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# PractEx1.pdf

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McMaster University

Mathematics

MATH 1LS3

Chris Mc Lean

Winter

Description

Name: _________________u______________ u Student Number:__________________u__
MATHEMATICS 1M03
Winter Session, 2011
Final Examination - Practice Version
Please Read the Instructions: They will be the same as on the actual examination!
FINAL EXAMINATION
DAY CLASS
DURATION OF EXAMINATION: 3 hours
MAXIMUM GRADE: 27
MCMASTER UNIVERSITY EXAMINATION
Thursday,April 8, 2010
THIS TEST INCLUDES 12 PAGESAND 25 QUESTIONS. YOUARE
RESPONSIBLE FOR ENSURING YOUR COPY OF THE TEST IS COMPLETE.
BRINGANY DISCREPANCYTO THEATTENTION OF YOUR INVIGILATOR.
Instructions:
1. Only the Casio FX-991 calculator is allowed to be used on this test.
2. Make sure your name and student number is at the top of each page.
3. Each question is worth one mark.
4. Ablank answer is an automatic zero for any question, even if the correct solution is circled on
the question itself.
5. Unless specifically stated otherwise in the question, incorrect or multiple answers are also worth
zero marks. No negative marks or part marks will be assigned.
6. In the event of a discrepancy between instructions provided in a question and these instructions, the
instructions in the question supersede those written here.
7. Rough work materials will be provided.All rough work must be handed in with the test, but any
solutions written on the rough paper will NOT be graded.
8. Good Luck!
________________u__________________u_______________
PLEASE READ THE OMR INSTRUCTIONS ON PAGE #2 Page #2 of 12
Name: _______________________________ Student Number:____________________
OMR EXAMINATION INSTRUCTIONS
NOTE: IT IS YOUR RESPONSIBILITYTO ENSURE THAT THEANSWER SHEET IS PROPERLY
COMPLETED: YOUR EXAMINATION RESULT DEPENDS ON PROPERATTENTION TO THESE
INSTRUCTIONS.
The scanner which reads the sheets senses shaded areas by their non-reflection of light.Aheavy mark must be
made, completely filling the circular bubble, with an HB pencil. Marks made with a pen or a felt–tip marker will
not be sensed. Erasures must be thorough or the scanner may still sense a mark. Do not use correction fluid on
the sheets. Do not put any unnecessary marks or writing on the sheet.
1. Print your name, student number, course name, section number, instructor name,
and the date in the spaces provided at the top of Side 1 (red side) of the sheet. Then
you must sign in the space marked SIGNATURE.
2. Write your student number in the space provided and fill in the corresponding
bubble numbers underneath.
3. Mark only one choice from the alternatives (1, 2, 3, 4, 5, or A, B, C, D, E) provided
for each question. The question number is to the left of the bubbles. Make sure that
the number of the question on the scan sheet is the same as the question number on
the test paper.
4. Pay particular attention to the Marking Directions on the form.
5. Begin answering the questions using the first set of bubbles, marked “1”.
134
Continued on page #2 Page #3 of 12
Name: _________________u______________ u Student Number:__________________u__
Remember: All answers must be entered on the OMR card - This paper will NOT be graded.
#1. Evaluate:
e
x lnx dx
∫
1
2 1 2 1 2 2
a) (2e + 1) / 4 b) 2 ln e − 4 c) (e + 1) 4 d) 1/4 e) + ( 1)
__________________g__________________g_
#2. Evaluate:
∞
2e x
∫ dx
(1+e x )
0
a) 1 b) −2/e c) 0 d) /e e) 2
__________________g__________________g_
#3. A scientist discovers a new radioactive element, "Zorkium" with a half-life of 4 days.
If he has 10g of pure Zorkium when he announces his discovery to the world, how much will
he have left in 8 days when he receives his Nobel Prize?
a) 1.25g b) 2.5g c) 3.33g d) 6.66g e) 8g
__________________u__________________u_
Continued on page #4 Page #4 of 12
Name: _________________u______________ u Student Number:__________________u__
Remember: All answers must be entered on the OMR card - This paper will NOT be graded.
#4. At what point(s) does the function:
f(x, y)= 4x3 2/y
2 2
attain it's maximum value when restricted to the x + y: 12 =
a) (1,‒1),(‒1,1) b) ( 2√2, ‒2 ),( ‒2√2, 2 )c) ( ‒2√2, ‒2 ),( 2√2, 2 )
d) ( 2√2, 2 ) only e) ( 1, 1 ) only
_____________________________________
#5. Given the function:
xy
f(x, y) = xe
Evaluate f (1,0).
xy
a) 0 b) e c) 1 d) 2 e) 3
_____________________________________
#6. Find the average value on [-1,2] of the function:
p(x) = 4 ‒ 3x ³
a) l b) 1/2 c) 1/4 d) −11.75 e) 4 x −1 x 4
3 4
__________________u__________________u_
Continued on page #5 Page #5 of 12
Name: _________________u______________ u Student Number:__________________u__
Remember: All answers must be entered on the OMR card - This paper will NOT be graded.
#7. Find the area enclosed between the graphs:
y= e ,x =y −3e , = x ln2
a) 9/8 b) 12 c) 3+2ln2 d) 1e + 1 5− e) 29/ 24
2 3e3 6
__________________u__________________u_
#8. Which of the given points is in the domain of both functions.
1
Q( x, y)= P (x ,y) ln(+ 2y 4)
25− 4x2 y −
a) ( 0, 0 ) b) ( 0 ,−2 )c) ( 1, 5/2 ) d) (−2, 2 ) e) ( 1, 1 )
__________________u__________________u_
#9. Solve the equation for x:
ln(4− 3 x ) 7 =
7 7
4−e 4− e
a) x=1 b)x 3ln(4/7) c)x= 3 d) x=log7(4/3) e) x= 3
__________________u__________________u_
Continued on page #6 Page #6 of 12
Name: _________________u______________ u Student Number:__________________u__
Remember: All answers must be entered on the OMR card - This paper will NOT be graded.
#10. Find the (approximate) mean, μ, of the random variable x with the probability density
function given below defined on the given interval.
1
4 ≤ x 1 6
f (x) = 4 x
0 otherwise
a) 7 b) 12 c) 9.3 d) 4 e) 9
__________________u__________________u_
#11. Given the function:
f(x, y)= x 2 4+xy+ y
and the points:
1 1 1 1 1
i) ( 0, 0 ) ii)− , iii)− iv) − v) ,0 ( 1, 1 )
4 8 4 8 4
which are critical points?
a) i) andii) b) ii) andiic) i) anddi)) ) oniv e) ), ) a indii ) iii
__________________u__________________u_
#12. The population of Mogwai in a wilderness preserve follows the equation:
P(t)= B
−0.1t
20+ 10 e
Here, P is the population in thousands of Mogwai, and t is time in months.
If, after 10 months the population is found to be at 20 thousand Mogwai, what is
(approximately) the carrying capacity of the preserve?
a) 4

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