Canadian International Matriculation Programme
Mathematics of Data Management (MDM4U)
FINAL EXAMINATION
Time: 2.30p.m – 4.30p.m
Length: 2 HOURS
Date: 7 December, 2015 (Monday)
Lecturers:
(Please circle your teacher’s name)
Ms. Chia Yeng
Ms. Janice Wong
Student Name: ______________________________
Section/Period: _______
Please read the following instructions carefully before you begin the examination:
1. This exam paper has fourteen 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
23
42
80
TIME ALLOCATION
20 MINS
30 MINS
70 MINS
120 MINS
4. The answers to the Multiple Choice Questions must be written on page 13 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 14), which you may detach
For office use only:
Part A
Part B
FINAL EXAMINATION/MDM 4U – Dec 2015
Part C
Total
Page 1
PART B Short Answer [23 marks]
[Knowledge: 5 marks; Application: 8 marks; Thinking: 6 marks;
Communication: 4 marks]
Show your working in the space provided.
16. Mr. Dave has 6 red bins, 7 blue bins and 4 green bins for a recycling campaign. If a student
randomly selects 4 bins to be placed in his classroom, determine the probability that he has
picked 2 red bins, 1 blue bin and 1 green bin.
[A/3]
17.
Stem
8
9
10
11
12
13
Leaf
1 1 7
0 3 5 5 8 8
2 8
4 4 6 8
7 9
0
GC
Find the three quartiles for the stem-and-leaf plot above AND create a box-and-whisker plot to
show the spread of the data. (Label all key summary points with respective values on the plot).
[K/5]
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 2
18. Draw the Venn Diagram for which
,
, and
Indicate clearly the number of items in each sector of the Venn Diagram.
.
[T/3]
19. The Pie chart below shows favourite fruits of 72 students from Sunny College.
Mango
(90º)
Starfruit
(xº)
Rambutan
1200
Durian
(110º)
Favourite Fruits
Create a bar graph to show the exact number of students who like each fruit.
FINAL EXAMINATION/MDM 4U – Dec 2015
[C/4]
Page 3
20. The following is a list of seven whole numbers arranged from smallest to largest 1, a, 5, 5, b, 7.
List all the possible values of a and b if IQR is 4.
[T/3]
21. At a games arcade, players in a ring-toss game are successful on 7% of the tosses. Each
player is given 8 rings to toss. Players will win a prize if at least 3 of the ring tosses are
successful. What is the probability of someone winning a prize? (4 decimal places)
[A/3]
22. A lighted candle stopped burning at a height of 5cm. Using the regression shown below,
estimate the burning time of the candle (from the time the candle was lit until it stopped
burning).
[A/2]
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 4
PART C
Problem
[42 marks]
[Application: 13 marks; Thinking: 15 marks Communication: 14 marks]
Show your complete working in the space provided.
23. The following table shows the number of questions attempted by Shrek and Princess Fiona in
10 assignments. The time taken (in minutes) by each to complete the assignment is also
shown below.
GC
No.
Questions
Shrek’s
Time
Princess
Fiona’s time
a)
b)
c)
5
3
10
8
15
12
9
8
5
3
20
30
122
59
150
134
70
100
28
25
58
21
73
160
130
120
98
30
67
20
Determine who is more consistent in the time taken to complete assignments.
Explain why by using mathematical evidence.
[C/3]
Determine who is more efficient in the time taken to complete assignments.
Explain by comparing the relevant numerical measurements.
[C/3]
A linear regression is generated to analyse the relationship between the number of
questions answered and time taken by Shrek to complete the assignment.
i) Identify the independent variable. Explain why.
[C/2]
ii) Write the equation for the line of best fit.
[A/1]
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 5
iii) Use a relevant numerical measurement to describe the correlation between the two
variables and conclude how the time is affected by the number of questions.
[C/3]
iv) Discuss the accuracy of the line of best fit for Shrek by referring to a relevant numeric
measurement.
[C/3]
v) Princess Fiona’s performance indicates the presence of an outlier. Create a scatter plot
for her data and circle the outlier.
[T/4]
vi) Create quadratic regressions for both characters. Fill in the blank in the statement
below with reference to the plot on your graphing calculator:
[T/1]
Princess Fiona seems to be able to complete her assignments
faster than Shrek when the assignment has more than
_______ questions.
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 6
24.
Soo-Ling travels the same route to work every day. She has identified 3 events that
could happen during the journey to her office: There is a 0.7 probability that she will wait
for at least one red light, a 0.4 probability that she will hear her favourite song and a 0.8
probability that she will give a friend a ride to work.
a) Create a tree diagram to show all possible outcomes, together with the respective
probabilities.
[A/4]
b) During this journey, what is the probability that Soo Ling will stop at a red light, not
hear her favourite song and give her friend a ride to work?
[A/2]
c) Soo Ling has to arrive early on a certain day for an important appointment. In order for
her to be on time, she must not stop at any traffic lights and not pick up her friend.
What is the probability that she can be on time for her appointment?
[T/2]
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 7
25.
In the game of Twister, a spinner is used to determine what body part must be placed
on what coloured circle. There are four colours of equal size (green, red, yellow, blue) for
each of four different body parts.
Calculate the following :
(Show all calculations by applying the appropriate probability principles)
a) Probability that a spin ends on either Red or RIGHT HAND.
[T/2]
b) Probability that a spin does not land on a FOOT.
[T/2]
c) Probability that a spin lands on Green, given that it is also on the LEFT FOOT.
[T/2]
d) Probability that 3 consecutive spins results in Hand, Yellow , Yellow (in that order).
[T/2]
FINAL EXAMINATION/MDM 4U – Dec 2015
Page 8
26.
A game is played by drawing cards from a deck that has no face cards and no aces.
The player draws a card and is paid the face value of the card in RM.
a) Complete the Probability Distribution Table below for all possible winnings (X)
in RM.
[A/3]
X
(Winnings)
P(X)
b) Each play costs RM 5.00. How much would you expect to win or lose if you played
the game 20 times?
[A/3]
(Note: Remember to complete the multiple choice answer sheet on the next page)
*****
FINAL EXAMINATION/MDM 4U – Dec 2015
END OF PAPER
****
Page 9
FORMULA SHEET
Unit 1
1-variable
σ =
Ʃ (x-μ)2
Statistics
Ʃ (x-x)2
Sx =
N
N–1
Unit 2
Bi-variate
Statistics
r =
nƩxy – (Ʃx)(Ʃy)
[nƩx2- (Ʃx)2] - [nƩy2- (Ʃy)2]
P( A) 
n( A)
n( S )
P( A)  1  P( A' )
P( A  B)  P( A)  P( B)
Unit 3
Probability
P( A | B) 
or
P( A  B)
P( B)
or P( B | A) 
P( A  B)  P( A)  P( B)
Pn, r  
P( A  B)  P( A)  P( B)  P( A  B)
P( A  B)
P( A)
or P( A  B)  P( A | B)  P( B)
 n
n!
  
 r  ( n  r )! r!
n!
(n  r )!
n!  n  ( n  1)  ( n  2 )  ......  3  2  1
Unit 4
Normal
Distribution
z
xx
s
z
or
x

( X )   xp ( x)
Probability
x
Distribution
n
P( X  x)    p x q n  x
 x
FINAL EXAMINATION/MDM 4U – Dec 2015
( X )  np
Page 10