Name:
Math 3G3 * Assignment 10
Due in class on Wednesday, 5 November * No late assignments are accepted *
1. [5] By n1 , n2 , . . . , nk we denote all divisors of N = 76334! except 1 and N. Prove that
ln n1 + ln n2 + ln n3 + + ln nk =
k ln N
2
2. [4] Posi
Name:
Math 3G3 * Assignment 8
Due in class on Tuesday, 21 October * No late assignments are accepted *
1. Assuming that AB = 1, nd the exact area A of the Pythagorean star following the
steps below.
A
B
(a)[4] Show that A =
5
tan 54o cot 54o
4
5
(b)[3] Sh
Math 3G3 * Assignment 9
1. Find the sum of all digits used in writing down the numbers from 1 to 1 million.
2. Which number is larger: 200! or 100200 ?
3. The sum of a collection of positive integers is 2014. What are these numbers if their
product is as
maewgm g
i. ' _
(0) ()9in WM 1_ I
2 i5? QGQ NWQQ 0Q WLEMWE) g KA-UA USMEL
0w: um¥ \o M M w Cm: uw'}: mp uwgg
Cowdr M SW \QC'AMA chMw Ev [QM What
waojc'Q/s N QRSVQE? WW WQ WM
42? 2 Me Wxaww " a)
bwgokw 3
_ @521 (W ._ me P3 MS I
_' (Vita; mm WAN: LOW k0
ASS \GNM\3T S -
[i> restart;
.> day = 3; month = 2gyear = 2014;
stariyear = 1492; R W eh
numberdbzears = [ year starvear} :
numberdlmonths = month 1 :
totaldays :2 day :
days := 0 : for i from 1 to numberfullmonths do
ifi=10ri=3 ori250ri=7ori=80ri= 10 0r
Name:
Math 3G3 * Assignment 16
Due in class on Wednesday, 3 December. No late assignments are accepted.
Please do not email the assignment but instead bring it to class.
_ l
1.
0° , l 00 n!
2. [4] It is known that f 3" d2: = . Use it to prove that / an
2014
Name:
ID:
Math 3G3 * FINAL EXAM
Due by 4pm on Tuesday, 9 December 2104
* No late exams are accepted *
Do not email your exam paper, bring it in person instead. Leave your exam
paper at the reception in Math and Stats oce, HH218. Note: If you think th
Name:
ID:
Math 3G3 * TEST 1
Due in class on Tuesday, 28 October 2014 * No late tests are accepted *
If you think that you will not be able to come to class, leave your solutions in
the Math and Stats oce HH218 no later than 10:30am on 28 October.
Staple a
Name: H ID:
Math 3G3 * TEST 2
Due in class on Tuesday, 25 November 2014 * No late tests are accepted *
If you think that you will not be able to come to class, leave your solutionsin
the Math and Stats ofce HH218 no later than 10:30am on 25 November.
Stap
Math 3G3 * Assignment 6.5
Fibonacci sequence problems
1. Denote by Fn the Fibonacci sequence, dened by F1 = F2 = 1, Fn+2 = Fn + Fn+1 .
2
2
(a) Show that, for every n 1, Fn+1 + Fn+2 is larger than Fn Fn+3 and 2Fn+1 Fn+2 .
(b) Show that the three numbers in
Chapter 2 Sample questions
Express each solution in terms of Mt), or Sx(t) or Fo(t) or Sam
1. What is the probability that a newborn dies within 5 years?
H (s)
2. What is the probability that someone age 40 dies within 12 years?
(-5
we ( I2)
3. What is th
Fractional Ages
Example 1
988/1000 12/1000
970/988 18/988
946/970 24/970
916/946 30/946
876/916 40/916
A) .5 922
B) 1/12 P22 2/12
C) .5 q 24
D) .25|.5q22
E) .75|.5Cl22
Under UDD we would calculate as follows:
a) .SFQQ : gi : 21 ' SCAQ-Zl 2
3G03
Introduction to Actuarial Mathematics
Fall 2016
Assignment #1
Instructions
Due in drop box: September 27, 2016 12:00 pm
The drop box is located in Hamilton Hall (near HH/105).
Use box C64 for last names beginning with A-L.
Use box C65 for last names
3G03
Introduction to Actuarial Mathematics
Fall 2016
Assignment #2
Instructions
Due in drop box: October 25, 2016 2:00 pm
The drop box is located in Hamilton Hall (near HH/105).
Use box C64 for last names beginning with A-L.
Use box C65 for last names beg
Life Tables Examples
Example 1
x
20
lx
55
dx
3
21
1
22
1
23
2
24
2
25
3
1. Complete the table
2. What is the probability that (20) survives 3 years?
3. Calculate
a. 2p22
b. q23
c. 2|1q21
d. e21: |
e. P(2<T20<3)
lx-dx
qx
px
Example 2
x
30
lx
10,000
dx
35
3
Chapter 2 Review
September 21, 2016
1. What is Tx in words?
2. If a person is aged 32 and omega is 112 what is the maximum future
lifetime for this person?
3. What is Sx(t)?
4. What are the conditions for Sx(t)?
5. If you need to calculate 10p20 and you a
Chapter 2 Sample questions
Express each solution in terms of Fx(t), or Sx(t) or F0(t) or S0(t)
1. What is the probability that a newborn dies within 5 years?
2. What is the probability that someone age 40 dies within 12 years?
3. What is the probability t
Name:
Math 3G3 * Assignment 4
Due in class on Tuesday, 30 September * No late assignments are accepted *
1. The context is the 3n+1 problem from Assignment 3.
NOTE: to attach a code in exercises means that you can: (a) print your code and attach
to your a