Assignment 2
Complete this assignment after you have finished Unit 3, and submit your work to your tutor for grading.
This assignment has one bonus question. There is no penalty if you do not attempt it but you may be rewarded
if you do. The maximum grade
Assignment 3
Complete this assignment after you have finished Unit 4, and submit your work to your tutor for grading.
Total points: 100
Weight: 10%
(9 points)
1. An Earth-observing satellite can see only a portion of the Earths surface. The satellite has
Assignment 1
Complete this assignment after you have finished Unit 1, and submit your work to your tutor for grading.
This assignment has one bonus question. There is no penalty if you do not attempt it but you may be rewarded
if you do. The maximum grade
Sample Midterm Examination
Time: 3 hours
Passing grade: 55%
Total points: 64
Solutions and Marking Scheme
5 points
6 points
.
1. Give the exact value of cos
12
Solution
cos
= cos
12
4 3
= cos
cos
+ sin
sin
4 3
3
4
1+ 3
1
3
= + =
2 2 2 2
2 2
(2 p
Correct Solutions: Learning from Mistakes
Unit 2
1. Define each of the functions below as a set of pairs.
a. The velocity v depends on the time t.
b. The bacteria population B depends on the amount of oxygen o.
Mistake The order of the variables is incorr
Sample Final Examination
Time: 3.5 hours
Passing grade: 55%
Total points: 100
20 points 1. Compute the derivatives of each of the functions given below. You may not need
to simplify your answers.
a. y = sin x cos(sin x2 )
1
1 + x3 3
b. y =
1 x2
p
c. y = 1
Correct Solutions: Learning from Mistakes
Unit 1
x
?
2
Mistake An inequality changes when it is multiplied (or divided) by a negative
number.
1. If x is any number in the interval [4, ), in which interval is 1
Solution
x
. Therefore,
If x is in [4, ), th
Sample Final Examination
Time: 3.5 hours
Passing grade: 55%
Total points: 100
Solutions and marking Scheme
Take note of how the points are assigned in each question.
20 points 1. Compute the derivatives of each of the functions given below. You may not ne
Correct Solutions: Learning from Mistakes
Unit 3
1. Draw the graph of a single function f , such that
a. lim f (x) = 3
x0
b. lim f (x) =
x2
c. lim f (x) = 1.
x
Mistake The graph given is not the graph of a function because it fails the
vertical line test
Correct Solutions: Learning from Mistakes
Unit 4
1. The displacement (in km) of a moving car is given by s(t) = 3t3 + 4t 2,
where t is measured in hours.
a. Give the average velocity in the time period [1, 5].
b. Give the two different interpretations of
Crime Scene Investigation: Case Profile
The vicTim in The following case is a 35-year old whiTe male named Tony DeMoy. IniTial
invesTigaTors say They found several signs around The deaTh siTe ThaT suggesT foul play. FoUr possible
causes of his unTimely de
Sample Midterm Examination
Time: 3 hours
Passing grade: 55%
Total points: 64
5 points
.
1. Give the exact value of cos
12
6 points
2. Let f (x) = 2x2 5 and g(x) =
x+5
.
2x 9
Find the composite functions and their corresponding domains.
a. f (g(x)
b. g
Mathematics 265
Introduction to Calculus I
Study Guide
Athabasca University a
Course Team
Course Professor: Maria Luisa Torres, Ph.D.
Author: Maria Luisa Torres, Ph.D.
Editor: Gilda Sanders
Cover Design: Ian Grivois
Illustrations: Jingfen Zhang and Margar
Introduction
Welcome to Mathematics 365: CalculusSeveral Variables, a three-credit
course designed to introduce students to practical applications of calculus to
problems two and three dimensions, and to a theoretical understanding of
some aspects of calc
1
Economics 248 Assignment 1 (version B)
This assignment has a maximum total of 100 marks and is worth 10 percent of your total grade
for this course. You should complete it after completing your course work for Units 1, 2, and 3.
Answer each question cle
Base your answers to the questions on this information: In one day, Canada can produce either 200 tonnes of wheat or 90 to
ingots. In one day, Chile can produce either 120 tonnes of wheat or 175 tonnes of copper ingots.
(10
marks)
a. Calculate Canadas opp
PROTECTED WHEN COMPLETED - B
PAGE 1 OF 2
DOCUMENT CHECKLIST
FOR A STUDY PERMIT
This document checklist is one of the forms that you need to submit with your application.
Consult the Instruction Guide (IMM 5269) to find out if you are required to provide s
1
(4 points)
The velocity of an ant running along the edge of a shelf is modeled by the function
5t , 0 t 1
v(t)
6 t , 1 t 2
where
is
2
4 cm
v
is in centimeters per second. Estimate the time at which the ant
from its starting position.
(16 points)
Calcul
(4 points)
1. Use the prime decomposition of integers to express the listed radical in its minimal
expression. Do not use decimals.
a.
220500
b.
c.
d.
3
68600
3
3267 4400
1125 2420
(8 points)
2. Fill in the table below. Note that you should refer to the s
1
(9 points)
An Earth-observing satellite can see only a portion of the Earths surface. The satellite has
horizon sensors that can direct the angle
shown in the accompanying figure. Let be the
r
radius of the Earth (assumed spherical) and
h
the distance o
1
(6 points)
As shown in the figure below, a camera is mounted on a point 30 m from the base of a rocket
launching pad. The rocket rises vertically when launched, and the cameras angle is
continually adjusted to follow the base of the rocket.
a
Express th
Assignment 4
Complete this assignment after you have finished Unit 7, and submit your work to your tutor for grading.
Total points: 80
Weight: 10%
(4 points)
1. The velocity of an ant running along the edge of a shelf is modeled by the function
5t , 0 t <