A Project in
Next Century Mathematics
“Advanced Algebra, Trigonometry,
and Statistics”

Michael Roy Lansang

Immanuel C. Canoy
Mathematics 10 Teacher

1.1 Reviewing the Cartesian Coordinate Plane

Math FYI
The words, functions, coordinate, abscissa, and ordinate, as now use in mathematics, were introduce by Gottfried Wilhelm Leibniz (1646-1716) of Germany. Leibniz was the great genius of the 17th century. He was also Newton’s rival in the invention of the calculus.

1.2 Relation

Math FYI
The 14th century was a mathematically barren one. Inclusive of this century was the hundred years’ war and black death which killed more than 1/3 of Europe’s population. However, mathematics during this period did not entirely die out. The greatest mathematician of this period was Nicole Oresme (1323-1282) of Normandy. He wrote five mathematical works. In one of this appears the process of locating points by coordinates, which foreshadowed modern coordinate geometry.

1.3 Function

Math FYI
The conventionalization of the functional notation f(x) was contributed by Leonhard Euler of Switzerland.

1.4 Graphs of Functions

Math FYI
The word function was first introduced by Leibniz in 1694 to denote any quantity connected with a curve. In 1718, Johann Bernoulli regarded function as any expression made up of variables and constants. Later Leonhard Euler (1707-1783) considered function as any equation and formula. But it was Lejeune Dirichlet (1805-1859) who first associated the concept of correspondence in the definition of function.

1.5 Operations with Functions

Math FYI
A “chain” process of combining two relations in a given order to produce composite relation is called composition of relations. For instance, the relation “is the mother of” and the relation “is the father of” yield the composite relation “is the mother of the father of,” that is, “ is the paternal grandmother of”....

...
Final Project: Nyke Shoe Company
Barbara Greczyn
STA 201 - Principles of Statistics
Instructor Alok Dihtal
April 26, 2015
Introduction
Nyke Shoe Company has been in business for over 50 years. Over the last five years, the company has been undergoing some financial hardship due to an erratic market and an inability to understand what the consumer actually needs. In a last ditch effort to avoid bankruptcy, they have adopted a new business model which entails the development of only one shoe size. In order to achieve this goal, statistical data must be utilized and applied to make the best choice. The data used will be explained to the fullest and a conclusion will be then obtained.
Methodology
A sample group of 35 participants was gathered, 18 females and 17 males. Their heights and shoe sizes were gathered and their data was processed in three categories: shoe size, height, gender. Descriptive statistics was applied to three separate data sets, one with all participants included, one sets with just female participants, and one with just male participants. Then a two sample t-test was conducted with the assumption that there were unequal variances amongst both male and female data sets.
Results
There is a normal distribution of the data with ranges in size from size 5 to size 14 amongst the participants. With these ranges, the mean is 9.142, with a standard deviation of 2.583 and a variance...

...~TUDENTIDNO
FIRST TRIMESTER EXAMINATION, ZOO+2005 SESSION
PMT 0045 - IT MATHEMATICS 1
( Alpha Information Technology studdnts only )
17 AUGUST 2004
9.00 a.m - 11 .OO a.m
( 2 Hours )
INSTRUCTIONS TO STUDENT
1. This Question paper consists of 4 pages excluding the qover page and formula sheet.
2. Answer FOUR out of FIVE questions.
3. Please print all your answers in the Answer Booklet prcivided. All necessary working
MUST be shown.
Instruction: Answer FOUR questions only.
1 uestion
O
(a) Verify the identity
:
(b) Find the exact value of
cscB-sinB =cotBcosB.
.
(
3 marks )
(
3 marks )
(c) If cosA =f with A in Quadrant I and cosB = i with B in Quadrant IV, find the
exact value of
0
cos(A + B)
ii)
sin 23
iii)
sin2
A
( 9 marks )
(d) Solve the equation 2 cos2 x - 1 lcosx = -5,
0 < x c 27~
( 5 marks )
Continued.......
NilLCY/GWW
l/4
17 AUGUST 2004
IT MATHEMATICS I
PMT 0045
Ouestion 2:
(a) Solve A ABC, given a = 22 meters, b = 12 meters and A = 41’. Find the remaining
side and angles by using Law of Sines. Give your answer id two decimal places.
( 7 marks )
(b) Find the remaining angles and side of triangle below. Give tour answer in two
decimal places.
( 6 marks )
ii)
Convert from polar to rectangular coordinate for
( 7 marks )
Continued..
NIILCYIGWW
214
I
.....
Question 3:
(a) Find the equation of the...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed...

...138 | 0.167 | 0.173 | 0.205 |
| | | | | | | | | | |
| | | | | | | | | | |
-------------------------------------------------
Top of Form
For this project, I compared the sugar content of equal serving sizes of 10 various breakfast cereals. Since serving sizes varied from brand to brand, the results were computed based on a serving size equal to 50 grams. The sugar content per 50 gram serving size was computed by using the following formula:
50 grams = Serving size to be compared
(50 x Sugar per serving) / Serving Size
Example: (50 * 1) / 30 = 1.67g of sugar per 50.00g serving
A histogram was created using a bar chart to display the sugar content per 50 gram serving size of the various cereals. The raw data (sugar content and serving size) was obtained from the nutritional content label located on the side of each box of cereal.
Median: The median is 11.82 grams of sugar per serving. (7.5+16.13=23.63/2)
Sample Mean: 13.50 grams of sugar per serving (134.96/10= sum of the sugars, divided by the sample size)
Range: 26.18 (27.78-1.6) Difference between the maximum and minimum
Sample Variance: 86.49866667 (Calculation shown on the next page: used a spreadsheet and pasted into the document)
Sample Standard Deviation: 9.300465938 (Calculation shown on the next page: used a spreadsheet and pasted into the document)
Data Set: 1.6 5.17 6.0 6.03 7.5 16.13 18.73 22.58 23.44 27.78
Mode: Since...

...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These well-defined geometric relationships can be useful when teaching GCSE-level students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle and the
length of the sides are observables, and the functions
that connect them are the definitions. These welldefined geometric relationships can be useful when
teaching GCSE-level students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a
better understanding...

...Dani Socher
StatisticsProject
Mr. Seufer
1/15/2013
Shooting Guards and Field Goal Percentage
In the NBA, games are won by shooting the ball well, which makes sense. The more times your team’s players get the ball in the hoop, the more points are scored. And the more points scored, the more games won. Obviously, it is a little more complicated than that in reality, given how important defense is. But field goal percentage should be a solid indicator of games won. Field goal percentage is as simple as made shots divided by shot attempts. Once we discover if field goal percentage indicates team success, we should then examine how teams can choose players in the draft with higher field goal percentages; better shooters. We will be focusing on shooting guards, as they are the players who shoot unassisted the most.
To start, a scatterplot searching for the correlation between winning percentage of NBA teams so far in 2012-2013, and the NBA team field goal percentages.
Win%
Win%
FG%
FG%
There is a fairly strong positive correlation, as can be seen from the scatterplot. The correlation coefficient, or R, should be examined to confirm what the eye test tells us.
R = .638
.638 shows a fairly strong positive correlation, as it is close to 1.
It is clear that a higher field goal percentage means your team has a much better shot at finishing with a good winning percentage, although it is not a perfect rule.
With this knowledge, one would...

...because it gives me headache and it always irritates and annoys me especially when it comes in solving equations and problems. And I need to deal and associate mathematics with the experience of terrible and strict teachers. I just hate the fact that some of my math teachers were too strict that cause me to hate them and their subject. But, now that I am older, however, I need mathematics because I also have a growing curiosity and interest for it. And it’s even part of our daily activities in life and other. Despite of, hating mathematics I still have to manage to learn more about mathematics and love it as well.
Experiences? There are many experiences that I encounter in learning mathematics. Mathematics is a challenging subject for me as being a senior high school student because it’s one of the major subjects in the academic curriculum in the High School Department. And based on my experiences, I have a fear in the back of my mind that my knowledge and understanding of mathematics is not sufficient enough. I also seem to have some problem grasping even the simplest mathematic questions, problems and equations. But now that I am a Senior high school student I promised to myself that I will conquer my fear in mathematics and educate myself. First meeting in Algebra class, Sir Cenita asks us if what...

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