Distance between two points ( x1 , y1 , z1 ) and ( x2 , y2 , z2 ) Coordinates of the midpoint of a line segment with endpoints ( x1 , y1 , z1 ) and ( x2 , y2 , z2 )
x1 + x2 y1 + y2 z1 + z2 , , 2 2 2
Mathematics SL formula booklet
2
Topics
Topic 1—Algebra
1.1 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence The nth term of a geometric sequence un = u1 + (n − 1)d
S n=
n n (2u1 + (n − 1)d ) = (u1 + un ) 2 2
un = u1r n −1
The sum of n terms of a u1 (r n − 1) u (1 − r n ) , r ≠1 = = 1 Sn finite geometric sequence r −1 1− r The sum of an infinite geometric sequence 1.2 Exponents and logarithms Laws of logarithms S∞ = u1 , r 0
− cos ∫ sin x dx = x + C = ∫ cos x dx sin x + C
∫e
6.5 Area under a curve between x = a and x = b
x
d= e x + C x
b
A = ∫ y dx
a
b Volume of revolution V = ∫ πy 2 dx a about the xaxis from x = a to...
...Jonghyun Choe
March 25 2011
MathIBSL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 1
1 1
Row 2
1 32 1
Row 3
1 64 64 1
Row 4
1 107 106 107 1
Row 5
1 1511 159 159 1511 1
Step 1: This pattern is known as Lascap’s Fractions. En(r) will be used to represent the values involved in the pattern. r represents the element number, starting at r=0, and n represents the row number starting at n=1. So for instance, E52=159, the second element on the fifth row. Additionally, N will represent the value of the numerator and D value of the denominator.
To begin with, it is clear that in order to obtain a general statement for the pattern, two different statements will be needed to combine to form one final statement. This means that there will be two different...
...IB Mathematics SL Year 1
Welcome to IB Mathematics. This twoyear course is designed for students who have a strong foundation in basic mathematical concepts. The topics covered in this course include:
* Algebra
* Functions
* Equations
* Circular functions
* Trigonometry
* Vectors
* Statistics
* Probability
* Calculus

Resources:
* Textbook: Mathematics SL 3rd edition. Haese Mathematics 2012
ISBN: 9781921972089
* Edmodo: A virtual learning website where students can get homework assignments, ask homework questions, access class documents, and communicate with peers. https://iam.edmodo.com/
* Class code: ybu2s4
* Quest: Virtual learning website where students will complete graded homework assignments. https://quest.cns.utexas.edu/
* Graphing Calculator. Recommended for this course and all subsequent math courses. The TiNspire or Ti84 plus silver edition are both good choices. http://education.ti.com
* Khan Academy: http://www.khanacademy.org. Will be used to provide students with alternative resources.
* Geometer’s Sketchpad: Graphing software. Will be installed on student computers. http://www.dynamicgeometry.com/
* Additional print, online resources and worksheets may be used.

Assignments:
There...
...Alma Guadalupe Luna
Math IA (SL TYPE1)
Circles
Circles
Introduction
The objective of this task is to explore the relationship between the positions of points within circles that intersect.
The first figure illustrates circle C1 with radius r, centre O, and any point P. r is the distance between the centre O and any point (such as A) of circle C1.
Figure 1
The second diagram shows circle C2 with radius OP and centre P, as well as circle C3 with radius r and centre A. An intersection between C1 and C2 is marked by point A. The intersection of C3 with OP is marked by point P’.
Figure 2
Through this investigation I will examine how the r values correlate with the values of OP in determining the length of OP’ when r is held as a constant variable and the value of OP is the variable that is subject to change. I will then venture on to study the inverse, the relationship when the r values becomes the variable that is changed and the OP value is held constant.
r as a Constant
If we let the value of r be equal to 1, we can use that information to find the length of OP’ when OP=2, 3, and 4. The first thing one can deduce is that by using the points A, O, P’, and P two isosceles triangles can be formed; ∆AOP and ∆AOP’. To rationalize this assertion through an analytic approach it should first be understood that all line...
...MathSL Portfolio – Tips and Reminders Checklist
Notation and Terminology
Check for the following:
• I did not use calculator notation. (I didn’t include things like ‘x^2’ for or Sn for Sn)
• I used appropriate mathematical vocabulary.
Communication
Check for the following:
• The reader will not need to refer to the list of questions in order to understand my work.
• My responses are not numbered.
• I have an introduction, conclusion, title page, and table of contents.
• All graphs are labeled – Each graph has a title, labeled axes, and appropriate scale.
• My graphs and tables are within the body of my work. They are not separate or in an appendix.
• I have explained why I made the choices I did when going through the task.
• I did not include key stroke sequences, e.g. “I pressed the 2nd key, then TRACE…”
• My tables do not straddle pages.
• My tables are labeled well, including my variable definitions in each column.
Use of Technology
Check for the following:
• I used technology to illustrate my points and ideas. I didn’t just “stick in” a graph.
• Each graph or table (or other piece of tech.) is accompanied by explanations and my ideas.
• I did not include too many graphs on the same axes – my graphs are easy to read.
Mathematical Process (Type 1)
Check for the following:
• I explicitly defined variables and parameters the first time I used them, even if they were
already defined in...
...geometric shapes lead to the special numbers of 1, 4, 9, 16, and 25. To find these outcomes, simply all that is needed to be done is to square the nth term of the sequence. For example, 12=1, 22=4, 32=9, 42=16, and 52=25, therefore the resulting formula for square numbers would be n2=Tn where T=total amount of n. For this investigation though, the geometric shapes of equilateral triangles are studied. Triangular numbers are the amount of dots that evenly fit inside the triangle. After solving the sequence of the triangular numbers and finding a formula to solve for all equilateral triangles, the knowledge attained from triangular numbers will then be used to find and solve the correlation between triangular numbers and stellar (star) numbers.
Here is a sample of the first 5 terms in the triangular numbers sequence:
The row of numbers above the triangles is the number of each term or n.
The rows of numbers below the triangles are triangular numbers of each term or n.
` n1 n2 n3 n4 n5
Here is a sample of the first 4 stages of pstellar shapes that are being investigated. P indicates the amount of vertices in the stellar shape. In this case the stellar shapes being investigated are 6stellar, however after deriving a formula, the stellar number of any p vertices may be found.
Sn is the different stellar shape terms, and the numbers aligned in a row below S1S4 are the pstellar numbers, in this case the 6stellar...
...Taipei European SchoolMath Portfolio

VINCENT CHEN 
Gold Medal Heights
Aim: To consider the winning height for the men’s high jump in the Olympic games
Years  1932  1936  1948  1952  1956  1960  1964  1968  1972  1976  1980 
Height (cm)  197  203  198  204  212  216  218  224  223  225  236 
Height (cm)
Height (cm)
As shown from the table above, showing the height achieved by the gold medalists at various Olympic games, the Olympic games were not held in 1940 and 1944 due to World War II.
Year (1=1932, 2 = 1936 and so on)
Year (1=1932, 2 = 1936 and so on)
Using autograph, the graph above is a scatter graph showing the high jump results from the table.
The plot suggests that the high jump heights start off with a steep positive slope then coming to a decreasing negative slope, however without the 1940 and 1944 high jump competitions, it may not be certain. Then finally, it starts increasing again with a fairly steep positive slope.
However, it would not be realistic if the function has an infinitely increasing range, such as quadratic, exponential and linear because of the limitations that humans have due to natural forces like gravity. Therefore, narrowing down the options that may fit this graph to natural logarithm and logistics
Since the statistics given starts from year 1896, in order to make sure that calculations can be as simplified as possible, I have decided to rearrange the table with the assumption that...
...IB Art SL: Artist Statement
Art is my way of expressing my ideas, emotions, and creativity. Because art is a reflection of life, I’m able to use art to channel my ideas or events that relates to my life. Some of my art are made to celebrate something whether it be a holiday, a joyful event, or just life itself. Some however, give a darker vibe and expose pain, sorrows, and tragedies. I wish to expose these unpleasant elements because they bring in raw emotions. Through my art, I aim to make people realize the importance of appreciation for beauty. In my perspective, beauty isn’t necessary a portrait of flowers, or pictures that have an aesthetic appeal but rather what draw out feelings and understanding. I aspire to make art not only decorative but also meaningful.
I choose themes, mediums, and ideas base upon my sub conscious. Usually, I look for inspirations through pictures and articles, instead my subconscious recognize something that I’m interested in expanding on, I can get an idea of what I might want to do for my artworks. On occasions however, my artworks are dependent on my mood. If I’m confused, there would be notable or even excessive lines.I aim to break boundaries with my artworks and be different from others. For this reason, my wood burning aims at mimicking tattoo designs because since they both etch into their canvases and are permanent, I can see how tattoos might influence wood burnings. When doing my...
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