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 x-axis from x = a to...

...IB Mathematics SL Year 1
Welcome to IB Mathematics. This two-year 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...

...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...

...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,...

...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...

...Evaluate/Compare and Contrast/Discuss/Examine models or theories of one cognitive process with reference to research studies (22)
Human beings actively process information and it is cognitive processes that guide behavior. These cognitive processes are influenced by social and cultural factors. One of the cognitive processes is memory. Many researchers and psychologies have proved that the mind can be studies scientifically by developing theories and using a number of scientific research...

...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...

...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...

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