OpenLLM-France/wikimedia huggingface dataset:
# A-level Physics/Application of Physics
## Telecommunication
### Public Switch Telephone Network

The Public Switched Telephone Network, or PSTN, is the worldwide network of lines used to carry telephone calls. It is a "switched" network because a connection is made between caller and receiver before any communication begins. Originally, a physical circuit (formed via a number of switches) had to be formed between the caller and receiver, limiting the capacity of the network. This problem was resolved with the development of time division multiplexing.
The first telephone exchanges (where the circuit switches were located) were operated manually by the telephone operator. This was a slow process. Over time, the human operators were replaced with electromechanical switches. These were in turn superseded by electronic switches.
The telephone network can be visualised as a "hub and spokes" arrangement. When the call is made, if it is local to the exchange, then the signal is carried along a spoke to the local exchange (i.e., the hub) then routed down another spoke to the receiver. If the call is a "trunk" call (i.e., not local to the exchange) then the local exchange routes the call to the trunk exchange for onward delivery to the exchange local to the receiver. For international calls, the local exchange will route to an international gateway.

### Mobile Phone

A mobile phone is a handset consisting of a radio transmitter and receiver. A number of different frequencies and encoding techniques are used (hence the need for dual, tri and quad band phones if worldwide usage is required). The handset is constantly in touch with the nearest base station via a low power signal. When a call is made or received, the handset establishes stronger radio wave link with the nearby base station. Each base station is linked to the cellular exchange by a communication cable. The cellular exchange allows entry to the PSTN.
The increasing use of mobile phones does not make it possible for each mobile phone to have its own carrier frequency as the range of carrier frequencies for linking between mobile phones and base stations is limited. Hence the same carrier frequency must be used by many mobile phones at the same time (repeated cells). This is done using UHF which has a limited terrestrial range and using low power transmitters. Each base station has an omnidirectional antenna and the transmitted radio wave are powered so as to have a range approximately equal to the radius of the cell (a few Km) The advantage of operating on UHF is that the aerial of the mobile phone will be very short. Neighbouring cells will typically use different range of carrier frequencies so as to prevent interference.
# A-level Physics/Cosmology/How the universe may evolve

The question of whether the Universe is infinite or not depends crucially on the value of the quantity know as Ω. Such a value, although not determined yet, depends basically on the rate of expansion, or the Hubble Constant, of the Universe.
In simple terms, the quantity Ω is the ratio of the density of the universe (mass per unit volume) to the critical value which determines expansion or collapse. There are three possible outcomes from this value -
* Steady State: the Universe will continue to expand up to a point, whereupon the Universe will stay in a constant state. This would occur if Ω = 1.
* Continuous Expansion: The Universe will continue to expand. This will occur if Ω<1. The result of continuous expansion would be, according to the 1st Law of Thermodynamics, a Universe which would gradually cool down until the temperature became 0 Kelvin.
* Regression: The Universe will grow, and then collapse on itself. This will occur if Ω>1. It has been postulated that if the Universe were to carry on this course, all matter would recondense into a singularity, and recreate another big bang.
# A-level Philosophy/AQA - Updated Specification
## Paper One
### Topic 1 - Epistemology

* Definitions of Knowledge
* Knowledge from Reason
* Knowledge from Perception
* Limits of Knowledge

### Topic 2 - Moral Philosophy (Ethics)

* Utilitarianism
* Kantian Deontological Ethics
* Aristotle's Virtue Ethics
* Meta-Ethics

## Paper Two
### Topic 3 - Metaphysics of God

* The Concept of God
* Arguments for the Existence of God
* The Problem of Evil
* Religious Language

### Topic 4 - Metaphysics of Mind

* Arguments for Dualism
* Issues with Dualism
* Arguments for Physicalism
* Functionalism
# A-level Physics
## Contents
### Examination Boards

* AQA
* OCR
* Edexcel
# A-level Physics/Cosmology
## Contents

* Models of the known universe
* Stars and Galaxies
* Structure of the universe
* Information from stellar observation
* How the universe may evolve
* Relativity
# A Guide to the GRE/Trapezoids
## Trapezoids
### Rules

The area of a trapezoid equals the average of the bases divided by the height.
The area equalsor 72.
When not given, the height of a trapezoid can often be deduced using the Pythagorean Theorem
In this figure, we split the trapezoid into a right triangle with a leg of 3 (10 - 5 -2) as seen to the right. The height of the triangle is 52 minus 32, which is equal to 4.

### Practice

1. If the trapezoid below has an area of 22, what is the length of its top side?
2. What is the area of the trapezoid above?

### Answers to Practice Questions

1. 4
The area of a trapezoid equals the average of its bases multiplied by its height. Since the height of this trapezoid is 4, the average of its bases must equal 22 divided by 4, or 5.5. At this point, the top side can be determine by solving the equation= 5.5, which works out to 4.
2. 192
This trapezoid can be split into a right triangle with sides of 20 and 16, the latter determined by subtracting 8 from 24. This means that the height of the trapezoid is the third side of the right triangle, which equals or 12. 12 multiplied by the average of the bases - 16 - equals 192.
# A Guide to the GRE/Triangles
## Triangles

The angles of a triangle add up to 180º.
In this triangle, c is equal to 60 because the angles of a triangle add up to 180º.
The greater the angle in a triangle, the greater the corresponding side.
Angle f is greater than angle g but less than angle h, because the corresponding sides are larger and smaller, respectively.
The Four Types of Triangles

### Practice

1.
If FG is equal to GH but less than FH, then the measure of angle FGH must at least be greater than how many degrees?
2.
If i is 8 degrees greater than k and 4 degrees greater than j, what is the measure of i?
3.
If LM and MN both have lengths of 10, and angle LMN has a measure of 80º, what are the measures of the other two angles of the triangle, MLN and LNM?

### Answers to Practice Questions

1. The angle measure must be greater than 60º.
The angles of a triangle add up to 180º. The greater the length of a side of a triangle, the greater its opposite angle.
If FH is greater than the other two sides, its angle measure must be greater. If all three angles were equal, they would equal 60º (180º divided by 3), but since this side is greater, its opposing angle must be greater than 60º, while the other two must be less than 60º.
2. 64º
The angles of a triangle add up to 180º. Thus, i + j + k = 180.
i + j + k = 180. Take the initial equation.
i + (i - 4) + (i - 8) = 180 Substitute the known values of the other two variables in terms of i.
i + i -4 + i - 8 = 180 Expand the parentheses.
3i - 12 = 180 Consolidate the constants and variables.
3i = 192 Add 12 to both sides.
i = 64 Divide both sides by 3. i is equal to 64.
3. 50º
Since LM and MN have identical lengths, the angles opposite these sides have identical lengths. The angles of a triangle add up to 180º; thus, since the third angle is equal to 80º, the other two angles must have a combined measure of 100º. Since they are equal, the measure of each is 50º.
# The GRE Writing Section

The writing section is of rather small importance in admissions decisions compared to the other two; nonetheless, it is worthwhile for test takers to do the best they can on it.
As stated at the beginning, there are two writing sections. One is an analysis of an issue; the other is an analysis of an argument.
There are three things to remember about the writing section.
1. Write a lot. The single strongest objective predictor of high essay grades is length.
2. Sound intelligent.
| ✗Bad | ✓Good |
| Things like social security are a good idea. It is good to have a social safety net for seniors. Social security helps keeps seniors out of poverty. | The beneficial nature of social security is clear, given the public interests furthered by the safety net it provides, and the extent to which it keeps seniors out of poverty. |
3. Don't ramble.
| ✗Bad | ✓Good |
| Direct voting by the public on political issues would help in some cases. It would depend, however, on the complexity of the matter - some things would be incomprehensible to the lay person. This raises an interesting question - is the average person cut out to make leadership decisions? Historically democracies have usually exercised some level of autonomy. Of course, there are varying levels of autonomy in the United States. Nonetheless, the United States has managed to accede to public will on most issues historically. | Direct voting by the public on political issues would help in some cases. The government can only remain stable and effective if it serves the people, and direct voting would bring about this end. However, the question arises as to whether some issues are too complex for the average voter. Many laws are quite complicated, and the lay person may not have the necessary expertise to properly evaluate changes to them. |
Keep thoughts concise and coherent; and, generally, use common sense on the writing section. Again, however, the section is not particularly important. Do not let it take away from the other very important sections.
# A Guide to the GRE/The Up and Down Rule
## The "Up & Down" Rule

Increasing by a fraction or percentage requires decreasing by a smaller fraction or percentage to get back to the same quantity.
If a dress that sells for $100 increases in price by 25%, its price goes up to $125. To return the dress to its original price, its price would have to be reduced by 20%, not 25%. This is because the base number has increased. Increasing 60 by 20% yields a value of 72. 72, however, will have to be reduced by a lower percentage - about 16% - to get back to 60. With fractions, going down takes less than going up, since fractions are based on parts of the whole.

### Practice

1. A grocery store sells one third of its shortening. What percentage of its remaining shortening will it have to restock to restore the shortening supply to its present value?
2. An accountant's fees increase by 15%, but the account promises a discount to loyal customers which will make prices equal to the rate before the increase. What fraction of the new rate will the accountant have to charge customers receiving the discount?
3. Office supply sales increase by 40% in April but fall back to their original value in May. What fraction of April's office supply sales are May's office supply sales?

### Answers to Practice Questions

1. 50%
After selling of the shortening, remain. We are looking for the amount needed to return the shortening to the previous level. Let r equal the fraction that will be restocked.
+ r= 1 Take our initial equation.
r= Subtract from both sides.
r = .5 = 50% Divide both sides by r equals 50%.
2.
Let f equal the fraction that the account will charge of the new rate.
115(f) = 100
f == Divide both sides by 115. The fraction is
3.
# Standard Deviation

Standard deviation measures how much a given set of numbers varies. It does not in any way reflect the average value of data or the quantity of the elements.
Thus, the numbers 1, 700, 62,000 and 1,000,000 would have a greater standard deviation than the numbers, 4, 5, 6, and 7.
The GRE does not test the formula for standard deviation nor does it expect test takers to remember “normal” distribution. It does, however, expect test takers to understand the concept. The test will frequently ask trick questions hoping that test takers will confuse standard deviation with mean or median value or range, such as those below for you to practice on.

## Practice

1. Data Set 1 has a range of 1-100. Data Set 2 has a range of 200-500. Is it possible to determine which set has a greater standard deviation?
2.
The chart above shows a normal distribution for hours spent watching television per week in Springfield, with a mean of 8 and a standard deviation of 6. What percentage of the population of Springfield watches fewer than 2 hours of television per week?
3.
| Series I | Series II |
| 5, 6, 6, 7, 8, 10 | 1, 2, 3, 7, 15, 24 |
Which series has a greater standard deviation?

## Answers to Practice Questions

1. No, the difference in standard deviation cannot be determined
Standard deviation is a tool to measure how varied the results are from a given mean. It has nothing to do with the value of the numbers or the quantity of numbers in the set, except to the extent that these influence average distance from the mean.
2. 16%
Since the mean is 8 and the standard deviation is 6, 84% of the data sample will fall above 8-2, pursuant to the chart. The cutoff is represented by the “m - d” on the chart.
3. Set II has a greater standard deviation.
Standard deviation measures how close or far apart a set of numbers are from the mean. Set II is clearly more spread apart than Set I, thus, it has more standard deviation.
Again, the GRE does not expect test takers to know the standard deviation formula but it expects them to understand the concept.
# A Guide to the GRE/The Two Types of GRE Math Questions
## The Two Types of GRE Math Questions

There are two types of GRE math questions: quantity comparison, and ordinary problem solving.

### Quantity Comparison

A quantity comparison question will give two quantities and ask the test taker to compare them. For example:
    1. Ashley's pet cockatoo eats ${\tfrac {7}{4}}$ as much bird food as her pet parakeet. Ashley has no other pets.
    Quantity A: the percentage of total bird food eaten by Ashley's cockatoo
    Quantity B: 65%
    (A) Quantity A is greater.
    (B) Quantity B is greater.
    (C) The two quantities are equal.
    (D) The relationship cannot be determined from the information given.
(The correct answer is (A)).

### Problem Solving

A problem solving question asks a "normal" multiple choice or open-ended question which requires mathematical reasoning to solve.
    11. Vivie's pet cockatoo eats as much bird food as her pet parakeet. Vivie has no other pets. What fraction of the total bird food is eaten by Vivie's cockatoo?
    (A)${\tfrac {7}{4}}$
    (B)${\tfrac {4}{7}}$
    (C)${\tfrac {11}{4}}$
    (D)${\tfrac {11}{7}}$
    (E)${\tfrac {7}{11}}$
(The correct answer is (E))
The question prompt may be multiple choice or may be open-ended, asking test takers to bubble in the value. Additionally, some may have three or seven choices and more than one correct answer. This will be clearly indicated. Also, approximately four problem solving questions around questions 17-20 will be based on a chart.
# A Guide to the GRE/Social Science Passages

GRE passages are often about complicated social science topics.
Linguists are uncertain as to why languages change and modify the way they do - changes perhaps attributable to mere idiosyncratic factors. Whatever the case, 5 the diversity of languages occasioned by geographic dispersal is all too apparent, such as with the Latin-based languages of Italian, Spanish, French, and Portuguese - all of which trace their roots, at least in 10 part, to a uniform common ancestor. Curious, however, is the fact that Portuguese - geographically the furthest of any of the Romance languages from Rome - bears the closest resemblance to Latin, the language of the ancient Romans. The 15 Portugal example perhaps suggests that it is exchange and intermingling which change languages, not time or distance alone, and that Portugal, isolated in its corner of Europe, therefore saw the least of 20 such mingling. The example of Scandinavian languages is certainly consistent with this theory. Norwegian, Swedish, and Danish all trace their roots to the Old Norse spoken by the 25 Vikings. Yet it is Icelandic - the furthest tongue from the Scandinavian peninsula - which bears the strongest resemblance to Old Norse, further supporting the notion that intermingling is a primary cause of 30 linguistic change. 1. What is strangely true about both Icelandic and Portuguese, based on the passage?
2. According to the author of the passage, why might it be the case that Portuguese and Icelandic both bear these characteristics discussed?
3.08 Social Science Passages

## Answers to Practice Questions

1. According to the passage, both Icelandic and Portuguese are the closest to their linguistic ancestors - Old Norse and Latin, respectively - despite being furthest from the source of these languages.
2. This passage discusses the idea that it may be the interspersal and intermingling of people and cultures which produces a change in languages, not distance and time alone. The author is stating that the reason that Portuguese is most similar to Latin may be the fact that Portugal is more isolated from the rest of the world, while France, Spain, and Italy were much more subject to intermingling with other cultures. The author thinks it may be this “intermingling” which produces linguistic change, as new words and linguistic devices are exchanged, adopted, and substituted into a language.
# A Guide to the GRE/Squares
## Squares

The area of a square equals its side squared.
Area = s$^2$
The diagonal of a square equals its side multiplied by ${\sqrt {2}}$
This comes from the Pythagorean theorem. The diagonal is the greatest distance between any two points on the square.

### Practice

1. The diagonal of a square is equal to 5. What is the length of a side of the square?
2. Square A has 3 times the size of Square B. If Square B's side has a length of 10, what is the length of a side of Square A?

### Answers to Practice Questions

1.
The diagonal of a square is equal tomultiplied by its side; thus, the side of a square is equal to its diagonal divided by, or multiplied by In the case of this particular square, this means that the diagonal is equal to
2.
The area of a square is its side squared. Thus if a2 = 3b2 then a must equalSince the length of one side of the latter square is 10, the first square's side must equal
# A Guide to the GRE/Systems of Equations
## Systems of Equations

Two equations with two variables can be solved by adjusting one equation so that one variable is expressed in terms of another, and substituting this value into the other equation.
In 3x + 3y = 15, x and y could conceivably have many values, from 1 and 4 to 7 and -2, and so on. Both variables can not be determined using this equation. However, if a second equation is added, it is possible.
3x + 3y = 15 These two are known as a “system of equations.”
x - y = 1 To solve, begin with the second equation.
x = y + 1 Phrase the second equation in terms of one variable. In this case, this is done by adding y to both sides.
3(y +1) + 3y = 15 Substitute this value into the other equation.
3y + 3 + 3y = 15 Expand the parentheses.
6y + 3 = 15 Combine the variables.
6y = 12 Subtract 3 from both sides.
y = 2 Divide both sides by 6. y is 2 (making x 3).

### Practice

1. 5a - 3b = 21
    2a + b = 15
If a and b satisfy the system of equations above, what is the value of a + b?
2. 2f - g = 2
If f and g satisfy the system of equations above, what is the value of f?
3. q + 4r = 21
If q and r satisfy the system of equations above, what are the values of both q and r?

### Answers to Practice Questions

1. 9
5a - 3b = 21
2a + b = 15 Take the second equation.
b = 15 - 2a Convert this equation to express one variable in terms of the other. In this case, subtract 2a from both sides.
5a - 3(15 - 2a) = 21 Substitute this value into the first equation.
5a - 45 + 6a = 21 Expand the parentheses.
11a - 45 = 21 Consolidate the variables.
11a = 66 Add 45 to both sides.
a = 6 Divide both sides by 11. a is 6, b is 3, and a + b = 9
2. 4
2g + 2f = 20 Take the second equation.
2g = 20 - 2f Convert this equation to express one variable in terms of the other. In this case, subtract 2f from both sides.
g = 10 - f Divide both sides by 2.
2f - (10 - f) Substitute this value into the first equation.
2f - 10 + f= 2 Expand the parentheses.
3f - 10 = 2 Consolidate the variables.
3f = 12 Add 10 to both sides.
f = 4 Divide both sides by 3. f is 4.
3. 5, 1
2r - q = 9 Take the second equation.
-q = 9 - 2r Convert this equation to express one variable in terms of the other. In this case, subtract 2r from both sides.
q = 2r - 9 Multiply both sides by -2
(2r - 9) + 4r = 21 Substitute this value into the first equation.
2r - 9 + 4r = 21 Expand the parentheses.
6r - 9 = 21 Combine the variables.
6r = 30 Add 9 to both sides. r is 5; q 1.
# Arithmetic/Bases/Another Look at Decimal (Base 10)

In order to understand bases, you should look at decimal to see how they work first.
For example, look at the number 123:
The 1 in the 100s place means 1 x 100 1 x 100 = 100
The 2 in the 10s place means 2 x 10 2 x 10 = 20 100 + 20 = 120
The 3 in the 1s place means 3 x 1 3 x 1 = 3 100 + 20 + 3 = 123
Notice how 100 = 10$^2$, 10 = 10$^1$, and 1 = 10$^0$.
# Arithmetic/Estimation
## Estimation

Estimation involves working out a rough answer to a calculation. The most common way to estimate a solution to a calculation is to round the numbers up or down to numbers which are easier to calculate with.
An example: Estimate the answer to 99 × 9. In this case we can easily see that 9 is almost 10, and multiplying by 10 is really easy, so we can replace our calculation with 99 × 10 which is far more easy to calculate. As we rounded a number up we know that our estimate is going to be larger than the real answer.
Why don't we just call this a guess? The difference is that a guess is just that, a completely wild guess. An estimate is based on some extra information. So whilst you might guess that 99 × 9 is something around 1000 by just pulling a number out of the air, we estimate that 99 × 9 is close to 99 × 10, then we work out 99 × 10 exactly, which gives 990 as an estimate of 99 × 9.
When we estimate, we want our estimate to be close enough to the actual value so as to be useful. (This also applies to approximation.) In our example above, the answer deviates from the actual value by about 10%, which might not be acceptable. Estimation often involves some guesswork, so we might not actually know how accurate our estimate is. (And yes, that figure 10% is itself an estimate.)
A better way to estimate 99 × 9 is to say that 99 is close to 100, then we work out 100 × 9 exactly, which gives 900 as an estimate of 99 × 9. This estimate is 1.0101...% off. The reason this is a better estimate is that 99 deviates from 100 much less than 9 deviates from 10 in percentage terms (although the absolute difference is one in each case).
# Arithmetic/Highest Common Factor

The highest common factor (HCF) or greatest common divisor (GCD) can be found in a similar fashion. In this case, the product of the prime factors common to all the numbers gives the HCF.
For example, if we wish to find the HCF of 60, 12 and 102 we write
${\begin{matrix}60=2^{2}\cdot 3\cdot 5\\12=2^{2}\cdot 3\\102=2\cdot 3\cdot 17\end{matrix}}$
Now the HCF is $2\cdot 3=6$.
Two numbers which have an HCF of 1, for example 12 and 5, are said to be coprime - they have no factors in common (except 1).