Canadian International Matriculation Programme
Mathematics of Data Management (MDM4U)
FINAL EXAMINATION
Time: 11.30a.m – 1.30p.m
Date: 29 May, 2012 (Tuesday)
Length: 2 HOURS
Lecturers:
(Please circle your teacher’s name)
Ms. Chia Yeng
Ms. Grace So
Mr. Lawrence Welch
Student Name: ______________________________
Mr. Nithyanathan
Section/Period: _______
Please read the following instructions carefully before you begin the examination:
1. This exam paper has fifteen printed pages, including this cover page.
2. The examination is worth 30 percent of your final mark.
3. The examination consists of three parts: PARTS A, B and C.
PARTS
A
B
C
CONTENT
Multiple Choice
Short Answer
Problem
TOTAL
MARKS
15
28
57
100
TIME ALLOCATION
20 MINS
30 MINS
70 MINS
120 MINS
4. The answers to the Multiple Choice Questions must be written on page 14 of this
booklet. All other answers must be written in the space provided. If you need more
space, continue on the blank page to the left of the relevant question and do indicate your
intention.
5. Scientific or graphing calculators are permitted, but NO sharing is allowed.
You can ONLY use the special function of the graphing calculator when you see the
following symbol GC
. Otherwise, use the common functions only.
7. Marks for each question are indicated inside square brackets, [
].
8. Formula sheet is at the rear of this booklet – Page 15
For office use only:
Part A
Part B
FINAL EXAMINATION/MDM 4U – May 2012
Part C
Total
Page 1
PART A
Multiple Choice
[Knowledge : 15 marks]
PART B Short Answer [28 marks]
[Application: 9 marks; Communication 9 marks; Thinking 10 marks]
Show your working in the space provided.
16. A committee consisting of 3 students is to be randomly selected from 4 males and 5 females.
Calculate the probability that there are exactly 2 males in the committee.
[A/ 3 marks]
17. The Cultural Club is deciding a destination for their field trip. The selection is based on 3
criteria: historical sites, distance and budget; with respective weightings of 5, 3 and x.
For a trip to Malacca, the students have given scores of 8, 9 and 4 respectively. If the overall
weighted score was 7.5, what is the value of x (i.e.: the weighting for budget)?
[A/ 3 marks]
18. During a “Special Offer Week” at a clothing store, the manager reported a mean daily profit of
RM400 from Monday to Saturday and a profit of RM450 on Sunday.
Determine the mean daily profit for this particular “Special Offer Week”.
[A/ 3 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 2
19. Five digit numbers are formed using the numbers 0 to 8. Determine how many numbers
greater than 50000 can be made if each digit can only be used once.
[T/ 3 marks]
20. A group of visitors to the aquarium were asked whether they enjoyed the Dolphin Show and
whether they bought souvenirs from the gift shop. The results are shown in the following
table.
Enjoyed Dolphin
Show?
Bought
Souvenirs
Didn’t buy
Souvenirs
YES
15
28
NO
22
12
a) Create a split bar graph to display the results above.
[C/4 marks]
Frequency
Legend :
Did you enjoy the Dolphin Show?
b) Does the Dolphin Show influence a person’s decision to buy a souvenir from the
gift shop? Justify your answer by referring to the split bar graph drawn.
[C/ 2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 3
21. A maximum allowance of 20kg checked-in luggage is allowed for each passenger on a flight
to Toronto. Although most passengers would follow this rule, there are still a few who will
check in luggage above the weight limit.
Suppose that the weight of every checked-in luggage on a certain flight to Toronto is
recorded and then plotted as a histogram. Identify the shape of the distribution and briefly
explain your choice.
[C/3 marks]
22. Calvin’s Chocolates manufactures colour-coated chocolate candies. There are four possible
colours for the coatings as shown in the pie chart above.
Suppose a customer orders a small box of twenty chocolates.
a)
Create a frequency table to show the contents of the box.
[T/3 marks]
b) What is the best measure of central tendency to describe the above data? Explain why.
[T/2 marks]
c)
Sally randomly draws 8 candies from the box, one after the other with replacement.
What is the probability that she gets exactly 3 blue candies?
FINAL EXAMINATION/MDM 4U – May 2012
[T/2 marks]
Page 4
PART C
Problem
[57 marks]
[Knowledge: 11 marks; Application: 16 marks; Communication: 15 marks;
Thinking: 15 marks]
Show your complete working in the space provided.
23. The following stem and leaf plots display the time (in minutes) for Mei and Jon to complete
their MDM4U assignments.
Mei
Stem
1
2
3
4
5
Jon
Leaf
9
Stem
1
2
3
4
5
2 5 7 7 8 9
1 5 6
3
Leaf
1
3 4
0 2 6 9 9
7
8
a) Calculate the following measures for both students.
[C/6 marks]
MEDIAN
IQR
GC
Standard
Deviation
MEI
JON
b) Which student is more consistent in completing his/her assignments? Briefly explain why.
[C/2 marks]
c) Ravi has to tutor one student to fulfill his community hours. He decides to teach the student
who is less effective. By using the measures you have calculated in (b), explain which
student will be selected for Ravi’s tutorial?
[C/2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 5
24. A game is designed in which you roll two die. If you roll doubles (i.e. repeated numbers) you
win RM100, if you roll anything else, you pay RM5.
a)
Complete the distribution table below :
Outcome
Amount
win/lose
(RM)
[T/2 marks]
Probability
Doubles
Anything
Else
b) Tabulate the amount you expect to win or lose if you play 10 games.
[T/3 marks]
c) Assume that the RM5 you have to pay for rolling “anything else” is maintained. To make
this a fair game, how much should you win when you roll “doubles”?
[T/2 marks]
25. A box contains 6 silver rings and 4 gold rings. A game is played whereby a student is given a
chance to remove two items (one after another), without replacement, from the bag.
a) Draw a tree diagram to illustrate all possible outcomes (include the corresponding
probabilities)
[K/3 marks]
b) If the items match, the student is allowed to keep both items What is the probability that
he/she gets to keep any pair of items?
[K/2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 6
26. The following data represent the amount of nuclear power generation for the past 20 years.
Nuclear Power
Generated (millions of
megawatt hours)
(Continued)
1990
250
2004
650
1991
280
2005
680
1992
290
2006
680
1993
300
2007
630
1994
320
2008
680
1995
390
2009
720
1996
410
1997
450
1998
530
1999
530
2000
590
2001
610
2002
610
2003
600
Year
Year
Nuclear Power
Generated
(millions of
megawatt hours)
GC
a) Construct the line of best fit and curve of best fit by using your graphing calculator.
(Write the respective equations below),
Find the coefficient of determination for the line of best fit and curve of best fit.
(Note: Answer each part by rounding every number to four decimal places).
[A/4 marks]
b) Which regression (line or curve) provides a more accurate fit to the data?
Briefly explain why.
[A/2 marks]
c) Use the equation you selected in part (b) to predict the amount of nuclear power that will
be generated in the year 2020.
[A/2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 7
27. The Nature Club recorded the number of cans recycled and the number of bottled drinks
sold by a street vendor at 1 hour intervals.
No. cans
recycled
7
2
4
9
8
4
12
No. bottled
drinks sold
36
30
28
30
23
18
15
a) Identify the dependent variable. Briefly explain why.
[C/2 marks]
b) Use the correlation coefficient to explain if there is any relationship between the number of
cans recycled and the number of bottled drinks sold.
[C/3 marks]
28. 50 students from 3 colleges were surveyed to find out whether they usually access the
Internet from home or college.
Matrix College
Access Internet Access Internet
from home
from college
10
X
Sunny College
7
8
Victoria College
4
9
\
a)
Determine n( Matrix College ∩ Access Internet from college)
b)
Event A = students who access the Internet from home. Determine n(A’). [K/1 marks]
c)
Given that a student is not from Sunny College, what is the probability that he/she
usually accesses the Internet from college?
[K/2 marks]
d)
What is the probability that a randomly selected student is either from Matrix College
or usually accesses the Internet from college? (Show the use of the relevant
probability formula)
[K/2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
[K/1 mark]
Page 8
29. A study was conducted on 1000 rivers worldwide to determine the pollutants within each of
them.
323 rivers were polluted with crude oil
439 rivers were polluted with phosphates
463 rivers were polluted with sulphur compounds
150 rivers contained crude oil and phosphates
100 rivers contained sulphur compounds and crude oil
180 rivers contained sulphur compounds and phosphates
28 rivers were polluted by all three pollutants.
a) Draw a Venn diagram to illustrate pollutant content of the rivers.
b)
[A/4 marks]
How many rivers are contaminated with only one pollutant?
[A/2 marks]
c)
A randomly selected river is found to contain sulphur compounds. What is the probability
that this river is also contaminated with crude oil? (Support your answer with a relevant
probability principle)
[A/2 marks]
FINAL EXAMINATION/MDM 4U – May 2012
Page 9
30. A shopper randomly selects four cables from a display of 20 cables that is known to contain 3
defective cables.
a) Prepare a probability distribution for the random variable X that would represent the
number of defective cables in the shopper’s purchase.
[T/4 marks]
b) What is the probability that at least 3 of the cables chosen are faulty?
[T/2 marks]
c) How many faulty cables would he expect to get?
[T/2 marks]
*****
FINAL EXAMINATION/MDM 4U – May 2012
END OF PAPER
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