MATH 3630 - Actuarial Mathematics I - Sample Test 1 - Time Allowed - 1 hour

Q: What is the duration and total marks of the Sample Test 1?

The time allowed is 1 hour and the total marks are 100 points.

Q: How many written-answer questions are included, and must all be answered?

There are ten written-answer questions and you are to answer all ten.

Sep 27, 2026

Uploaded by Kyle

A one-hour sample test for MATH 3630, Actuarial Mathematics I, covering actuarial survival and mortality models. The assessment includes ten written-answer questions worth 100 points total, requiring full solutions with working shown for partial credit. Topics include deMoivre’s law, illustrative life tables, survival and probability calculations between ages, use of UDD assumptions, force of mortality and integrated lifetime measures, substandard mortality adjustments, and select-and-ultimate mortality table interpolation. The exam instructs candidates to write legibly and avoid answering after the time expires.

LanguageEnglish

CategoryExam

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Sample Test 1

Instructions and scoring

Questions 1-10

MATH 3630 Actuarial Mathematics I Sample Test 1 Time Allowed: 1 hour Total Marks: 100 points Please write your name and student number at the spaces provided: Name: Student ID: 􀀏 There are ten (10) written-answer questions here and you are to answer all ten. Each question is worth 10 points. 􀀏 Please provide details of your workings in the appropriate spaces provided; partial points will be granted. 􀀏 Please write legibly. 􀀏 Anyone caught writing after time has expired will be given a mark of zero. Question No. 1: Let X be the age-at-death random variable. Assume X follows deMoivre's law with ! = 100. Calculate 10m20. Question No. 2: Assume that mortality follows the Illustrative Life Table. Calculate the probability that a life (65) will die between ages 80 and 90 . Question No. 3: You are given: kj q 0 = 0.1 (k + 1), for k = 0, 1, 2 and 3 . Suppose UDD holds between integral ages. Compute the value of 2.75p 0 and interpret this probability. Question No. 4: You are given: 4 5p 40 = 5 3 10p 45 = 5 2 10p 55 = 5 Find the probability that a life (40) will die between ages 55 and 65 . Question No. 5: Suppose you are given the survival function: SX(x ) =􀀐1 􀀀 x!􀀑 􀀋 , for 0 􀀔 x 􀀔 !. Prove the following: 􀀖x 􀀁 x = 􀀋 􀀋 + 1 . Question No. 6: Suppose that for an 80-year-old fellow, his force of mortality is given by 1 􀀖80+t = 10 􀀀 t , for 0 􀀔 t < 10. Calculate the probability that this fellow will die between ages 85 and 90 . Question No. 7: The following is an extract from a standard mortality table: x qx 40 .00278 41 .00298 42 .00320 A substandard table is obtained from this standard table by adding a constant c = 0.10 to the force of mortality. This results in mortality rates denoted by qsx, with the superscript s denoting substandard. Calculate the probability that a substandard life (40) will die between ages 41 and 42 . Question No. 8: Suppose you are given the following select-and-ultimate mortality table: | x | ` [x] | ` [x]+1 | `x+2 | | --- | --- | --- | --- | | 95 | 300 | 60 | 15 | | 96 | 175 | 10 | 0 | | 97 | 15 | 0 | 0 | | 98 | 1 | 0 | 0 | Assuming UDD between integral ages, calculate 2j0.5q [95] . Question No. 9: Suppose you are given that: `x = 1000 􀀒 27 􀀀 3~~10~~x 􀀓 1=3 , for 0 􀀔 x 􀀔 90. Calculate the average future lifetime of a newborn.

FAQs

What is the duration and total marks of the Sample Test 1?

The time allowed is 1 hour and the total marks are 100 points.

How many written-answer questions are included, and must all be answered?

There are ten written-answer questions and you are to answer all ten.

What happens if a candidate writes after the time has expired?

Anyone caught writing after time has expired will be given a mark of zero.

Sep 27, 2026

Uploaded by Kyle