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Mathematics B30
Module 4
Assignment 10
Mathematics B30
269
Assignment 10
Mathematics B30
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Assignment 10
Optional insert: Assignment #10 frontal sheet here.
Mathematics B30
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Assignment 10
Mathematics B30
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Assignment 10
Assignment 10
Multiple Choice: Select the correct answer for each of the following and circle your answer
on this question sheet.
(9.1)
1.
The simplified form of
A.
B.
C.
D.
(9.1)
2.
B.
C.
D.
3.
1 2
2 x 2
2 0
is ***.
2x4
x4
x4
2
x4
32
2 1
The simplified form of 1
is ***.
2  2 3
A.
(9.2)
4 x  6 x 
4
5
8
9
5
8
The simplest exponential form of
A.
a
B.
a
C.
3
D.
Mathematics B30
a  3 a  6 a is ***.
a
3
2
a2
2
3
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Assignment 10
(9.2)
4.
2
A.
B.
C.
D.
(9.2)
5.
6.
0
1 , 3
 1,  3
1,  3
The solution to 5 x
A.
B.
C.
D.
(9.3)
 
The solution to 4 x  64 4 2 x is ***.
2
x 1
 5 is ***.
0, 1
5
1
2
The graph of y  2  x 5 is ***.
y
A.
B.
y
5
1
x
x
y
C.
D.
y
5
5
x
Mathematics B30
274
x
Assignment 10
(9.4)
7.
The half-life of Carbon-14 is 5 760 years. If the original amount of Carbon-14
in a fossil is estimated to be 6.3 gm and the present amount is 0.8 gm, the age
of the fossil is about ***.
A.
B.
C.
D.
(10.1) 8.
The exponential form of y  log 5 x is ***.
A.
B.
C.
D.
(10.1) 9.
y  10 5 x
x  5y
x  2y
5 x  10 y
 
The value of log 10 9 3
A.
B.
C.
D.
(10.2) 10.
45 360 years
40 000 years
25 016 years
17 149 years
3
is ***.
3  log 3 10
3.5  log 3 10
3.5 log 3 10
3  log 10 3
The domain of f x   log 1  3 x  is ***.
A.
B.
C.
D.
Mathematics B30
1
3
1
x
3
x 0
all real numbers
x
275
Assignment 10
(10.3) 11.
The expression log 2 x  
A.
B.
C.
D.
(10.4) 12.
log
x
2 x 1 x
2x 1  x
log
x
4.69 days
5.00 days
5.69 days
56.9 days
In an arithmetic sequence t 2  2 m  n and t 3  3m  2n . The tenth term is
***.
A.
B.
C.
D.
(11.1) 14.
3 
1  x 
log  x   log 

2 
 2 
log 2 x 1  x
A growth (decay) formula for a certain population is the exponential equation
1
N  N 0 10 kt . If the amount N is N 0 after 3 days, the time required for 360 to
4
remain if N 0  5000 is ***.
A.
B.
C.
D.
(11.1) 13.
1
1
log 1  x   log x is equivalent to ***.
2
2
10 m
10 m
10 m
10 m
 9n
 25 n
 31 n
 10 n
Five years after Dale invested a certain amount of money the accumulated
value was $3 550 and after 7 years it was $3 988.78. After each year the
accumulated value was r times the amount of the previous year. The amount
originally invested was ***.
A.
B.
C.
Mathematics B30
$3 000.00
$2 811.93
$2 701.50
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Assignment 10
D.
Mathematics B30
$2 500.00
277
Assignment 10
(11.2) 15.
The positive mean proportional between  36 and  9 is ***.
A.
B.
C.
D.
(11.3) 16.
27
25
22.5
18
The finite sum
9
 2 k  1 is ***.
k 1
A.
B.
C.
D.
(11.3) 17.
17
80
81
162
The sum
12
 2i
k
is ***.
k 1
A.
B.
C.
D.
(11.4) 18.
4i
1i
0
2i
1i
2
The one convergent geometric series is ***.
A.
2  2  1   2  1   2  1   ...
2
3
B.
C.
a  a 2  a 2   a 2   ...
1  4  9  16  ...
D.
1 1 1
1         ...
3 3 3
2
2
Mathematics B30
3
3
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Assignment 10
(11.4) 19.
The sum of 10  2 
A.
B.
C.
D.
(12.1) 20.
B.
C.
D.
3
cm
10
3 cm
2
2 cm
5
1
3 cm
3
The accumulated value of $100 invested for 4 years at 6% compounded
quarterly is ***.
A.
B.
C.
D.
(12.3) 22.
infinite
20
1
12
2
25
The first blow of a hammer drives a nail 2 cm into the wood. Each following
2
blow drives the nail
as far as the preceding blow did. The maximum
5
distance the nail can be driven into the wood is ***.
A.
(12.2) 21.
2
 ... is ***.
5
$254.04
$126.90
$102.43
$124.00
If money earns 8% compounded semiannually, the amount that is to be
invested today so that $500 can be withdrawn at the end of each year of
investment for 5 years is ***.
A.
B.
C.
D.
Mathematics B30
$2 000
$1 988
$1 798
$1 776
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Assignment 10
(13.1) 23.
One card is drawn from a standard deck of 52 playing cards. A represents the
event that a red card is drawn. B represents the event that a number 10 is
drawn. The number of ways A or B can happen is ***.
A.
B.
C.
D.
(13.1) 24.
(13.2)
A committee of 3 girls and 2 boys is to be selected from a group of 6 girls
and 6 boys. The number of ways this can be done is ***.
A.
B.
C.
D.
(13.1) 25.
(13.2)
C3 6 C2
6 C3  6 C 2
12 C5
12 C3 12 C 2
6
A committee of either 3 girls and 2 boys or 4 boys and 1 girl is to be
selected from a group of 7 girls and 8 boys. The number of ways this can be
done is ***.
A.
B.
C.
D.
(13.2) 26.
2
26
28
30
2 15 C5 
7 C3  8 C 2  8 C4  7 C1
15 C5
7 C3  8 C2  8 C4  7 C1
A committee of 3 is to be chosen from 7 people to fill the positions of president,
secretary, and treasurer. The number of ways this can be done is ***.
A.
B.
C.
D.
Mathematics B30
C3
7 7 7
7 P3
7 6 5 4
7
280
Assignment 10
(13.2) 27.
If a fair coin is tossed two times, the odds that heads will come up both times
are ***.
A.
B.
C.
D.
(13.3) 28.
In the Venn diagram the shaded area is
represented by ***.
A.
B.
C.
D.
(13.4) 29.
1 to 1
3 to 1
1 to 3
1 to 4
C
If the probability of event A is
A.
B.
C.
D.
(13.4) 30.
A
B C
A  B C
B C  A
B C  A
P A  B  
B
1
3
, the probability of event B is , and
4
4
3
then ***.
8
events A and B are dependent
events A and B are independent
events A and B are virtually exclusive
events A and B are random
A box contains 5 red marbles, 6 white marbles and 10 blue marbles. One
marble is drawn, and then, without replacing the first marble a second marble
is drawn. The probability that a red marble and then a blue marble are
drawn is ***.
A.
B.
C.
D.
Mathematics B30
1 1

5 10
5 10

21 21
5 10

21 20
5  10
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Assignment 10
Mathematics B30
282
Assignment 10
(13.4) 31.
As in Question 30, a box contains 5 red, 6 white and 10 blue marbles. One
marble is drawn, and then, without replacing the first marble a second marble
is drawn. The probability that a red and blue marble are drawn is ***.
A.
B.
C.
D.
(14.1) 32.
The coefficients of the expansion of  x  y  add up to ***.
6
A.
B.
C.
D.
(14.2) 33.
(14.2) 34.
5
21
5
42
100
441
10
441
16
32
64
128
The middle term(s) of the expansion of 2 y  b 
10
A.
10
B.
10
C.
10
D.
10
C 5 2 y   b  ,
5
5
C 5 2 y   b 
5
C 6 2 y   b 
4
10
6
5
C 5 2 y  b 
5
5
C 4 2 y   b 
6
4
The 12th term of the expansion of 2 x  i 
16
A.
B.
C.
D.
Mathematics B30
is(are) ***.
is ***.
8 736 ix 5
 8 736 ix 5
139 776 ix 5
 139 776 ix 5
283
Assignment 10
(14.3) 35.
In a family of 5 children the probability of having 2 girls or 3 girls is ***.
A.
B.
C.
D.
(14.2) 36.
(14.2) 37.
The first 3 terms of the expansion of
A.
81 3  729 i 2  1 944 3
B.
81 3  729 i 2  1 944 3
C.
81 3  729 i 2  1 944 3
D.
1 813 3  729 i 2

3 i 2

9
are ***.
In the expansion of 5 a  2 b  the coefficient of a 5 b 2 is ***.
7
A.
B.
C.
D.
(15.1) 38.
(15.2)
7
8
3
8
1
2
5
8
21
1 050
2 100
262 500
On a recent quiz, the twenty-two students of Mr. Campbell received the
following scores out of a total of 57.
29
43
38
44
39
48
37
46
24
51
48
51
42
50
47
54
46
49
36
44
52
45
The mean x and standard deviation  , respectively, are ***.
A.
B.
C.
D.
Mathematics B30
x
x
x
x
 45 .86 ,
 44 .28 ,
 43 .77 ,
 43 .77 ,
  6 .69
  7 .29
  7 .31
  6 .87
284
Assignment 10
(15.1) 39.
The median of the data in Question #38 is ***.
A.
B.
C.
D.
(15.2) 40.
45
44
46
45.5
The heights for ten basketball players are given. Using the formula given in
the course, the standard deviation of the data to two decimal places is ***.
188
202
A.
B.
C.
D.
(15.3) 41.
190
202
192
207
196
198
199
5.88
5.59
5.58
5.43
Given the following frequency table, the mean x of the data is ***.
Class
1
2
3
4
A.
B.
C.
D.
(15.3) 42.
196
Class
Interval
0-4
4-8
8-12
12-16
Frequency
3
7
6
2
9.5
6.2
7.6
7.5
From a sample, the speeds in km per hour of
bicycles on a pathway are shown on the
histogram. The standard deviation of the
population is ***.
A.
B.
C.
D.
Mathematics B30
Frequency
  2.33
  2.99
  3.11
  14 .5
f(x)
4
3
2
1
8 10 12 14 16 18 20
Speed
285
Assignment 10
x
(16.1) 43.
A population has a normal distribution with mean x and standard deviation
 . The percent of the population that lies in the interval from x   to x  2
is ***.
A.
B.
C.
D.
(16.1) 44.
It is known that a certain population has a normal distribution with mean 50
and standard deviation 10. A sample of 200 items is drawn from that
population. The approximate number of items in the sample that have values
between 40 and 60 is ***.
A.
B.
C.
D.
(16.1) 45.
68.26%
81.85%
84.00%
47.72%
68
95
136
190
The data represented by the curve is ***.
f(x)
x
A.
B.
C.
D.
(16.1) 46.
skewed to the left
skewed to the right
a normal distribution
spread out further to the right
The weight of northern pike fish is normally distributed with a mean weight of
2.3 kg and a standard deviation of 0.8 kg. The range of weights that you would
expect 95.44% of the fish to fall between is ***.
A.
B.
C.
D.
Mathematics B30
1.5 kg to 3.1 kg
0 kg to 4.6 kg
0.7 kg to 4.6 kg
0.7 kg to 3.9 kg
286
Assignment 10
(16.2) 47.
The average number of frost-free days in communities throughout
Saskatchewan in 1997 was 116.2 days with a standard deviation of 8.8 days.
Moose Jaw recorded 122 frost free days. The z-score for Moose Jaw is ***.
A.
B.
C.
D.
(16.2) 48.
0.4066
0.0934
0.9066
0.3907
During a major-league career of 25 seasons, a baseball player averaged 150
hits a season with a standard deviation of 20 hits. The number of seasons that
the player had at least 170 hits was ***.
A.
B.
C.
D.
(16.2) 50.
 0 .66
 0 .68
 1 .02
 1 .22
The probability of an event occurring with a z-score greater than 1.32 is ***.
A.
B.
C.
D.
(16.2) 49.
z
z
z
z
1
2
3
4
The yearly Beeswax production in Saskatchewan has been recorded over the
past 25 years. The mean yearly production is 156 912 pounds with a standard
deviation of 39 987 pounds. The probability that in the next year the
production will be greater than 175 000 pounds is ***.
A.
B.
C.
D.
Mathematics B30
0.4523
0.6736
0.3413
0.3264
287
Assignment 10
Mathematics B30
288
Assignment 10