April 2009
Mathematics 103
Name
Page 2 of 10 pages
Marks
[24]
1.
Multiple Choice Questions: Select ONE correct answer (a, b, c, d, or e) for each question and
write it in the table on the next page. You will not be graded for any work or answers outside
those boxes.
(Q1) Which of these integrals does the sum
N
X
k
=1
±
3
N
²
"
±

2 +
3
k
N
²
3

1
#
approximate as
N
→ ∞
?
(a)
Z
3
0
x
3
dx
(b)
Z
1

2
(
x
3

1)
dx
(c)
Z
3
0
(
x
3

2)
dx
(d)
Z
1

2
x
3
dx
(e)
Z
1
0
(
x

2)
3
dx
(Q2) You are out Fshing. Every time you cast your line, the probability that you catch a Fsh is
1
/
4. What is the probability that you catch at least one Fsh within the Frst 2 attempts?
(a)
1
/
16
(b)
7
/
16
(c)
1
/
2
(d)
9
/
16
(e)
15
/
16
(Q3) ±or which of these di²erential equations is
y
= 3 a steady state solution?
(a)
dy
dt
= 2
y

6
(b)
dy
dt
=
y
2
+ 9
(c)
dy
dt
=
1
3

y
(d)
dy
dt
= cos(
πy
)
(e)
dy
dt
= 3
(Q4) A Math 103 class of 100 students took a test.
The following graph shows how many
students’ marks were in each of the intervals 1–10, 11–20,
. . .
, 91–100.
0
5
10
15
20
25
students
20
40
60
80
100
marks
What was (approximately) the median?
(a)
50
(b)
60
(c)
70
(d)
80
(e)
90
(Q5) A charged molecule moves in a changing electric Feld which results in an acceleration of
a
(
t
) = cos(
t
) (in appropriate units).
At time
t
= 0, the molecule is at rest at position
x
(0) = 1. What is the position
x
(
t
) when the molecule’s velocity reaches the value

1
for the Frst time after time 0?
(a)

1
(b)
0
(c)
1
(d)
2
(e)
The velocity never reaches

1
Continued on page 3
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View Full DocumentApril 2009
Mathematics 103
Name
Page 3 of 10 pages
(Q6) Each mouse born with a certain genetic mutation has probability 0.7 of contracting a
certain disease. Out of 10 mice born with the mutation, the probability that exactly 8
will contract the disease is
(a)
45(
.
7)
8
(
.
3)
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 Winter '10
 Dr.AlejandroCortas
 Math, Variance, The Land, Probability theory, probability density function

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