OpenLLM-France/wikimedia huggingface dataset:
# IB Maths Studies/Functions
## Functions as a mapping

* relation - is a set of ordered pairs such as Q = {(2,3) (7,1) (8,3)}
* function - is a relation is which no two different ordered pairs have the same X coordination
* Domain - of a function is the set of independent values that are allowed
* Range - of a function is the set of all dependent values that are allowed.
X = Domain Y = Range

## Relation Properties

* Linear: y = mx + c; (Straight Line)
* Quadratic: y = ax^2 + bx + c; (Parabola)
* Polynomial: y = ax^3 + bx^2 + cx + d; (Cubic)
* Exponential: y = a * b^(k*x) + c; (Exponential)
* Reciprocal: y = (a / (x – b) + c; (Rectangular Hyperbola)
* Square Root: y = a √(x) + b; (Sideways Parabola)
* Reciprocal Squared y = (a / (x – b)^2) + c; (Truncus)
* Circular: r^2 = (x – a)^2 + (y - b); (Circle)
# IB Maths Studies/Number and Algebra

The Number Sets of N, Z, Q and R
N - Natural Numbers. These are in the set (0, 1, 2, 3...)
There is actually rather a lot of debate within the math community about the inclusion of zero as a natural number. However, the IB Studies curriculum considers 0 to be a natural number.
Z - Integers. The set includes (...-3, -2, -1, 0, 1, 2, 3...)
Q - Rational Numbers. These are the fractions created by dividing any integer by any non-zero integer. This set can include decimals numbers as long as they can be transformed into a fraction (in other words, either a terminating decimal number or a repeating decimal number).
R - The Real Numbers. A real number is any number that can be used to measure a distance (positive or negative). These include all of the above. In addition, it includes the irrational numbers such as pi (3.14...) or e (2.71...). Irrationals are real decimal numbers that follow no pattern and are without end. Any decimal that ends or follows a pattern is a rational number.
Real Numbers can be understood best by comparing them with their "partners" - the imaginary numbers. Imaginary numbers are found when someone tries to take the square root of a negative number. Mathematicians use "i" to represent an imaginary number. Real numbers and Imaginary numbers work together as pairs to make up a large number system called "The Complex Numbers". Real numbers are called so because they measure real distances. Complex numbers measure more complex items and are used in a variety of scientific areas. Luckily, we do not use imaginary numbers in Math Studies.
Significant Figures
Unless otherwise written, answers in IB Math Studies are always to be given to three significant figures. So, what, you are dying to know, is a significant figure? Significant figures are like gremlins, they have to follow certain rules or things get out of control. So here are the rules for keeping Gizmo safe:
1. Always count nonzero digits
Example: 348 has three significant figures. 27 has two.
2. Never count leading zeros
Example: 021 and 0.021 both have two significant figures
3. Always count zeros which fall somewhere between two nonzero digits
Example: 20.8 has three significant figures, while 0.00104009 has six
4. Zeros after the last non-zero digit in whole numbers may not be significant (see NOTE)
Example: 498,000 has three or more significant figures depending on the context.
5. Zeros after the last non-zero digit in decimal numbers are significant, and are required to explicitly show the degree of accuracy
Example: 3.98 is accurate to three significant digits whereas 3.9800 is accurate to five significant digits.
NOTE: The ambiguity of accuracy in a number such as 5100 is one reason scientific notation is often preferred for general usage.
Example: 5.1 x 10^3 signifies two digit accuracy whereas 5.10 x 10^3 signifies three digit accuracy.
# IB Maths Studies/Project

The IB Math Studies Internal Assesment (IA) will be assessed on 7 criteria. Students should read them carefully, and always check any work done on the project against the criteria.
The Criteria are
A) Introduction
Mark Descriptor 0 The student does not produce a clear statement of the task.
1 The student produces a clear statement of the task.
2 The student produces a title, a clear statement of the task and a clear description of the plan.
B) Information and Measurement
Mark Descriptor 0 The student does not collect relevant information or generate relevant measurements.
1 The student collects relevant information or generates relevant measurements.
2 The relevant information collected, or set of measurements generated by the student, is organized in a form appropriate
3 The relevant information collected, or set of measurements generated by the student, is organized in a form appropriate
C Mathematical Processes
Mark Descriptor 0 The student does not attempt to carry out any mathematical processes
1 The student carries out simple mathematical processes.
2 The simple mathematical processes are mostly or completely correct, or the student makes an attempt to use at least one
3 The student carries out at least one sophisticated process, and all the processes used are mostly or completely accurate.
4 The student carries out at least one sophisticated process; the processes used are mostly or completely accurate and all the processes used are relevant.
5 The student accurately carries out a number of relevant sophisticated processes.
D Interpretation of Results Mark Descriptor 0 The student does not produce any interpretations or conclusions.
1 The student produces at least one interpretation or conclusion.
2 The student produces at least one interpretation and/or conclusion that is consistent with the mathematical processes used.
3The student produces a comprehensive discussion of interpretations and conclusions that are consistent with the mathematical processes used.
E Validity
F Structure and Communication
G Commitment
# IB Maths Studies/Geometry and Trigonometry

Tips for drawing proper graphs in IB Math Studies:
* Use pencil.
* Draw the graph with the help of a ruler (no freehand).
* Label your axes. Sometimes a simple x for horizontal axis and y for vertical will be OK. However, most of the problems that you get in Paper 2 will have a fixed scale given. Use, and label, the scale for maximum points.
* Plot the points that the problem gives you exactly. Don't guess.
# IB Music/Exam

IB Music scores, like other subject scores, are divided into several components. These components and their weights differ between the Standard Level and Higher Level of examination.

## Standard Level

The Standard Level examination consists of an External Assessment and an Internal Assessment portion.

### External Assessment

The External Assessment portion is 50% of the overall score. It consists of the:
* Listening Paper - 30% of the overall score
* Musical Investigation - 20% of the overall score

### Internal Assessment

The Internal Assessment portion is 50% of the overall score. It consists of a choice of:
* Solo Performance
* Group Performance
* Composition

## Higher Level

The Higher Level examination consists of an External Assessment and an Internal Assessment portion.

### External Assessment

The External Assessment portion is 50% of the overall score. It consists of the:
* Listening Paper - 30% of the overall score
* Musical Investigation - 20% of the overall score

### Internal Assessment

The Internal Assessment portion is 50% of the overall score. It consists of:
* Solo Performance - 25% of the overall score
* Composition - 25% of the overall score
Guide to higher level 2009-2011 syllabus
The IB music booklet can be found on this site,just scroll down http://www.stedwards.oxon.sch.uk/music-curriculum.html
# IB Maths Studies

The IB Mathematical Studies SL curriculum consists of eight compulsory topics (for first examinations in 2006) In addition, students are required to take part in a project that requires them to take measurements or collect data, and subsequently analyse and evaluate it in a report.

## Topics

Topic 1—Introduction to the graphic display calculator. Teaching Hours - 3
Topic 2—Number and algebra. Teaching Hours - 14
Topic 3—Sets, Logic, and Probability. Teaching Hours - 20
Topic 4—Functions. Teaching Hours - 24
Topic 5—Geometry and trigonometry. Teaching Hours - 20
Topic 6—Statistics. Teaching Hours - 24
Topic 7—Introductory differential calculus. Teaching Hours - 15
Topic 8—Financial mathematics. Teaching Hours - 10
Project Internal Assessment. Teaching Hours - 20
Total Hours - 150

## Assessment

Mathematical Studies SL is graded through an external and internal assessment. The external assessment, worth 80% of the final mark, is composed of a Paper 1 and a Paper 2. The internal Assessment is marked by your teacher, and is worth the remaining 20% of your mark.

### Paper 1

Composed of 15 required short answer questions based on the entire syllabus. Weighted equally with Paper 2 (worth 40% of final mark)
Exam duration: 1 hour 30 minutes.

### Paper 2

Composed of 6 required extended response questions based on the whole syllabus. Accounts for 40% of the candidates final mark.
Exam Duration: 1 hour 30 minutes
# IB Music

IB Music is organized into two major volumes: Music History and Music Theory. Preceding both is a short introduction to the study of music. You will need to be familiar with all of these sections to analyze a piece of music well.

## Volumes

* Introduction
* Music History
* Music Theory
* Prescribed Works-2014
* About the Exam
* Contributors
* Listening Paper

## External links

* Introduction to Music Theory and History
http://keepingscore.org/ for looking at scores, music history..
music history & different forms http://www.patriciagray.net/Musichtmls/Flash/flash.html
http://musicatschool.wordpress.com/ charts of techniques used in different types of music
http://rpfuller.com/gcse/music/ GCSE music history notes
http://www.bbc.co.uk/schools/gcsebitesize/music/ GCSE bitesize, great site for basic theory & listening
http://www.uwosh.edu/faculty_staff/liske/musicalelements/index.html Examples of the different types of textures
glossary of musical terms
Listening
Brilliant site http://www.musiclisteningrevision.co.uk/higher/learnconcepts.htm it also has a brilliant listening glossary:http://www.ltscotland.org.uk/nq/resources/learnlisteningonline/atozdictionary/index.asp other listening glossary from free online book http://www.wwnorton.com/college/music/enj9/chronological/index.htm
voices in opera http://arts.endow.gov/national/GAV/voicetypes.html
Cadences http://www.gmajormusictheory.org/Listening/cadences/cadences.html http://www.good-ear.com/servlet/EarTrainer?chap=4&menu=1 http://smu.edu/totw/cadences.htm
diff periods,listening
Example of mark scheme
# General Chemistry/Basic Chemical Concepts

* Properties of Matter
* Atoms and Molecules
* Nomenclature
* Calculations
* Molar Concepts
* Stoichiometry
* Gas Stoichiometry
* Solution Stoichiometry
# General Chemistry/Book Cover

General Chemistry
A Free Online Textbook
Proceed to Table of Contents
A three-dimensional representation of an atomic 4f orbital.

## About General Chemistry

General Chemistry is an introduction to the basic concepts of chemistry, including atomic structure and bonding, chemical reactions, and solutions. Other topics covered include gases, thermodynamics, kinetics and equilibrium, redox, and chemistry of the elements.
It is assumed that the reader has basic scientific understanding. Otherwise, minimal knowledge of chemistry is needed prior to reading this book.

## Other Chemistry Books

* Organic Chemistry
* Inorganic Chemistry
* Biochemistry
* Other Chemistry Books

## About Wikibooks

This is a wiki textbook. Anyone from around the world can read, as well as write it! All of the content in the book is covered by the GNU Free Document Licence, which means it is guaranteed to remain free and open.

### Authors and Significant Contributors

* NipplesMeCool (talk)
* Orngjce223 (talk)
(Add your user name if you help write General Chemistry!)
# General Chemistry/Chemical Equilibria

* Equilibrium
* Le Chatelier's Principle
* Acid-Base Equilibrium
* Solutions in Equilibrium
# General Chemistry/Behaviour of Gases

← Phase Changes ·Diffusion and Effusion →

## Evaporation of Liquids

An open bottle of vinegar standing at room temperature will spread odor across the room despite the fact that it is not boiling. This is because kinetic energy is unevenly distributed throughout a liquid. Some molecules are moving faster than others. This allows the liquid to evaporate into a gas. In order for evaporation to occur, the entire liquid does not need to be at the boiling temperature; only some individual molecules. At a given temperature a liquid evaporates at a specific rate, causing gas pressure above the liquid in the system that contains it. Can you guess the vapor pressure of water at 100 degrees Celsius? If you guessed 760 torr or 1 atm, you're right. Liquids boil when their vapor pressures equal the atmospheric pressure around them. Some liquids are more volatile than others, meaning they evaporate more readily.
Evaporation occurs because of the uneven distribution of kinetic energy. This is called a Boltzmann distribution. Although the average kinetic energy of the liquid is below the boiling point, some molecules have above average energy. That gives them enough energy to overcome their bonds and break free of the liquid. At the same time, a gas molecule could strike the liquid and slow down enough to become part of it. There is an equilibrium between the amount of evaporating liquid and the amount of liquifying gas. Higher temperatures will have an equilibrium that favors more gas.

## Motion of Gas Particles

Gas particles move in random, straight-line motion. Gas particles possess a greater kinetic energy than the particles of a liquid or solid. The greater kinetic energy is due to gases existing at higher temperatures than liquids or solids. As temperature increases, particles move faster and, thus, have greater kinetic energy. The particles of a gas have minimal interactions, except collisions with each other.

### Diffusion and Effusion

Due to their random motion, gases will eventually escape from a container if there is a hole in it. This is called effusion. Gases also spread out across a room, or mix together in a container. This is called diffusion.
More information about diffusion and effusion is presented in the next chapter.

## Dalton's Law of Partial Pressures

The total amount of pressure exerted by a gas is equal to the sum of its components:
$P_{total}=P_{1}+P_{2}+P_{3}+...$
For instance, if you add 300 torr of nitrogen gas to a container, then you add 250 torr of oxygen to that container, the total pressure will be 550 torr (assuming volume and temperature stayed constant).
Another way of stating this law is that the pressure exerted by a particular gas in a mixture (gases always form homogeneous mixtures with each other) is equal to its mole fraction multiplied by the total pressure.
# General Chemistry/Book Structure
## Overall Structure

The general structure of information in the book was developed from pages already here. It seems to make sense logically, and works quite well as a wiki.
* Topic 1
** Module 1
** Module 2
* Topic 2
** Module 1
** Module 2
Each topic is one reasonably defined area of study (e.g. Acids and Bases, Basic Quantum Chemistry). Each module should contain one specific concept or idea to learn (e.g. Covalent Bonding, Lewis Acids and Bases). Each module is one page, but can contain multiple subheadings.
This layout corresponds roughly to Chapters and Subchapters in a "paper and ink" textbook.
Note: Chemistries of the Various Elements should not contain details like melting point, boiling point, mass, and a list of every possible use and source of the element. That is what Wikipedia is for. Rather, it should point out the most unique and interesting properties of the elements, and more importantly, supply some significant chemical reactions involving the elements.

## Technical Points

Each page should begin with {{msg:GeneralChemTOC}} so people can find their way around.
Each page should end with {{BookCat}} to put the page in the proper category (General Chemistry).
# General Chemistry/Buffer Systems

← Titration and pH ·Reactions of Acids and Bases →

## Introduction

Buffer systems are systems in which there is a significant (and nearly equivalent) amount of a weak acid and its conjugate base—or a weak base and its conjugate acid—present in solution. This coupling provides a resistance to change in the solution's pH. When strong acid is added, it is neutralized by the conjugate base. When strong base is added, it is neutralized by the weak acid. However, too much acid or base will exceed the buffer's capacity, resulting in significant pH changes.
| ${\hbox{HA}}+{\hbox{H}}_{2}{\hbox{O}}\leftrightarrow {\hbox{H}}_{3}{\hbox{O}}^{+}+{\hbox{A}}^{-}$ | Consider an arbitrary weak acid, HA, and its conjugate base, A$^-$, in equilibrium. |
| ${\hbox{A}}^{-}+{\hbox{H}}^{+}\rightarrow {\hbox{HA}}$ | The addition of a strong acid will cause only a slight change in pH due to neutralization. |
| ${\hbox{HA}}+{\hbox{OH}}^{-}\rightarrow {\hbox{H}}_{2}{\hbox{O}}+{\hbox{A}}^{-}$ | Likewise, the addition of a strong base will cause only a slight change in pH. |
Buffers are useful when a solution must maintain a specific pH. For example, blood is a buffer system because the life processes in a human only function within a specific pH range of 7.35 to 7.45. When, for example, lactic acid is released by the muscles during exercise, buffers within the blood neutralize it to maintain a healthy pH.

## Making a Buffer

Once again, let's consider an arbitrary weak acid, HA, which is present in a solution. If we introduce a salt of the acid's conjugate base, say NaA (which will provide the A$^-$ ion), we now have a buffer solution. Ideally, the buffer would contain equal amounts of the weak acid and conjugate base.
Instead of adding NaA, what if a strong base were added, such as NaOH? In that case, the hydroxide ions would neutralize the weak acid and create water and A$^-$ ions. If the solution contained only A$^-$ ions, then a strong acid like HCl were added, they would neutralize and create HA.
As you can see, there are three ways to create a buffer:
Buffers :
| 1 HA + 1 A$^-$ 1 HA + ½ OH$^-$ 1 A$^-$ + ½ H$^+$ | 1 B + 1 HB$^+$ 1 B + ½ H$^+$ 1 HB$^+$ + ½ OH$^-$ |
All six of the combinations will create equal amounts of a weak acid and its conjugate base, or a weak base and its conjugate acid.

## Buffers and pH

To determine the pH of a buffer system, you must know the acid's dissociation constant. This value, $K_{a}$ (or $K_{b}$ for a base) determines the strength of an acid (or base). It is explored more thoroughly in the Equilibrium unit, but for now it suffices to say that this value is simply a measure of strength for acids and bases. The dissociation constants for acids and bases are determined experimentally.
The Henderson-Hasselbalch equation allows the calculation of a buffer's pH. It is:
${\hbox{pH}}={\hbox{pK}}_{a}+\log {\frac {[{\hbox{A}}^{-}]}{[{\hbox{HA}}]}}$
For a buffer created from a base, the equation is:
${\hbox{pH}}={\hbox{pK}}_{b}+\log {\frac {[{\hbox{B}}]}{[{\hbox{HB}}^{+}]}}$
Using these equations requires determining the ratio of base to acid in the solution.
# General Economics/Introduction to Economics

Economics is a study of human behavior. To be more precise, economics studies the individual choices made by people to allocate rare resources or the interactions made by people to other people. It not only studies the businesses' and consumers' choices, it also stuides the everday choices made by other people. An economist studies how people make choices based on limited resources.
# General Chemistry Laboratory/Types of Chemical Reactions
## Precipitation

In a precipitation reaction, an insoluble substance forms and separates from the solution. The solid is known as a precipitate, and the solution above the precipitate is called the supernatant. Generally, the experiment begins with two homogeneous solutions, and a precipitate forms when they are combined. After the maximum amount of substance that can dissolve in the solutions has dissolved, the remainder forms a precipitate.
Solutions with soluble components do not form a precipitate if they are not saturated. Ionic compounds generally dissociate in water.
Precipitation reactions are often used to isolate a particular ion from the solution. The process allows for selective removal of ions through properties of solubility.
The calculations for precipitation reactions are to be determined quantitatively; stoichiometry is heavily involved.

## Acid-Base

In an acid-base reaction, molecules classified as acids and bases interact with each other in a particular way. There are multiple definitions of acid and base molecules. One of the most common of these is the Brønsted-Lowry definition, which indicates that an acid is a proton donor, while a base is a proton acceptor. Another common definition is the Lewis definition, which indicates that an acid is an electron acceptor, while a base is an electron donor.
# General Economics

This course is designed as an overview of economics for students in high school general economics classes. This is a class project that will continue through June 2013 or until the last chapter is completed. It is intended to be a dynamic text with links to resources and videos, images, and embedded quizzes for review. Contributors to this course are mainly students at Henry Sibley High School in Mendota Heights, Minnesota.

## Contents

* Chapter 1: Introduction to Economics
* Chapter 2: Economic Systems
* Chapter 3: Demand
* Chapter 4: Supply
* Chapter 5: Prices
* Glossary
# General Economics/Economic Systems

All societies must answer three economic questions. The way that they answer those questions determines the type of economic system they use. This chapter describes how a centrally planed economy works. A single bureaucracy decides what items to produce and who gets them. The government owns both land and capital. It also controls how much people are paid. This chapter also describes socialism and communism. Socialism is the belief that wealth should be evenly distributed. Communism is when the government owns and controls resources and production. A market is any arrangement that allows buyers/sellers to exchange things. A market allows us to exchange the things we have for the things we want. Specialization is the concentration of the productive effort of individuals and businesses and without specialization markets would not be necessary. In a free market economy, individualists make their own choices. Individualists answer the three economic questions. Traditional Economy: relies on the 3 key economic questions.
* What goods and services should be produced?
* How should these goods and services be produced?
* Who consumes these goods and services?
# General Economics/Prices

Prices are signals in the market. They tell producers how much to produce and help determine the amount consumers are willing and able to purchase.
Cost in input used for production will affect supply. Rise and fall in the cost of input will cause either a fall in supply or an increase in supply. If costs of inputs increase enough marginal cost could become higher than the price. Therefore, the ﬁrm may not be as proﬁtable. If this is the case, production must be cut until marginal cost equals the lower price. If supply falls, the supply curve shifts left. If the supply rises, the supply curve will shift right. Another way to lower production costs is by advances in technology.

## The role of prices

This section is on comparing prices of goods and choosing the cheapest possibility. In a free market, price system is flexible and there is a wide variety of goods and services. An advantage to the price system is that it is a universal language.