## SPM Form 5 Add Maths Project 2010 - Tugasan 2

### SPM Form 5 Add Maths Project 2010 - Tugasan 2

Notes: The Complete answer is available in the Premium Discussion Board. Register as a user now to see the full answer.(Registration is Free)

The purpose I create this post is for student to discuss their add math project. Copying is not encouraged. Just use the information here as a reference and then complete the work by yourself. Don't waste your time to email or personal message me to request for answer because I will not reply any such email.

Add Math Project 2010 Tugasan 1
Add Math Project 2010 Tugasan 2
Add Math Project 2010 Tugasan 3
Add Math Project 2010 Tugasan 4

I think they may provide answer as well later.

Discussion for other tugasan.
Tugasan 1, Tugasan 2, Tugasan 3, Tugasan 4
Last edited by sekqy on Wed Jun 23, 2010 4:27 pm, edited 4 times in total.
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

I just found 2 very useful "rolling dice applet" in the internet. Just in case you don't have dice at home, you can use these digital dice to do your experiment.

http://www-cs-students.stanford.edu/~nick/settlers/
http://leepoint.net/notes-java/examples ... ldice.html
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

Reminder: This is only a guide but not the complete answer. You should try to complete the project by yourself

Part 1
(a) Ok, this is about history of probability and its applications. There are tonnes of internet web page discussing about this topic, so I think this shouldn't be any problem to you all, right?

(b) This is about theoretical and empirical probability. There are also tonnes of discussion in internet. So, just Google it. Basically, theoretical knowledge means knowledge that you obtain through your thinking, while empirical knowledge is knowledge obtain through your experience and experiments.

Part 2
(a) {1,2,3,4,5,6}
(b)

Chart
Click on the image to expand
chart.png (28.89 KiB) Viewed 43653 times

Table
table.png (24.27 KiB) Viewed 43653 times

Tree Diagram
Click on the image to expand
tree.png (40.52 KiB) Viewed 43653 times

Total Outcome
{ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
Last edited by sekqy on Fri Jun 04, 2010 11:24 pm, edited 1 time in total.
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

Part 3
(a)
Click on the image to expand
table2.png (67.64 KiB) Viewed 43646 times

(b)
A = { (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),}

The proposed answer is corrected on 11.55am 15/6/2010. The outcome (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6) was deleted from the list.

B = ø

P = Both number are prime
P = {(2,2), (2,3), (2,5), (3,2), (3,3), (3,5), (5,2), (5,3), (5,5)}

Q = Difference of 2 number is odd
Q = { (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5) }

C = P U Q
C = {1,2), (1,4), (1,6), (2,1), (2,2), (2,3), (2,5), (3,2), (3,3), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,5) }

R = The sum of 2 numbers are even
R = {(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,4), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2(, (6,4), (6,6)}

D = P ∩ R
D = {(2,2), (3,3), (3,5), (5,3), (5,5)}

The proposed answer above is corrected on 8.52pm 21/6/2010. The outcome (3,2) and (5,2) are added to set P and the outcome (3,5) is added to set R.
Last edited by sekqy on Mon Jun 21, 2010 11:23 pm, edited 1 time in total.
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

Part 4 (a)
In this case, you need to toss dice and record your result in the table. Just in case you don't have dice at home, you can use these digital dice to do your experiment.

http://www-cs-students.stanford.edu/~nick/settlers/
http://leepoint.net/notes-java/examples ... ldice.html

The following are the data I obtained. You should do your experiment and collect your own data. Everybody should have different set of data.

table3.png (32.67 KiB) Viewed 43640 times

From the table,
\sum {f = 50}

\sum {fx = 329}

\sum {f{x^2} = 2467}

(i)
Mean = \bar x = \frac{{\sum {fx} }}{{\sum f }} = \frac{{329}}{{50}} = 6.28

(ii)
\begin{array}{l} Variance,{\sigma ^2} = \frac{{\sum {f{x^2}} }}{{\sum f }} - {{\bar x}^2} \\   = \frac{{2467}}{{50}} - {6.58^2} \\   = 6.0436 \\  \end{array}

(iii)
\begin{array}{l} {\rm{Standard Deviation}} = \sqrt {\frac{{\sum {f{x^2}} }}{{\sum f }} - {{\bar x}^2}}  \\   = \sqrt {\frac{{2467}}{{50}} - {{6.58}^2}}  \\   = 2.458 \\  \end{array}
Last edited by sekqy on Fri Jun 04, 2010 11:23 pm, edited 1 time in total.
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

Notes: The Complete answer is available in the Premium Discussion Board. Register as a user now to see the full answer.(Registration is Free)
sekqy

Posts: 52
Joined: Mon May 31, 2010 8:45 am

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

any1 know how to do further exploration???
siow11

Posts: 1
Joined: Mon Jun 14, 2010 4:40 pm

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

sekqy wrote:Notes: The Complete answer is available in the Premium Discussion Board. Register as a user now to see the full answer.(Registration is Free)

The purpose I create this post is for student to discuss their add math project. Copying is not encouraged. Just use the information here as a reference and then complete the work by yourself. Don't waste your time to email or personal message me to request for answer because I will not reply any such email.

Add Math Project 2010 Tugasan 1
Add Math Project 2010 Tugasan 2
Add Math Project 2010 Tugasan 3
Add Math Project 2010 Tugasan 4

I think they may provide answer as well later.

Discussion for other tugasan.
Tugasan 1, Tugasan 2, Tugasan 3, Tugasan 4
kokilavani manimaran

Posts: 1
Joined: Fri Jun 25, 2010 8:46 pm

### Re: SPM Form 5 Add Maths Project 2010 - Tugasan 2

how do you do the reflection???
cynthia93

Posts: 2
Joined: Wed Jun 09, 2010 11:24 am