2023W1_MATH_100B_ALL_2023W1.2Q5DY184P603.WW1
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School
University of British Columbia *
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Course
100
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
7
Uploaded by PrivateElectronGull36
Kaitlyn Tse
2023W1
MATH
100B
ALL
2023W1
Assignment WW1 due 09/15/2023 at 11:59pm PDT
Problem 1.
(1 point)
Match each resource to its description.
The answers to this question can be found on the Canvas course
page. The purpose of questions such as this one is to encourage
you to read the entire page, not just skim it to find a few answers.
You aren’t expected to memorize it, but if you have a general idea
of what is there, you can look up policies that are relevant to you
as they arise.
In addition to course questions, this assignment contains pre-
calculus problems which test skills that are useful in this course.
?
1. Calculus Contact Form
?
2. Math Learning Centre
?
3. Piazza
?
4. Office hours
A. A discussion board where you can interact with fellow
students and ask questions about homework.
B. Scheduled places to meet instructors
C. Webform used to express any personal concerns or issues
related to the course; in most cases this will replace email-
ing your instructor
D. A place to work with classmates and also have access to
graduate student TAs when you have a question
Problem 2.
(1 point)
For each assessment type, choose the course of action given in the
syllabus.
1.
Webwork assignment
?
2.
Regrading
?
3.
Final Exam
?
Problem 3.
(1 point)
Match each assessment to its grade calculation.
?
1. Webwork quiz
?
2. Final Exam
?
3. Midterm tests
?
4. Webwork assignments
?
5. Engagement
?
6. Written group assignments
A. 4 typed assignments, completed in teams, worth 10
B. 11 weekly assignments, the top 10 worth 10
C. 2 in-class tests worth 20
D. 50
E. Not for grades, but for authentic practice for Part 1 of the
final exam
F. A score based on engagement in small classes as well as
other completion-based tasks (eg. Diagnostic test)
Problem 4.
(1 point)
This course is organized into 2-hour large classes and 1-hour small
classes held each week. Learning will take place in both classes,
but the type of instruction will differ, so it is important to know
what to expect.
Select all true statements about small classes. There may be more
than one correct answer.
•
A. Small classes always review what was taught in large
classes
•
B. Small classes explore applications of the material
learned in class
•
C. Small classes are opportunities for you to work on
homework
•
D. Attending small classes is optional
•
E. Engagement marks are given in small classes
•
F. Small classes are a way to learn new material in an
active way
1
Problem 5.
(1 point)
Please complete the following survey:
https://ubc.ca1.qualtrics.com/jfe/form/SV
e
sx
01
P
7
OIMWTMeW
This survey will help the Department of Mathematics build
a complete picture of students’ attitudes and perceptions in
first-year mathematics courses at UBC. It will only take 5-10
minutes to complete, and there are no wrong answers.
The survey answers will be kept confidential; only the re-
searchers collecting the data will see them.
• ?
•
I clicked on the link!
• I did not click on the link.
Problem 6.
(1 point)
This question, and the next several questions, cover mathe-
matical content from high school. If you find yourself unsure
about any of these topics, it’s a good idea to study them now.
You’ll need to understand them in order to progress in calcu-
lus.
There are many resources available for reviewing prerequi-
site content. You have access to a Precalculus Review
course
on Canvas, which contains high-school topics that are used in
this course.
Our textbook, CLP Calculus
, has an appendix
with selected topics from pre-calculus. Of course, you can also
look through your old notes, or find other resources that are
helpful to you.
Factor the polynomial
20
x
2
+
9
x
-
20
.
Your answer can be
written as
(
5
x
-
B
)(
Cx
+
D
)
with
B
,
C
, and
D
integers
where
B
equals:
and
C
equals:
and
D
equals:
Problem 7.
(1 point)
Solve
100
e
7
m
=
25
+
50
e
7
m
for
m
.
Problem 8.
(1 point)
The equation
|
x
|
=
|
y
|
is satisfied if
x
=
y
or
x
=
-
y
. Use this
fact to solve the following equation.
|
1
-
2
x
|
=
|
3
-
x
|
Answers (separate by commas):
x
=
Hint:
There are two solutions.
Problem 9.
(1 point)
For what values of
x
is
4
-
x
2
>
0
?
•
A.
x
<
-
2
and
x
>
2
•
B.
x
<
2
•
C.
x
>
-
2
•
D.
-
2
<
x
<
2
•
E.
-
4
<
x
<
4
Problem 10.
(1 point)
For what values of
w
is
w
(
w
+
3
)
-
(
3
w
+
4
)
w
-
2
>
0
?
•
A.
w
>
2
•
B.
w
>
-
2
•
C.
-
2
<
w
<
2
and
w
>
2
•
D.
-
∞
<
w
<
∞
•
E.
w
<
-
2
Problem 11.
(1 point)
To say that
x
-
6
3
≤
4
is the same as saying
x
is in the closed
interval
[
A
,
B
]
where
A
is:
and
B
is:
Problem 12.
(1 point)
Let
r
(
x
) =
tan
2
(
x
)
. Which of the following best describes its
fundamental algebraic structure?
•
A. A composition
f
(
g
(
x
))
of basic functions
•
B. A sum
f
(
x
)+
g
(
x
)
of basic functions
•
C. A product
f
(
x
)
·
g
(
x
)
of basic functions
•
D. A quotient
f
(
x
)
/
g
(
x
)
of basic functions
where
f
(
x
) =
g
(
x
) =
Problem 13.
(1 point)
Let
f
(
x
) =
x
2
+
5
x
and
g
(
x
) =
x
-
2
. Evaluate the following:
1.
(
f
◦
g
)(
x
)
=
2.
(
g
◦
f
)(
x
)
=
3.
(
f
◦
f
)(
x
)
=
4.
(
g
◦
g
)(
x
)
=
2
Problem 14.
(1 point)
Fill in the missing values in the tables below for
p
(
t
)
,
q
(
t
)
, and
their composition
r
(
t
) =
q
(
p
(
t
))
.
t
p
(
t
)
q
(
t
)
r
(
t
)
0
4
1
2
1
2
0
3
2
0
4
4
1
5
5
0
1
3
Problem 15.
(1 point)
To get a better look at the graph, you can click on it.
The curve above is the graph of a sinusoidal function.
It
goes through the point
(
6
,
0
)
. Find a sinusoidal function that
matches the given graph. If needed, you can enter
π
as
pi
in
your answer.
f
(
x
) =
Problem 16.
(1 point)
Match the functions with their graphs. Enter the letter of the
graph below which corresponds to the function. (Click on im-
age for a larger view.)
1.
y
=
-
2sin
x
2.
y
=
1
+
sin
x
3.
y
=
|
cos
x
|
4.
y
=
4
-
2cos
x
A
B
C
D
Problem 17.
(1 point)
The graph below could represent which of the following?
•
A.
y
=
log
x
•
B.
y
=
x
3
•
C.
y
=
e
x
•
D.
y
=
e
-
x
•
E.
y
=
1
/
x
Problem 18.
(1 point)
() Consider the functions
A.
y
=
x
n
B.
y
=
x
1
/
n
C.
y
=
x
-
n
where
n
is an integer greater than 1 (
n
=
2
,
3
,
...).
Which of these functions increases most steeply for values of
x
greater than 1? [?/A/B/C]
Which decreases for large values of
x
? [?/A/B/C]
Which of these functions is not defined at
x
=
0
? [?/A/B/C]
3
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Problem 19.
(1 point)
Interactive graph best viewed online
() Compare the functions
f
(
x
) =
x
11
and
g
(
x
) =
e
x
shown in
red and blue respectively in the graph above. By zooming in
and out, view the functions using several viewing scales. When
does the graph of
g
finally surpass the graph of
f
?
The graphs intersect for the last time at
x
≈
. (Round
your answer to four significant figures.)
Hints: You can manually adjust the axes of the graph by click-
ing on the settings tool in the top right. To get this much ac-
curacy you may need to zoom in very close to the intersection
point.
You must round your answer or it will be marked wrong.
Problem 20.
(1 point)
() Which of the graphs below corresponds to the function
g
(
x
) =
5
x
3
-
5
x
4
?
(Hint: Consider which power dominates near the origin and
which dominates far away from the origin.)
•
A.
(click on image to enlarge)
•
B.
(click on image to enlarge)
•
C.
(click on image to enlarge)
•
D.
(click on image to enlarge)
•
E. None of the above
Problem 21.
(1 point)
() Let
a, b, k,
and
n
denote constants, and consider the
exponential functions
e
x
(in blue),
ae
kx
(in green), and
be
nx
(in red) whose graphs are each labeled on the axes
below.
Which of the following statements about the values
of the constants
a
,
b
,
k
, and
n
are true? Select all true
statements and submit your answers.
•
A.
a
=
1
•
B.
b
>
1
•
C.
b
<
1
•
D.
k
<
0
•
E.
a
>
b
•
F.
b
=
1
•
G.
a
=
b
•
H.
k
>
1
•
I.
n
<
0
•
J.
0
<
n
<
1
•
K.
n
>
1
•
L.
a
<
b
•
M.
a
>
1
•
N.
0
<
k
<
1
•
O.
a
<
1
(Click on graph to enlarge)
4
Problem 22.
(1 point)
() Without using a calculator, match each exponential
function with its graph.
?
e
-
0
.
03
t
?
e
0
.
1
t
?
e
-
0
.
3
t
?
e
0
.
03
t
(Click on graph to enlarge)
Problem 23.
(1 point)
() Without a calculator, match each function with its
graph.
?
y
=
4
x
?
y
=
log
3
(
x
)
?
y
=
5
x
?
y
=
e
-
3
x
?
y
=
log
(
x
)
(Click on graph to enlarge)
5
Problem 24.
(1 point)
() Consider the four functions graphed in the figure below, and
assume the equations for
A
,
B
,
C
, and
D
, can all be written
in the form
y
=
ab
t
.
Which two functions have the same value for
a
?
?
(click on image to enlarge)
Problem 25.
(1 point)
() Consider the function
f
(
x
) =
x
3
+
2
x
2
-
4
x
+
2
.
Suppose
we wish to know the value of
x
where this function assumes
its minimum value on the interval
[
0
,
1
]
. Later in the course
we will learn how to compute this
x
-value analytically, but for
now, let’s compute it numerically using a spreadsheet.
Open a spreadsheet program such as Excel or Google Sheets
(available for free online) and create a spreadsheet that looks
like the one below.
Assume all cells not shown begin blank. A downwards arrow
indicates the contents from the cell above will be copied down.
x
f
(
x
)
A
B
1
0
?
2
0.01
↓
3
0.02
↓
4
0.03
↓
5
0.04
↓
6
0.05
↓
7
0.06
↓
8
↓
↓
a) A1 has 0 entered into it, and you want to generate the rest
of the entries in column A. You will type something into A2,
and copy it down to A3, A4, A5, and A6. What should you
type into A2? Select the best answer.
•
=0.01
•
=A2+0.01
•
=A1+0.01
•
A1=0.01
•
A2=A1+0.01
•
=0+0.01
•
A2=0.01
•
0+0.01
•
A1+0.01
•
A2+0.01
6
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b) In column B, we want to generate values for
f
(
x
)
. What
formula should be written in cell B1 and then be copied down
to the cells below?
•
=x
3
+
2
x
2
-
4
x
+
2
x
3
+
2
x
2
-
4
x
+
2
•
=
B1
3
+
2
*
B1
2
-
4
*
B1
+2
•
=
A2
3
+
2
*
A2
2
-
4
*
A2
+2
•
=
A1
3
+
2
*
A1
2
-
4
*
A1
+2
•
A1
3
+
2
*
A1
2
-
4
*
A1
+2
c) Use your spreadsheet to estimate the value of
x
in the inter-
val
[
0
,
1
]
for which
f
(
x
)
assumes its minimum value. Give your
answer correct to 2 decimal places.
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7