– 6 – MATME/PF/M11/N11/M12/N12
For final assessment in 2011 and 2012
STELLAR NUMBERS SL TYPE I
Aim: In this task you will consider geometric shapes which lead to special numbers. The simplest example of these are square numbers, 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3 and 4. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1,3,6,)…. 1 3 6 10 15

Complete the triangular numbers sequence with three more terms. Find a general statement that represents the nth triangular number in terms of n. Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The first four representations for a star with six vertices are shown in the four stages S1–S4 below. The 6-stellar number at each stage is the total number of dots in the diagram. S1 S2 S3 S4

Find the number of dots (i.e. the stellar number) in each stage up to S6. Organize the data so that you can recognize and describe any patterns. Find an expression for the 6-stellar number at stage S7.

Find a general statement for the 6-stellar number at stage Sn in terms of n. Now repeat the steps above for other values of p.
Hence, produce the general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at stage Sn. Test the validity of the general statement.
Discuss the scope or limitations of the general statement.
Explain how you arrived at the general statement.

...Introduction: In this following assignment, I will be considering geometric shapes that lead to special numbers. The simplest examples of these are square numbers (1, 4, 9, 16, etc), which are derived from squaring 1, 2, 3, and 4. From this I got the equation y= x2. This equation is illustrated in the table below.
y=x2
|x |y |
|1 |1 |
|2 |4 |
|3 |9 |
|4 |16 |
In the table on the left, I observe that from the y value 1 to the y value 4 there is an increase of 3. From the y values 4 to 9, there is an increase of 5. From the y values 9 to 16, there is an increase of 7. This shows that it goes: +3, +5, +7, which is then increasing by 2 between each of those numbers.
Below, is the graph of y=x2
[pic]
The equation y=x2 comes from the general equation y= ax2-bx+c.
Y=x2 is the same as y=x2+0x+0. Therefore, a=1, b=0, and c=0.
The next example I am going to show you is similar to the one above. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1, 3, 6, 10, 15, 21, 28, 36).
|Tn |y |
|1 |1...

...
StellarNumbers
Results
1. Triangular Numbers
Observation of the number pattern of polynomial type or different pattern needed.
Identifying the order of the general term by using the difference between the succeeding numbers.
Students are expected to use mathematical way of deriving the general term for the sequence.
Students are expected use technology GDC to generate the 7th and 8th terms also can use other graphic packages to find the general pattern to support their result
The general term in this stage is
2. 6- stellarnumbers
Stage
No of dots
1
1
2
13
3
37
4
73
5
121
6
181
Students are expected to make the stellar shape for the next to stages and count the no of dots to get the 6-stellarnumber in 5th and 6th stage
Diagrams can be hand made or using technology
Communication or observation of the number pattern has to be given
From the observation, the expression of the terms of this sequence has to be identified
Expression for the 7th term
General expression 6 – stellar shape
or
p n (n-1) +1
Other stellar shapes – based on the no of vertices the students choose...

...The aim of this task is to investigate geometric shapes, which lead to special numbers. The simplest example of these are square numbers, such as 1, 4, 9, 16, which can be represented by squares of side 1, 2, 3, and 4.
Triangular numbers are defined as “the number of dots in an equilateral triangle uniformly filled with dots”. The sequence of triangular numbers are derived from all natural numbers and zero, if the following number is always added to the previous as shown below, a triangular number will always be the outcome:
1 = 1
2 + 1 = 3
3 + (2 + 1) = 6
4 + (1 + 2 + 3) = 10
5 + (1 + 2 + 3 + 4) = 15
Moreover, triangular numbers can be seen in other mathematical theories, such as Pascal’s triangle, as shown in the diagram below. The triangular numbers are found in the third diagonal, as highlighted in red.
The first diagrams to be considered show a triangular pattern of evenly spaced dots, and the number of dots within each diagram represents a triangular number.
Thereafter, the sequence was to be developed into the next three terms as shown below.
The information from the diagrams above is represented in the table below.
Term Number (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Triangular Number (Tn) | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 |
Establishing...

...think everybody knows. It are the following 10 things:
1. If you want to scroll down on the internet, don’t go with your mouse on the slider, a waste of time. Use the spacebar. With the spacebar you will scroll down one page.
2. If you enter an address form on the internet. In the pop-up menu to fill in your province, don’t open it, its a waste of time. Type the first letter of your province and you will find it in 1 second.
3. Also on the Internet if the text is too small, use the CTRL + plus button.
4. If you type something on your iPhone, don’t go to your text keys to the number keys to enter the space and then the capital. Press two times just into the spacebar. The phone will then keep the point or capital self.
5. If you want to repeat your last call, push the call button and the most recently number is coming on your screen. And if you push again, the number is calling.
6. Bij ? leaving a massage on a voicemail. After: “leave a massage”. There coming fifteen other difficult (verrekte) instructions. There is one button, waarmee je direct nar de piep kunt springen. He is telling that’s in the most of time hash on your mobile, but you have to fin it out for yourself.
7. With Google you could find more than only a website. It’s a dictionary, flight database and also a calculator.
8. If you want to select a word in your word document, ga niet als een groentje (nubie) met je muis erover slepen....

...PORTFOLIO
{draw:frame}
William Yohanes Numberi
01120090183
Faculty of Economic
Management
2009
Daftar Isi
Cover depan…………………………………………………………………………..1
Daftar isi…………………………………………………………………………………2
Kata pengantar……………………………………………………………………….3
Bab I……………………………………………………………………………………….4
-Mengenal diri sebagai pembelajar
Bab II………………………………………………………………………………………6
-Kegiatan perkuliahan
-Rangkuman
-Strategi belajar
Bab III…………………………………………………………………………………….13
-Time management
Bab IV…………………………………………………………………………………….18
-Kesimpulan Akhir
Daftar pustaka……………………………………………………………………….19
Lampiran……………………………………………………………………………….20
Kata Pengantar
Portfolio ini dibuat dengan tujuan agar apabila kita menjadi pemimpin, kita dapat melaksanakan tugas kita dengan baik dan dapat menjadi pemimpin yang baik dan bijaksana.
Demikian portfolio ini saya buat semoga kita dapat menjadi lebih baik lagi dan mencapai hal-hal yang lebih produktif.
BAB I
Mengenal diri sebagai pembelajar
{draw:frame}
BAB II
Kegiatan Perkuliahan
Leadership
Tanggal : 14 Januari 2010
Pertemuan : 1
Topik pembahasan : Pengenalan tentang leadership
Situasi kelas : Tertib
Rangkuman
Perkenalan antara dosen dan mahasiswa dan penjelasan tentang tata tertib kelas leadership dan bahan – bahan yang akan dipelajari.
Dosen akan menerangkan bahan – bahan materi dalam leadership dan bahan – bahan yang...

...raster overlay techniques to find the areas where sand AND vegetation are present. Note that you need to provide the final result of the raster overlay process as well as a legend explaining the result. After you have provided the result, explain the importance of selecting the appropriate operator when working with raster overlay. [5 marks]
Figure 5
4.4
A police department claims that 127 (80%) of minor crimes have occurred within 182 meters of parks. You are given a digital map in a GIS (Figure 6) showing locations of crime incidences and parks within each district in Kagera municipality.
Figure 6: Crime incidences from parks within Kagera municipality.
4.4.1
Explain any spatial operations you would use to confirm or identify the number of crime points within 182 metres of parks. (2 marks)
4.4.2
Explain any spatial operations or queries you would use to identify the distance between the furthest crime points to the park within the Bukoba District. (1.5 marks)
4.4.3
Describe how you would illustrate district areas of high crime incidences from the least incidences and explain the type of map you will use. (1.5 marks)
Question 5 [ 20 marks]
Figure 7: Earthquake events in 2009
On 3 September 2009 a magnitude 5.1 earthquake struck Khorixas, Namibia. The quake originated at a moderate depth of 10 kilometres. Buildings were damaged and the earthquake was felt over a wide area.
5.1 Describe the technique you would use to find Khorixas from the table...

...
Portfolio Assignment
SUS1501 – Sustainability and Greed
Student Name: Shitlhangu Mercy Tsakani
Student Number: 40525007
Date: 2014.05.06
Teaching Assistant Name: S GEORGE
Declaration:
By submitting this portfolio, I implicitly declare that this is my own work except for the “Introduction” which was kindly written for me by my lecturer.
Introduction
My aim in compiling this portfolio was to reflect on the things that have struck me throughout this crazy module.
My starting point for doing this was to revisit my opinions to the multiple choice questions which were presented in the Crossroads assignment. I present these current opinions, together with my original opinions, and some brief notes in the section entitled: “Back at the Crossroads!”
Once I have done this, I draw some key conclusions about this crazy module and about the things that did indeed strike me.
Back at the Crossroads!
1. “The assets of the three richest people in the world match the combined annual GDP’s of the 48 poorest countries.” My personal opinion on this statement is most closely described by:
a. Good for them – they worked hard to get their wealth
b. The only problem I have with this is that this money is in their bank account and not in mine
c. No problem with this – many of these people give huge amounts to charities
d. I think that it is morally wrong for anyone to have that...

...The numbers are overwhelming: Over the next 17 years, 350 million rural residents (more than the entire U.S. population today) will leave the farm and move to China’s cities. That will bring the Chinese urban population from just under 600 million today to close to 1 billion, changing China into a country where more than two-thirds of its people are city dwellers, says Jonathan Woetzel, a director in McKinsey’s Shanghai office. The change will reverse China’s centuries-old identity as a largely rural country. Thirty years ago, when China started modernizing its economy, more than 80% of Chinese lived in the countryside. And just six years ago it still was about 60%. Today China is just under 50% urban.
The newly urbanized population will live in eight megacities, those with a population of more than 10 million, as well 15 big cities with populations between 5 million and 10 million. In addition, by 2025 China will probably have at least 221 cities with a population over 1 million, estimates Woetzel. That compares with 35 cities of that scale across all of Europe today. These new urbanites are expected to be a powerful booster of growth: Urban consumption as a share of gross domestic product will most likely rise from 25% today to roughly 33% by 2025. “Urbanization is the engine of the Chinese economy—it is what has driven productivity growth over the last 20 years,” says Woetzel. “And China has the potential to keep doing this for the next 20 years.”...