– 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...

...
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...

...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...

...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...

...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...

...(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)...

...
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...

...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...