the number of claims filed?(A) (B) 1(C) (D) 2(E) 425. An advertising executive claims that, through intensive advertising, 175,000 of a city’s 3,500,000 people will recognize the client’s product after one day. He further claims that product recognition will grow as advertising continues according to the relationship an+1 = 0.95an +175,000, where an is the number of people who recognize the client’s product n days after advertising begins. If the advertising executive’s claims are correct, how many of the city’s 3,500,000 people will not recognize the client’s product after 35 days of advertising?(A) 552,227(B) 561,468(C) 570,689(D) 581,292(E) 611,88626. The bond yield curve is defined by the function y(x) for 0 < x _ 30 where y is the yield on a bond which matures in x years. The bond yield curve is a continuous, increasing function of x and, for any two points on the graph of y, the line segment connecting those points lies entirely below the graph of y . Which of the following functions could represent the bond yield curve?(A) y(x) = a a is a positive constant(B) y(x) = a + kx a, k are positive constants(C) , k are positive constants(D) y(x) = , k are positive constants(E) y(x) = a + k log(x + 1) a, k are positive constants27. A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold.P(X = 0, Y = 0) =1/6 P(X = 1, Y = 0) =1/12 P(X = 1, Y = 1) =1/6 P(X = 2, Y = 0) =1/12P(X = 2, Y = 1) =1/3 P(X = 2, Y = 2) =1/6 What is the variance of X ?28. Inflation is defined as the rate of change in price as a function of time. The figure below is a graph of inflation, I, versus time, t . Price at time t = 0 is 100 . What is the next time at which price is 100 ?(A) At some time t, t (0, 2) .(B) 2(C) At some time t, t (2, 4) .(D) 4(E) At some time t, t (4, 6) .29. An investor buys one share of stock in an internet company for 100 . During the first four days he owns the stock, the share price changes as follows (measured relative to theprior day’s price): If the pattern of relative price movements observed on the first four days is repeated indefinitely, how will the price of the share of stock behave in the long run?(A) It converges to 0.00 .(B) It converges to 99.45 .(C) It converges to 101.25 .(D) It oscillates between two finite values without converging.(E) It diverges to .30. Three radio antennas are located at points (1, 2), (3, 0) and (4, 4) in the xy-plane. In order to minimize static, a transmitter should be located at the point which minimizes the sum of the weighted squared distances between the transmitter and each of the antennas. The weights are 5, 10 and 15, respectively, for the three antennas. What is the x-coordinate of the point at which the transmitter should be located in order to minimize static?(A) 2.67(B) 3.17(C) 3.33(D) 3.50(E) 4.0031. Let R be the region bounded by the graph of x2 + y2 = 9 .Calculate(A) (B) (C) (D) (E)32. A study indicates that t years from now the proportion of a population that will beinfected with a disease can be modeled by Determine the time when the actual proportion infected equals the average proportion infected over the time interval from t = 0 to t = 3 .(A) 1.38(B) 1.50(C) 1.58(D) 1.65(E) 1.6833. A blood test indicates the presence of a particular disease 95% of the time when thedisease is actually present. The same test indicates the presence of the disease 0.5% ofthe time when the disease is not present. One percent of the population actually has thedisease.Calculate the probability that a person has the disease given that the test indicates the presence of the disease.(A) 0.324(B) 0.657(C) 0.945(D) 0.950(E) 0.99534. An insurance policy reimburses a loss up to a benefit limit of 10 . The policyholder’sloss, Y, follows a distribution with density function:What is the expected value of the benefit paid under the insurance policy?(A)1.0(B) 1.3(C) 1.8(D) 1.9(E) 2.035. A company insures homes in three cities, J, K, and L . Since sufficient distance separates the cities, it is reasonable to assume that the losses occurring in these cities are independent. The moment generating functions for the loss distributions of the cities are:MJ(t) = (1 – 2t)-3 MK(t) = (1 – 2t)-2.5 ML(t) = (1 – 2t)-4.5 Let X represent the combined losses from the three cities.Calculate E(X3) .(A) 1,320(B) 2,082(C) 5,760(D) 8,000(E) 10,56036. In modeling the number of claims filed by an individual under an automobile policyduring a three-year period, an actuary makes the simplifying assumption that for all integers , where pn represents the probability that the policyholder files n claims during the period.Under this assumption, what is the probability that a policyholder files more than one claim during the period?(A) 0.04(B) 0.16(C) 0.20(D) 0.80(E) 0.9637. Let S be the surface described by f(x,y) = arctany/x Determine an equation of the plane tangent to S at the point(A) (B) (C) (D) (E)38. An insurance policy is written to cover a loss, X, where X has a uniform distributionon [0, 1000] .At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible?(A) 250(B) 375(C) 500(D) 625(E) 75039. An insurance policy is written that reimburses the policyholder for all losses incurred up to a benefit limit of 750 . Let f(x) be the benefit paid on a loss of x .Which of the following most closely resembles the graph of the derivative of f ?(A) (B) (C) (D) (E)40. A company prices its hurricane insurance using the following assumptions:(i) In any calendar year, there can be at most one hurricane.(ii) In any calendar year, the probability of a hurricane is 0.05 .(iii) The number of hurricanes in any calendar year is independentof the number of hurricanes in any other calendar /doc/fb5f1bbcc77da26925c5b09e.html ing the company’s assumptions, calculate the probability that there are fewer than 3 hurricanes in a 20-year period.Course 1 May 2000 Answer Key1. A 21. B2. D 22. D3. D 23. A4. E 24. D5. C 25. D6. D 26. E7. C 27. B8. A 28. C9. B 29. A10. C 30. B11. D 31. D12. E 32. D13. E 33. B14. B 34. D15. C 35. E16. B 36. A17. C 37. B18. C 38. C19. D 39. C20. C 40. E。
soa北美精算师第二门FMTIA样题一
soa北美精算师第⼆门FMTIA样题⼀The In?nite Actuary’sJoint Exam2/FMSample Exam1by James Washer,FSA,MAAAlast updated-August14,2009Take this sample exam under strict exam conditions.Start a timer for3hours and stop imme-diately when the timer is done.Do not stop the clock when you go to the bathroom.Do not look at your notes.Do not look at the answer key.This exam contains35questions.Do not spend too much time on any one question.Choose the best available answer for each question.1.Which of the following is not a way to create a40-45-50butter?y?A.buy40-strike call,write two45-strike calls,buy50-strike callB.buy40-strike put,write two45-strike puts,buy50-strike putC.buy40-strike put,write45-strike call,write45-strike put,buy50-strike callD.buy40-strike call,write45-strike call,write45-strike put,buy50-strike putE.all of the above will create a40-45-50butter?y2.Letδt=14+t,0≤t≤15What is the?rst year for which the e?ective rate of discount is less than12.5%?A.3B.4C.5D.6E.73.A bond will pay a coupon of100at the end of each of the next three years and will pay the facevalue of1000at the end of the three-year period.The bond’s modi?ed duration when valued using an annual e?ective interest rate of20%is X.Calculate X.A.2.25B.2.61C.2.70D.2.77E.2.894.You are given the following table of interest rates:CalendarYear of PortfolioOriginal RatesInvestment Investment Year Rates(in%)(in%)y i y1i y2i y3i y4i y5i y+519928.258.258.408.508.508.3519938.508.708.758.909.008.6019949.009.009.109.109.208.8519959.009.109.209.309.409.1019969.259.359.509.559.609.3519979.509.509.609.709.70199810.0010.009.909.80199910.009.809.7020009.509.5020019.00A person deposits1000on January1,1997.Let the following be the accumulated value of the 1000on January1,2000.P:under the investment year methodQ:under the portfolio yield methodCalculate P+Q.A.2575B.2595C.2610D.2655E.27005.A loan is repaid with10annual payments.The?rst payment occurs one year after the loan.The?rst payment is100and each subsequent payment increases by10.The annual e?ective rate of interest is5%.The amount of principal repaid in the4th payment is X.Determine X.A.71B.76C.80D.84E.916.A1000par value10-year bond that pays9%coupons semiannually is purchased for X.Thecoupons are reinvested at a nominal rate of7%convertible semiannually.The bond investor’s nominal annual yield rate convertible semiannually over the10-year period is9.2%.Determine X.A.924B.987C.1024D.1386E.14427.Bill writes a$100-strike call option on stock XYZ with6months to expiration for a premium of$7.24.The risk-free rate is5%convertible semiannually.For what rage of prices at expiration does Bill make a pro?t?A.[0,92.58)B.(92.58,∞)C.[0,107.42)D.(107.42,∞)E.[0,107.60)8.10deposits of$2000are made every other year with the?rst deposit made immediately.Theresulting fund is used to buy a perpetuity with payments made once every3years following the pattern X,4X,7X,10X,...The?rst perpetuity payment is made3years after the last deposit of$2000.The annual e?ective rate of interest is6%.Determine X.A.408B.458C.471D.512E.6039.John buys a perpetuity-due with annual payments that are adjusted each year for in?ation.The?rst payment is100.In?ation is3%for years1-5and2%thereafter.Calculate the price of the perpetuity if the yield rate is an e?ective6%per annum.A.2750B.2760C.2770D.2780E.279010.Given the following information about the treasury market:Term Coupon Price10%96.6220%X30%88.90It is known that the2-year forward rate is4.5%.Calculate X.A.87.65B.89.70C.92.90D.93.45E.95.5011.A20-year bond is priced at par and pays R%coupons semiannually.The bond’s duration is 13.95years.Determine R.A.2B.3C.4D.5E.612.Which of the following is not true?A.An asset insured with a?oor is equivalent to investing in a zero-coupon bond and buying a call option on the asset.B.A short position insured with a cap is equivalent to writing a zero-coupon bond and buying a put option on the asset.C.A covered written call is equivalent to investing in a zero-coupon bond and writing a put option on the asset.D.A covered written put is equivalent to writing a zero-coupon bond and writing a call option on the asset.E.All of the above are true.13.A fairly smart actuary(also know as an FSA)is o?ered the following rates on a loan:1.X%nominal annual rate of interest compounded monthly2.X%nominal annual rate of discount compounded monthly3.X%annual e?ective rate of interest4.X%annual e?ective rate of discount5.X%constant force of interestWhich rate does the FSA take?A.1B.2C.3D.4E.514.An annuity pays1at the beginning of each year for n /doc/894fe700eff9aef8941e067b.html ing an annual e?ective interestrate of i,the present value of the annuity at time0is8.55948.It is also known that(1+i)n=3.172169.Find the accumulated value of the annuity immediately after the last payment.A.27.152B.28.456C.29.324D.30.765E.31.97315.Deposits are made at the beginning of every month into a fund earning a nominal annual rateof6%convertible monthly.The?rst deposit is100and deposit increase2%every year.In other words,deposits1-12are100,deposits13-24are100×1.02=102,deposits25-36are 100×1.022=104.04,and so on.Calculate the fund balance at the end of10years.A.16,569B.16,893C.17,257D.17,770E.17,85916.On January1a fund has a balance of$100.Sometime during the year a withdrawal of$20ismade.Immediately before the withdrawal the fund balance is$110.At year-end the balance is $95.If the time weighted and dollar weighted rates for the year are equal,then in what month was the$20withdrawal made?A.JuneB.JulyC.AugustD.SeptemberE.October17.A common stock pays annual dividends at the end of each year.The earnings per share inthe year just ended were J.Earnings are assumed to grow10%per year in the future.The percentage of earnings paid out as a dividend will be0%for the next5years and50%thereafter.Calculate the theoretical price of the stock to yield the investor21%.A.5J(1.1)4B.5J(1.1)5C.5J(1.1)6D.10J(1.1)5E.10J(1.1)618.You are the CFO of In?nite Life.In?nite Life only has one liability of$5000due in8years.In?nite Life uses a nominal rate of6%convertible semiannual to discount all liability cash?ows.You call up your favorite bond broker and ask him what bonds he has for sale today.Your broker says he has5-year and10-year bonds.Both bonds are priced to yield6%convertible semiannually.The5-year bond pays6%coupons semiannually and the10-year bond is a zero-coupon bond.The bonds can be bought in any face amount.What face amount of the5-year bond should you buy in order to meet the?rst two conditions of immunization?A.777B.888C.999D.1111E.2222。
北美精算师考试试卷
北美精算师考试试卷
考试科目：精算学基础
考试时间：3小时
注意事项：
1. 请在答题卡上填写您的姓名和考试编号。
2. 所有答案必须写在答题卡上，写在试卷上的任何答案无效。
3. 考试结束后，试卷和答题卡需一并上交。
第一部分：选择题（共40分）
1-10题：精算数学基础
- 1. 以下哪个不是精算学中常用的数学工具？
A. 微积分
B. 概率论
C. 线性代数
D. 统计分析
- 2. 以下哪个公式用于计算年金的现值？
A. PV = P * (1 + r)^n
B. PV = P * (1 - r)^n
C. PV = P / (1 + r)^n
D. PV = P * (1 - r^n) / r
...（此处省略其他选择题）
第二部分：简答题（共30分）
11题：请简述精算师在保险产品设计中的作用。
12题：解释什么是风险管理和精算师如何在此领域发挥作用。
...（此处省略其他简答题）
第三部分：计算题（共30分）
13题：给定一个年利率为5%的普通年金，每年支付1000美元，支付期为10年，请计算该年金的现值。
14题：一个保险公司面临两种风险：损失风险和投资风险。
请根据给定的数据，计算该公司的总风险价值。
...（此处省略其他计算题）
结束语：
考生请注意，考试结束后请立即停笔，将答题卡放在桌面上，等待监考老师收卷。
预祝您考试顺利！
请注意，以上内容仅为模拟试卷示例，实际考试内容、题型和难度可能会有所不同。
考生应根据SOA或CAS提供的官方学习材料和指南进行准备。
北美精算师(SOA)考试P 2001年真题和注解
{
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Course 1 Solutions
7
May 2001
11.
D Observe that x and y follow the constraint equation x + y = 160, 000 x = 160, 000 − y where 0 ≤ y ≤ 160, 000 Now this constraint equation can be used to express policy sales g(x, y) as a function f(y) of marketing y alone: f ( y ) = g (160, 000 − y, y ) = 0.001(160, 000 − y ) y 3/ 4 We can then compute f '(y) as follows: 3 −3/ 4 3/ 4 1/ 4 1 f ' ( y ) = − (160, 000 − y ) y + (160, 000 − y ) y −1/ 4 /1000 4 4 −1 −3/ 4 = (160, 000 − y ) y −1/ 4 y − 3 (160, 000 − y ) 4000 −1 −3/ 4 = (160, 000 − y ) y −1/ 4 ( 4 y − 480, 000 ) 4000 1 −3/ 4 = (160, 000 − y ) y −1/ 4 (120, 000 − y ) , 0 ≤ y ≤ 160, 000 1000 Note that f ' ( y ) > 0 for 0 ≤ y < 120, 000 ,
Course 1 May 2001 Answer Key
SOA真题May20XXCourse6第3页-精算师考试.doc
SOA真题May2002Course6第3页-精算师考试5.Youaregiventhefollowinginformationfora15-yearcallablebond:annualcouponrate:9%payable semi-annually price:95.32 effective duration:3.17 convexity measure(C):(67.31)CVVVVy22002bgCalculate thepriceofthebond aftera50basis point increase in interest rates.(A) 93.65(B) 93.97(C)95.32(D)96.67(E)96.99COURSE 6:MAY2002GOONTONEXT PAGEMORNING SESSION6.Youaregiventhefollowinginformation with respecttoasingle-period securities model:SPS010101113301101122bg LNMMMOQPPPDetermine thevalueofPwhichmakesthemodelarbitrage-free.(A)14(B)15(C)16(D)17(E)18COURSEMAY2002GOONTONEXT PAGEMORNING SESSION7-16. Eachofquestions7through16consistsoflists.Inthelistattheleftaretwo items,lettered XandY.Inthelisttherightare three items, numbered I,II,andIII.ONE ofthe lettered itemsis relatedsomewayto EXACTLY TWOofthe numbered items.Indicate therelated itemsusingthe following answercode:Lettered ItemIsRelatedto Numbered Items(A)XIandIIonly(B)XIIandIIIonly(C)IandIIonly(D) YIandIII only(E) The correct answer isnot given by(B),(C)or (D).7. X. Asian call options I. Payoffs depend onthe average priceof theunderlying asset during thelifeofthe option.Y. Lookback call options II. Guarantees the purchase ofthe assetatlowestpriceduringthelifeofthe option.III. Canuse averagesforthe exerciseprice.8. X.Cliquet optionGuaranteed exchange-rate contracts.Y. Quanto optionII.Aseriesofstandardcalloptions thatpaystheannual increasetheunderlying assets.III. Thestrikeresetsatthe beginning ofeach year.COURSE 6:MAY2002GOONTONEXT PAGEMORNING SESSION9.X.InterestratecorridorI.Thepurchaseofacapatonestrikerateandsaleofafloorata lowerstrike rate.Y. Interest ratecollarII.The purchase ofaatone strikerate andthesaleof another capat ahigher strike rate.III. Sometimes described asswappinginto abond.10. X.Zero-coupon convertible bondI.Sacrifice yieldY. Putable convertible bondII.Greater credit riskIII.premium11. X. Modified duration I.Allowsfor changing cashflows asinterest rates change.Y. Effective duration II.notallowforchanging cashflowsasinterestrates change.III.Notan appropriate measure forcallable bonds.COURSE 6:2002GOONTONEXT PAGEMORNING SESSION7-16. Eachofquestions7through16consistsoftwoInthelistattheleftaretwo items,lettered XandY.Inthelistatrightare three items, numbered I,II,andIII.ONE ofthe lettered itemsis relatedinwayto EXACTLY TWOofthe numbered items.Indicate therelated itemsusingthe following answer code:LetteredIs Relatedto Numbered Items(A) XIandIIonly(B)XIIandIIIonly(C)YIandIIonly(D) YIandIII only(E) The correct answer isnot given by (A),(B),(C) or。
期末试题(2000
14.22期末试题（2000年）回答全部问题。
你有三小时考试时间。
1．（60分钟—40分）简略回答下面每个子问题。
请写出你的计算过程，并在你不能给出正式结论时，提供大概的解释，那样我可以给你部分分数。
（a）给出正式的说明，指出一个观察到的行为无穷连续的多级博弈意味什么？为什么我们关心无穷博弈是否连续？（b）能利用迭代严格占优方法解出下面的博弈问题吗？它有唯一的纳什均衡吗？（c）陈述Kakutani理论。
在任何存在纳什均衡的有限博弈证明中，是如何应用它的？如果你想尝试用相同的方式使用kakutani理论来证明在“指出最大数＂博弈中存在一个均衡时，会发现论点在哪里不成立？（d）下面的表述是对还是错：“在一般有限正常博弈中，博弈者的均衡支付是正的。
＂ （e）找出下面扩展型博弈中所有的子博弈。
（f）给出一个博弈的例子，你可以在这个博弈中讨论子博弈完美均衡概念限制性太强，而排除了一个合理的结果。
给出一个博弈的例子，你可以在其中讨论子博弈完美均衡概念限制性不足，未能排除一个不合理的结果。
（简要解释你要就每个例子讨论什么。
）（g）找出下面博弈的全部纳什均衡。
（h ）找出这个同时采取行动的博弈的纳什均衡，该博弈中，博弈者1选择1a ∈ℜ，博弈者2选择2a ∈ℜ，支付是（i）假定课上我阐述了在分离贝叶斯均衡劳动市场信号传递模型中如下的轻微变化。
博弈者1的自然首次选择能力{}2,3θ∈（两个选择对等）。
博弈者1观察θ，并选择{}0,1e ∈。
博弈者2则观察e ，选择w ∈ℜ。
博弈者的效用函数是21(,;)/u e w w ce θθ=−。
对c=4.25，这个模型有两个混同均衡：和一个分离均衡：假定课后两个学生在走廊上向你走来，让你解决他们之间的争论，关于这个均衡是否没有达到Cho-Kreps 直观标准。
假设Irving 提出，混同均衡违背了直观标准。
3θ=类型可以表述为“我现在选择e=1。
我知道你认为任何得到教育的人是低类型，但这是不妥当的。
全美数学建模往年试题2000
Problem A Air traffic ControlDedicated to the memory of Dr. Robert Machol, former chief scientist of the Federal Aviation AgencyTo improve safety and reduce air traffic controller workload, the Federal Aviation Agency (FAA) is considering adding software to the air traffic control system that would automatically detect potential aircraft flight path conflicts and alert the controller. To that end, an analyst at the FAA has posed the following problems.Requirement A: Given two airplanes flying in space, when should the air traffic controller consider the objects to be too close and to require intervention?Requirement B: An airspace sector is the section of three-dimensional airspace that one air traffic controller controls. Given any airspace sector, how do we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of aircraft simultaneously passing through that sector (1) at any one instant?(2) during any given interval of time?(3) during a particular time of day? How does the number of potential conflicts arising during those periods affect complexity?Does the presence of additional software tools to automatically predict conflicts and alert the controller reduce or add to this complexity?In addition to the guidelines for your report, write a summary (no more than two pages) that the FAA analyst can present to Jane Garvey, the FAA Administrator, to defend your conclusions.Problem BRadio Channel AssignmentsWe seek to model the assignment of radio channels to a symmetric network of transmitter locations over a large planar area, so as to avoid interference. One basic approach is to partition the region into regular hexagons in a grid (honeycomb-style), as shown in Figure 1, where a transmitter is located at the center of each hexagon.Figure 1An interval of the frequency spectrum is to be allotted for transmitter frequencies. The interval will be divided into regularly spaced channels, which we represent by integers 1, 2, 3, ... . Each transmitter will be assigned one positive integer channel. The same channel can be used at many locations, provided that interference from nearby transmitters isavoided. Our goal is to minimize the width of the interval in the frequency spectrum that is needed to assign channels subject to some constraints. This is achieved with the concept of a span. The span is the minimum, over all assignments satisfying the constraints, of the largest channel used at any location. It is not required that every channel smaller than the span be used in an assignment that attains the span.Let s be the length of a side of one of the hexagons. We concentrate on the case that there are two levels of interference.Requirement A: There are several constraints on frequency assignments. First, no two transmitters within distance 4s of each other can be given the same channel. Second, due to spectral spreading, transmitters within distance 2s of each other must not be given the same or adjacent channels: Their channels must differ by at least 2. Under these constraints, what can we say about the span in,Requirement B: Repeat Requirement A, assuming the grid in the example spreads arbitrarily far in all directions.Requirement C: Repeat Requirements A and B, except assume now more generally that channels for transmitters within distance 2s differ by at least some given integer k, while those at distance at most 4s must still differ by at least one. What can we say about the span and about efficient strategies for designing assignments, as a function of k? Requirement D:Consider generalizations of the problem, such as several levels of interference or irregular transmitter placements. What other factors may be important to consider?Requirement E:Write an article (no more than 2 pages) for the local newspaper explaining your findings.。
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Determine the probability that the model year of this automobile is 1997 .
(A) (B) (C) (D) (E)
0.22 0.30 0.33 0.45 0.50
Course 1
4
May 2000
3.
The lifetime of a printer costing 200 is exponentially distributed with mean 2 years.
I
Course 1
2
1.
The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work.
4. Answer sheets are mechanically scored. BE SURE THAT EACH MARK IS BLACK AND COMPLETELY FILLS ONLY THE INTENDED ANSWER CIRCLE. Make no stray marks on the answer sheet. Choose only one answer for each question. If you change an answer, erase your first mark completely and mark your new choice. 5. Use the blank portions of booklet pages for your scratch work. You are not permitted to use extra scratch paper. 6. In questions involving money, no monetary unit is specified, and nothing is implied by the magnitude of the numbers. 7. Do not spend too much time on any question. If a question seems too difficult, go on to the next question. You may return to unanswered questions if you finish before time is called. 8. Your score will be based on the number of questions that you answer correctly, with each question having equal weight. There will be no deduction for wrong answers. It is therefore to your advantage to answer every question. 9. After time is called, the supervisor will collect the booklet and your answer sheet separately. DO NOT ENCLOSE THE ANSWER SHEET IN THE BOOKLET. All booklets and answer sheets must be returned. THE QUESTIONS ARE CONFIDENTIAL AND MAY NOT BE TAKEN FROM THE EXAMINATION ROOM. ©2000 by the Society of Actuaries and the Casualty Actuarial Society. All rights reserved. Society of Actuaries 475 N. Martingale Road, Suite 800 Schaumburg, IL 60173-2226
Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.
(A) (B) (C) (D) (E)
0.05 0.12 0.18 0.25 0.35
Example Calculate the value of x in the equation x + 6 = –3 . (A) (B) (C) (D) (E) –9 –3 –2 3 9
Sample Answer
GENERAL INFORMATION
1. 2. 3. ln x is the natural logarithm of x .
May 2000
3
Course 1
2.
A study of automobile accidents produced the following data:
Model year 1997 1998 1999 Other
Proportion of all vehicles 0.16 0.18 0.20 0.46
The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year.
R n is n-dimensional Euclidean space.
2 X E( X ) denotes the mean of a random variable X .
82 X Var ( X ) denotes the variance of X .
8 XY Cov( X , Y ) denotes the covariance of two random variables X and Y . 7 XY Corr ( X , Y ) denotes the correlation coefficient of X and Y .
n
X 4.
¦ Xi
i 1
n
denotes the mean of a sample X1,..., Xn .
The Normal Distribution
1 x w2 / 2 e dw for certain values 25 f of x . The integer part of x is given in the top row, and the first decimal place of x is given in the left column. Since the density function of x is symmetric, the value of the cumulative distribution function for negative x can be obtained by subtracting from unity the value of the cumulative distribution function for x . The table below gives the value of )( x ) x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 1 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 2 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 3 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 Selected Points of the Normal Distribution x (x) 0.800 0.842 0.850 1.036 0.900 1.282 0.950 1.645 0.975 1.960 0.990 2.326 0.995 2.576 May 2000
Mathematical Foundations of Actuarial Science SOCIETY OF ACTUARIES
1
Wednesday, May 24, 2000 DIRECTIONS
CASUALTY ACTUARIAL SOCIETY
1. DO NOT BREAK THE SEAL OF THE BOOKLET UNTIL THE SUPERVISOR TELLS YOU TO DO SO. 2. This test consists of 40 multiple-choice test questions. You will have a total of 180 minutes in which to answer them and record your answers on the answer sheet. NO ADDITIONAL TIME WILL BE ALLOWED FOR CODING YOUR ANSWER SHEET. Failure to stop writing or coding your answer sheet after time is called will result in the disqualification of your answer sheet and possible further disciplinary action. 3. There are five answer choices for each question, lettered (A) through (E). Answer choices for some questions have been rounded. For each question, choose the best answer. On your answer sheet, find the row of circles with the same number as the question. Then find the circle in that row with the same letter as your answer. Use a soft lead pencil and blacken the circle completely. INDICATE ALL YOUR ANSWERS ON THE ANSWER SHEET. No credit will be given for anything written in the booklet.