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MATH 2Z03 Quiz: Test 1 Solutions Group B (645 and 7pm).pdf


Department
Mathematics
Course Code
MATH 2Z03
Professor
David Lozinski
Study Guide
Quiz

Page:
of 16
MATH 2Z03: Test 1 Group B - Version 1
Instructor: Livia Corsi, Eric Harper, David Lozinski
Date: Thursday, October 16
Duration: 90 minutes.
Name: ID #:
Instructions:
This test paper contains 13 multiple choice and short answer questions printed on both
sides of the page. The questions are on pages 2 through 13. Pages 14 to 16 are available
for rough work. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF
THE PAPER IS COMPLETE. BRING ANY DISCREPANCIES TO THE ATTENTION
OF THE INVIGILATOR.
Select the one correct answer to each question and ENTER THAT ANSWER INTO
THE SCAN CARD PROVIDED USING AN HB PENCIL. Room for rough work has
been provided in this question booklet. You are required to submit this booklet along
with your answer sheet. However, only short answer questions will be graded from the
booklet. Point values are marked on each question. The test is graded out of 45.
SHORT ANSWER QUESTIONS MUST BE COMPLETED IN PERMANENT INK.
Computer Card Instructions:
IT IS YOUR RESPONSIBILITY TO ENSURE THAT THE ANSWER SHEET
IS PROPERLY COMPLETED. YOUR TEST RESULTS DEPEND UPON
PROPER ATTENTION TO THESE INSTRUCTIONS.
The scanner that will read the answer sheets senses areas by their non-reflection of light.
A heavy mark must be made, completely filling the circular bubble, with an HB pen-
cil. Marks made with a pen or felt-tip marker will NOT be sensed. Erasures must be
thorough or the scanner may still sense a mark. Do NOT use correction uid.
Print your name, student number, course name, and the date in the space provided
at the top of Side 1 (red side) of the form. Then the sheet MUST be signed in
the space marked SIGNATURE.
Mark your student number in the space provided on the sheet on Side 1 and fill
the corresponding bubbles underneath.
Mark only ONE choice (A, B, C, D, E) for each question.
Begin answering questions using the first set of bubbles, marked “1”.
McMaster University Math2Z03 Fall 2014 Page 1 of 16
1. (3 marks) Which of the following could be used to describe the diÆerential equation
cos(x)y000 +e2xy=xy2?
(a) linear, first-order, homogeneous
(b) autonomous, third-order, nonhomogeneous
(c) non-linear, third-order
(d) linear, third-order, nonhomogeneous
(e) autonomous, first-order
2. (3 marks) Which of the following could be a solution to the IVP
dy
dx +cos(x)y=0,y(0) = º?
(a) y=eRx
0cos(s)ds
(b) y=eRx
0sin(s)ds
(c) y=ceRº
0cos(x)dx
(d) y=ºe°sin(x)
(e) y=ºesin(x)°1
McMaster University Math2Z03 Fall 2014 Page 2 of 16
McMaster University Math2Z03 Fall 2014 Page 3 of 16
3. (3 marks) Which of the following most accurately describes the critical points of the
autonomous diÆerential equation
dy
dx =y2(y+2)(y°2) ?
(a) °2 is stable, 0 is semi-stable, 2 is unstable
(b) °2 is unstable, 0 is unstable, 2 is semi-stable
(c) °2 is stable, 0 is stable, 2 is stable
(d) °2 is unstable, 0 is unstable, 2 is stable
(e) °2 is stable, 0 is semi-stable, 2 is stable
McMaster University Math2Z03 Fall 2014 Page 3 of 16