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FINAL EXAMINATION/MDM 4U – June 2016

Canadian International Matriculation Programme

Mathematics of Data Management (MDM4U)

FINAL EXAMINATION Date: 6 June, 2016 (Monday) Time: 2.30p.m – 4.30p.m Length: 2 HOURS

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 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 CONTENT MARKS TIME ALLOCATION

A Multiple Choice 15 20 MINS

B Short Answer 27 30 MINS

C Problem 48 70 MINS

TOTAL 90 120 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 or as mentioned in the question . 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 Part C Total Communication (Refer Last page)

GC


PART B Short Answer [27 marks] [Knowledge: 5 marks, Application: 15 marks; Inquiry/Thinking: 7 marks] Show your working in the space provided.

16. A student has prepared a probability distribution graph. The random variable X is the number of vehicles in every household at a certain housing area. It is however incomplete as it does not show the probability for X=4. .

a) Complete the graph below by filling in the probability for X=4. Show your work.

[K- 2 marks]

b) What is the expected number of cars in each household at this housing area? Show your work.

[A- 2 marks]

17. The following is the ages of participants in an environmental survey.

Find the median and the IQR for the above distribution? Show your work.

[K- 3 marks]

STEM LEAF

1 1 3 6 7

2 2 2 8 8 9

3 1 3 4 5 5 6 9

4 4 5 7 8

5

6 0

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1 2 3 4 5

P(X)

No. vehicles in household


18. A researcher wants to study if the weather has any connection on the number of dengue fever cases. He recorded the number of rainy days together with the number of dengue cases reported in various districts in Malaysia, for the month of January.

No days of rain

No. Dengue cases reported

10 241

17 173

18 53

8 166

17 110

27 85

What is the relationship between the number of days of rain and the number of Dengue cases reported? Justify using mathematical evidence. You may use your graphing calculator for this question. [A- 3 marks]

19. 400 students are enrolled at various grades in a high school as shown in the table below.

If the school has RM 20,000 to spend on class activities, how much should be allocated to Grade 12, if the money is distributed according to the enrolment numbers. [A-3 marks]

GC

Grade 9 (96o)

Grade 10 (79o)

Grade 11 (83o)

Grade 12

Enrolment at a High School


20. Several people were asked to view a picture for a certain length of time. They were then asked several questions based on the picture. If they answered more than half of the questions correctly, they passed. The results are given in the following graph.

a) Prepare a Frequency table to show the number of failures for the respective times taken to

view the pictures. [I-3 marks]

b) In total, how many people failed the memory test? [A- 1 mark]


21. A Rock Band has 8 members; 5 boys and 3 girls. A team of 5 members will be formed to play for a performance. What is the probability that at least 2 girls are selected to form this team? You may use your graphing calculator. [A-3 marks]

22. 100 students in a school participated in a survey on their interest in music. Of those, 60 listen

to rock music, 20 listen to pop music, and 10 listen to both types of music. Determine the probability that a student listens to pop music, if it is known that he/she does listen to rock music. (Note: Show the use of the appropriate formula) [A-3 mark]

23. Angelina wants to enter “CIMP’s got talent” contest. At the audition, she is scored based on the following criteria.

Category Weighting Marks

Originality 3 58

Costume 1 63

Personality 2 84

Presentation 4 90

In order to qualify for the semi-finals, Angelina needs a minimum overall score of 80.

Will Angelina be eligible to for the semi-finals? Show your work and justify your answer using mathematical evidence. [I-4 marks]


PART C Problem [48 marks] [Knowledge: 2 marks; Application: 24 marks; Inquiry/Thinking: 22 marks]

Show your complete working in the space provided.

24. Bob and Stuart are competing for the “Employee of the year” award. The winner will be based

on the minion who has achieved a more consistent sales record in the year 2015. Their sales (in RM) are recorded as follows: You may use your graphing calculator for this question.

Month 1 2 3 4 5 6 7 8 9 10 11 12

Bob 1890 988 1522 1423 1811 1444 1248 1268 1555 1625 1700 1927

Stuart 2540 1020 1380 950 1248 1650 1230 2010 1230 1823 1570 2020

a) What is the mean sales achieved by each minion (to 2 decimal places)?

[A-2 marks] Bob : _____________ Stuart : ____________

b) What is the standard deviation for each of the distributions (to 2 decimal places)? Bob : _____________ Stuart : ____________ [A-2 marks]

c) Use one of the above measures to explain who will win the award. [I-2 marks]

d) Create a Box and Whisker Plot to show the spread of Bob’s Sales. (Clearly label the

names of the 5 key summary points, together with their respective values) [A- 5 marks]

GC

AND THE WINNER IS…


25. Human blood can contain either no antigen, the A-antigen, the B-antigen or both the A and B antigen. A third antigen, called the Rh antigen is important in human reproduction, and again may or may not be present in an individual. In a certain hospital, 120 patients were tested and the following data recorded:

25 patients had the A-antigen; 17 had the A and B antigens; 27 had the B-antigen; 22 had the B and Rh antigens; 12 had none of the antigens; 16 had the A and Rh antigens; and 15 had all three antigens

a) Draw a Venn diagram and use the given information to fill in the number of elements for each region. (Hint: Use 3 sets labeled A, B and Rh). [A-4 marks]

b) How many of these patients had exactly 1 antigen? [I-2 marks]

c) Find P(A U Rh)’ by applying the relevant probability formula. [I- 3 marks]


26. When writing an exam, Bart Simpson needs confidence to do well. The probability that he will get the first problem correct is 75%. When Bart Simpson gets a problem wrong, the likelihood of him answering the next question correctly decreases by 25%. If he answers a previous problem correctly, the likelihood of him answering the next question increases by 10%. This trend continues every following question.

a) Draw a tree diagram to represent Bart Simpson’s first 2 questions on his exam. Remember

to show the probabilities for all possible outcomes. [I- 4 marks] b) What is the probability that Bart Simpson answers both questions correctly or that both

answers are incorrect? [A-2 marks]


27. Joe and Tyson have been competing against each other in the 200m race for some years. The following table shows some of the best times they have achieved in several races from years 2001 to 2009. (**Note that the years for both runners are different)

a) Identify the Independent Variable. Briefly explain why. [I-2 marks]

b) State the equation for Joe’s timing using linear regression (4 decimal places) [K-1 mark]

c) State the equation for Tyson’s timing using quadratic regression (4 decimal places)

[K-1 mark]

d) Compare the regressions in (b) and (c) above. Which one seems to provide a more accurate fit to the data? Justify using mathematical evidence [I-3 marks]

e) By using the quadratic regression, estimate the time taken for Tyson to run the 200m

race in 2010. [A-2 marks]

f) Both runners recorded the same timing during the same year, twice in between 2000 to

2010. Using the regressions created in part (a) and (b), find the 2 years that this happened and time taken to complete the 200m race respectively. [I-4 marks]

Joe’s timing Tyson’s timing

Year Time (sec) Year Time (sec)

2002 20.61 2001 21.2

2003 20.4 2002 20.2

2004 20.5 2004 19.95

2005 20.03 2005 19.65

2006 19.96 2005 19.8

2007 19.91 2006 19.7

2008 19.3 2007 19.75

2009 19.19 2009 19.6

GC


28. Kim plans to visit her neighbors to sell her home baked cheese cakes to raise funds for the Nepal School Building Fund. There is a 0.28 probability that someone will buy her cakes. Kim plans to meet 4 neighbors this weekend.

a) Complete the Probability Distribution table for the number of neighbors who will purchase her cakes. Show your work (use 4 decimal places) [A-5 marks]

X No. Neighbors

P(X)

b) What is the probability that at least 1 neighbor will purchase the cheese cakes?

[I-2 marks]

c) Kim plans to meet 50 neighbors this month. If the price per cake is RM 65, how much can she expect to raise for the Nepal School Building Fund? [A- 2 marks]

(Note: Remember to complete the multiple choice answer sheet on the next page)

***** END OF PAPER ****


MULTIPLE CHOICE ANSWER SHEET

NAME : PERIOD : __ Answer all multiple choice questions on this sheet

1.

2.

3.

4.

5.

6. 7. 8. 9. 10.

11.

12.

13.

14.

15.


FORMULA SHEET

Unit 3

Probability

)(

)()(

Sn

AnAP

)'(1)( APAP

)()()( BPAPBAP or )()()()( BAPBPAPBAP

)(

)()|(

BP

BAPBAP

or

)(

)()|(

AP

BAPABP

)()()( BPAPBAP or )()|()( BPBAPBAP

)!(

!,

rn

nrnPP rn

!)!(

!

rrn

n

r

nCrn

123......)2()1(! nnnn

Unit 4 Normal Distribution

Probability

Distribution

s

xxz

or

xz

x

xxpX )()(

xnxqpx

nxXP

)(

npX )(

Communication Rubric

Criteria

Below

Level 1

Level 1

Level 2

Level 3

Level 4

The student organizes and expresses

their mathematical thinking and

ideas…

poorly or

not at all

with limited

effectiveness

with some

effectiveness

with

considerable

effectiveness

with a high

degree of

effectiveness

The student uses mathematical

conventions, vocabulary, symbols,

labels, units and terminology…

poorly or

not at all

with limited

effectiveness

with some

effectiveness

with

considerable

effectiveness

with a high

degree of

effectiveness

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