MAT 221
Fundamental Concepts of Math I
Homework Set 1
(Sections 1.1 – 1.4)
 The following Homework Assignments are selected problems from your textbook. Do ALL parts of an
assigned problem unless otherwise specified.
 Please start your assignments early to ensure you have enough time to seek help if necessary.
Remember that what you turn in should be your best work – neat, legible, all work/steps shown, and
clear, grammatically correct sentences when applicable.
 Each homework set must be submitted in the order it has been listed above.
 Several problems from the assignment are randomly chosen and graded for correctness (10 points total).
The other 5 points are for completeness: these points are pro-rated for skipping problems or not showing
work for all problems. Answers without supporting work/explanation will not be awarded points.
 You may hand in a homework set early, but please remember that late homework is not accepted
under any circumstances. The due date time is strictly enforced.
 I am available during office hours to discuss any questions you have as you are working on
these assignments. Please feel free to reach out.
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Homework Set #1:
 1.1
p. 6 – 8
# 12, 14
 1.2
p. 17 – 19
# 4(b, c), 16, 24
 1.3
p. 28 – 31
# 5(b, c), 8, 24, 26
 1.4
p. 39 – 41
# 4(a), 8, 14
 Problem A1) One morning, a caterpillar fell into a dry well 14 feet deep. It is climbing out of the well
toward the light and can climb 4 feet per hour. However, after each hour of climbing it needs to rest
for one hour and while resting slips back down 1 foot on the slick wall of the well. How long does it
take the caterpillar to reach the edge of the well so that it can climb out?
 Problem A2) The word JOURNEY is written over and over again on a long strip of paper (without any
th
blank spaces between words). What letter is the 1389 place counted from the beginning? [Note:
Do not do this by cutting and pasting on a computer in a brute-force approach. Reason your way to
the answer by thinking mathematically.]
MAT 221
Fundamental Concepts of Math I
 Work out the problems B1 and B2 on the next pages. You may directly write on the pages and
turn them in as part of your work.
Problem B1)
a) Look for a pattern and give the next two entries using the most likely choices for this sequence:
5,
12,
19,
26,
b) Fill in the following table:
Entry
first,
broken down
broken down further
n=1
5 =
=
second, n = 2
12 =
=
third,
n=3
19 =
=
fourth, n = 4
26 =
=
fifth,
n=5
=
=
sixth,
n=6
=
=
c) From the table, give a general formula for the nth entry.
d) Simplify the formula (if not simplified already).
e) Use an above version of the formula to find the 10th entry. (Use a formula, do not just continue
the pattern.)
f) Now perform a check finding the 10th entry by continuing the pattern until you reach entry 10.
[If your answers to part d) and e) match, you will be done. If not, you need to improve the formula.]
5,
12,
19,
26,
,
,
,
,
,
MAT 221
Fundamental Concepts of Math I
Problem B2)
Farmer Cornelius has 70 chickens and goats altogether in the barnyard.
In all, there are 198 feet. How many chickens and how many goats are in the barnyard? (Suggestion:
Use problem-solving strategy 7.)