OpenLLM-France/wikimedia huggingface dataset:
# FHSST Physics/Momentum

Momentum is the product of the mass and velocity of an object. In general the momentum of an object can be conceptually thought of as the tendency for an object to continue in its current state of motion, speed and direction.
As such, it is a natural consequence of Newtons first law.
Momentum is a conserved quantity, meaning that the total momentum of any closed system cannot be changed.

## Momentum in classical mechanics

If an object is moving in any reference frame, then it has momentum in that frame. It is important to note that momentum is frame dependent. That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame.
The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference. In physics, the symbol for momentum is usually denoted by ${\vec {p}}$ , so this can be written:
    ${\vec {p}}=m{\vec {v}}$
where
    ${\vec {p}}$ is the momentum,
    $m$ is the mass, and
    ${\vec {v}}$ is the velocity.
The velocity of an object is given by its speed and its direction. Because momentum depends on velocity, it too has a magnitude and a direction and is a vector quantity. For example the momentum of a $5kg$ bowling ball would have to be described by the statement that it was moving westward at $2{\frac {m}{s}}$ . It is insufficient to say that the ball has $10kg\cdot {\frac {m}{s}}$ of momentum because momentum is not fully described unless its direction is given.

## Conservation of momentum

As far as we know, momentum is a conserved quantity. Conservation of momentum (sometimes also conservation of impulse) states that the total amount of momentum of all the things in the universe will never change. One of the consequences of this is that the center of mass of any system of objects will always continue with the same velocity unless acted on by a force outside the system.
Conservation of momentum is a consequence of the homogeneity of space.
In an isolated system (one where external forces are absent) the total momentum will be constant: this is implied by Newton's first law of motion. Newton's third law of motion, the law of reciprocal actions, which dictates that the forces acting between systems are equal in magnitude, but opposite in sign, is due to the conservation of momentum.
Since momentum is a vector quantity it has direction. Thus when a gun is fired, although overall movement has increased compared to before the shot was fired, the momentum of the bullet in one direction is equal in magnitude, but opposite in sign, to the momentum of the gun in the other direction. These then sum to zero which is equal to the zero momentum that was present before either the gun or the bullet was moving.
# Modern Physics

"Modern Physics" concerns areas of Physics which have only recently begun to be explored. Such areas include quantum physics and the exploration of particles. By "recently" here we mean since about the beginning of the 20th century, like modern art, so most of the things that will be covered here are really already well verified and understood.
# The Momentum of a System

In Chapter 4 Forces the concept of a system was introduced. The bodies that make up a system can have different masses and can be moving with different velocities. In other words they can have different momenta.
   * Definition:
   * The total momentum of a system is the sum of the momenta of each of the objects in the system.
Since momentum is a vector, the techniques of vector addition discussed in This chapter must be used to calculate the total momentum of a system. Let us consider an example.

## Worked Example 34 Calculating the Total Momentum of a System

Question: Two billiard balls roll towards each other. They each have a mass of 0.3kg. Ball 1 is moving at $v_{1}=1\ m.s^{-1}$ to the right, while ball 2 is moving at $v_{2}=0.8\ m.s^{-1}$ to the left.
Calculate the total momentum of the system.
Answer:
Step 1 :
Analyse the question to determine what is given. The question explicitly gives
* the mass of each ball,
* the velocity of ball 1, ${\overrightarrow {v_{1}}}$ and
* the velocity of ball 2, ${\overrightarrow {v_{2}}}$,
all in the correct units!
Step 2 :
What is being asked? We are asked to calculate the total momentum of the system. In this example our system consists of two balls. To find the total momentum we must sum the momenta of the balls,
${\begin{matrix}{\overrightarrow {p}}_{total}&=&{\overrightarrow {p_{1}}}+{\overrightarrow {p_{2}}}\end{matrix}}$
Since ball 1 is moving to the right, its momentum is in this direction, while the second ball's momentum is directed towards the left.
Thus, we are required to find the sum of two vectors acting along the same straight line. The algebraic method of vector addition introduced in this chapter can thus be used.
Step 3 :
Firstly we choose a positive direction. Let us choose right as the positive direction, then obviously left is negative.
Step 4 :
The total momentum of the system is then the sum of the two momenta taking the directions of the velocities into account. Ball 1 is travelling at $1\ m.s^{-1}\ to\ the\ right$ or $+1\ m.s^{-1}$. Ball 2 is travelling at $0.8\ m.s^{-1}\ to\ the\ left$ or $-0.8\ m.s^{-1}$. Thus,
Right is the positive direction
${\begin{matrix}{\overrightarrow {p}}_{total}&=&m_{1}{\overrightarrow {v_{1}}}+m_{2}{\overrightarrow {v_{2}}}\\&=&(0.3kg)(+1\ m.s^{-1})+(0.3kg)(-0.8\ m.s^{-1})\\&=&(+0.3\ kg.m.s^{-1})+(-0.24\ kg.m.s^{-1})\\&=&+0.06\ kg.m.s^{-1}\\&=&0.06\ kg.m.s^{-1}{\textbf {\ to\ the\ right}}\end{matrix}}$
In the last step the direction was added in words. Since the result in the second last line is positive, the total momentum of the system is in the positive direction (i.e. to the right).
# Change in Momentum

If either an object's mass or velocity changes then its momentum too will change. If an object has an initial velocity ${\overrightarrow {u}}$ and a final velocity ${\overrightarrow {v}}$, then its change in momentum, $\Delta {\overrightarrow {p}}$, is
| $\Delta {\overrightarrow {p}}$ | = ${\overrightarrow {p}}_{final}-{\overrightarrow {p}}_{initial}$ $m{\overrightarrow {v}}-m{\overrightarrow {u}}$ |

## Worked Example 35 Change in Momentum

Question: A rubber ball of mass 0.8kg is dropped and strikes the floor at a velocity of $6\ m.s^{-1}$. It bounces back with an initial velocity of $4\ m.s^{-1}$. Calculate the change in momentum of the rubber ball caused by the floor.
Answer:
Step 1 :
Analyse the question to determine what is given. The question explicitly gives
* the ball's mass,
* the ball's initial velocity, and
* the ball's final velocity
all in the correct units.
Do not be confused by the question referring to the ball bouncing back with an ``initial velocity of $4\ m.s^{-1}$. The word initial is included here since the ball will obviously slow down with time and $4\ m.s^{-1}$ is the speed immediately after bouncing from the floor.
Step 2 :
What is being asked? We are asked to calculate the change in momentum of the ball,
${\begin{matrix}\Delta {\overrightarrow {p}}&=&m{\overrightarrow {v}}-m{\overrightarrow {u}}.\end{matrix}}$
We have everything we need to find $\Delta {\overrightarrow {p}}$. Since the initial momentum is directed downwards and the final momentum is in the upward direction, we can use the algebraic method of subtraction discussed in the vectors chapter.
Step 3 : Firstly, we choose a positive direction. Let us choose down as the positive direction. Then substituting,
Down is the positive direction
${\begin{matrix}\Delta {\overrightarrow {p}}&=&m{\overrightarrow {v}}-m{\overrightarrow {u}}\\&=&(0.8kg)(-4\ m.s^{-1})-(0.8kg)(+6\ m.s^{-1})\\&=&(0.8kg)(-10\ m.s^{-1})\\&=&-8\ kg.m.s^{-1}\\&=&8\ kg.m.s^{-1}{\textbf {\ up}}\end{matrix}}$
where we remembered in the last step to include the direction of the change in momentum in words.
# Introduction to the idea of a quantum

Imagine that a beam of light is actually made up of little "packets" or "bundles" of energy, called quanta.
It's like looking at a crowd of people from above. At first, it seems as though they are one huge patch, without any spaces between them. You would never suspect that they were people. But as you move closer, you slowly begin to see that they are individuals, and when you get even closer, you may even recognize a few. Light seems like a continuous wave at first, but when we zoom in at the subatomic level, we notice that a beam of light actually consists of little "packets" of energy, or quanta. (You will not be able to tell the particles of light apart though because they are of the same energy, and thus identical. The fact that they can't be distinguished has to do with how a laser works.)
The only thing which differentiates one quantum from another is the energy contained in individual quanta (or "packets"). The "packets" are assigned a particular energy, depending on the frequency (or to put it simply: the colour) of the light wave. Quanta of Violet coloured light have the maximum energy and that of Red have the minimum energy.
This idea introduces the concept of the quantum (particle) nature of light, which is demonstrated by the photoelectric effect. When a metal surface is illuminated with light, electrons can be emitted from the surface. This is known as the photoelectric effect . It was explained by the theoretical physicist Albert Einstein.
# Handbook of Genetic Counseling/Scheie Syndrome

Scheie Syndrome

## Contracting

* Medical update
* Physical exam
* Answer any new questions

## Medical Update

* How are your hands?
* Carpal tunnel repair… any complications?
* Current medications
* Current activities at school
* How's the replacement therapy going?
* How's your vision currently?

## Scheie Syndrome

* Definition: It is a mucopolysaccharidoses Type I disease. This means the body has trouble breaking down the large molecules in the lysosomes. Instead of breaking them down completely, they kick out only partially degraded molecules = storage occurs as well. So there is an increase of stuff in the lysosomes causing a build up in various parts of the body
* Incidence
** 1/500,000 births
* Characteristics
** Broad mouth and fill lips
** Clouding of corneas/visual impairment
** Aortic valve defects
** Hairy body
** Hernias are common
** Carpal tunnel syndrome
** Joint limitation leading to claw hand.
** Normal life span
* Genetics
** Autosomal recessive
** Chromosome 4p16 has a defect = the alph-L-iduronidase gene

## Recommendations

* Ophthgamology
* Cardiology
* Physical Therapy
* Occupational Therapy

## Treatment

* Bone marrow transplants -experimental
* Fetal tissue transplants - experimental
* Enzyme replacement - experimental (When lysosomal storage diseases were discovered, hopes were raised that they could be treated by enzyme substitution. When exogenous lysosomal enzymes are injected into the patient, this enzyme can eventually be taken up by enzyme-deficient cells. This uptake is regulated by certain receptors on the cell surface. Different tissue have different receptors. It is therefore necessary to change the natural enzyme to enable uptake in the tissue of interest. If properly designed, the missing enzyme could be injected regularly like the diabetic subject injects insulin. In many in vitro studies with the purified active enzyme added to the media of enzyme-deficient fibroblasts, the lysosomal substrate accumulation was corrected, but in vivo treatment has been hampered through the problem of producing the sufficient quantity of enzymes, immunological problems, and that the substituted enzyme does not pass the blood-brain barrier.
* Since it can be expected that enzymes supplied from the outside do not pass the blood brain barrier, suitable candidates for enzyme replacement are disorders without neurological involvement (e.g. Maroteaux Lamy, Morquio B, Fabry, late onset Pompe disease).

## Resources

* Human Genetic Disease, in Layman's Terms
    http://mcrcr2.med.nyu.edu/murphp01/lysosome/hgd5.htm
* National MPS Society
    www.mpssociety.org
    17 Kraemer Street Hicksville, NY 11801 (516) 432-1797

## Notes

The information in this outline was last updated in 2000.
# Handbook of Genetic Counseling/Short Chain Acyl-CoA Dehydrogenase (SCAD)

Short Chain Acyl-CoA Dehydrogenase (SCAD)

## General Information

* a disorder of lipid metabolism characterized by a defect in the oxidation of short-chain fatty acids resulting in neurologic and gastrointestinal manifestations
* SCAD is one of four enzymes in the mitochondria responsible for the breakdown of short-chain (C4-C6) fatty acids to 2-carbon fragments (acetyl-CoA) in the beta oxidation pathway
* homozygous patients are unable to mobilize large fat stores and are thus at risk for becoming hypoglycemic when stressed (i.e., during infection or fasting) during which time the long and medium acyl-CoA dehydrogenases are unable to compensate for the lack of SCAD
* gene map locus: 12q22-qter
* autosomal recessive inheritance

## Diagnosis

* diagnosis is difficult because patients do not consistently excrete characteristic metabolites
* it is necessary to collect and analyze several urine and plasma specimens in patients with neurologic abnormalities that suggest this disorder
* deficiency of SCAD activity in leukocytes and cultured skin fibroblasts
* prenatally, a deficiency of SCAD activity in cultured chorionic villi or amniocytes can be detected

## Clinical Evaluation

* two distinct clinical phenotypes have been identified :
* one type observed in infants with acute acidosis and muscle weakness (generalized)
* one type observed in middle-aged patients with chronic myopathy (localized to skeletal muscles)
* cases with neonatal onset have a variable phenotype
* includes metabolic acidosis, failure to thrive, developmental delay, seizures and myopathy
* no episodes of nonketotic hypoglycemia (characteristic of medium-chain and long-chain acyl dehydrogenase deficiencies)

## Infantile type

* metabolic: neonatal acidosis, low-normal plasma total carnitine, highly esterified
* GI: poor feeding, vomiting, failure to thrive
* muscle: progressive skeletal muscle weakness, hypotonia
* neurological: developmental delay
* laboratory results: generalized SCAD deficiency, ethylmalonate urinary excretion, low normal highly esterified muscle carnitine

## Adult type

* muscle: lipid-storage myopathy
* lab results: skeletal muscle carnitine low, deficiency of skeletal muscle mitochondrial short-chain acyl-CoA (butyryl-CoA)

## Support Groups

* James William Lazzaro Foundation
    4493 Liberty Road
    South Euclid, OH 44121
    Contact Person: Jamie Lazzaro
    Phone: (502) 254-2209
    Email: info@jwlsite.com
    Website: www.jwlsite.com
* FOD(Fatty Oxidation Disorders)Family Support Group
    2041 Tomahawk
    Okemos, MI 48864
    Contact Person: Deb Lee Gould, MEd
    Phone: (517) 381-1940
    Email: deb@fodsupport.org
    Website: www.fodsupport.org

## Sources

* Bhala A, Willi SM, Rinaldo P, Bennett MJ, Schmidt-Sommerfeld E, Hale DE. "Clinical and biochemical characterization of short-chain acyl-coenzyme A dehydrogenase deficiency." J Pediatr 1995 Jun;126(6):910-5
* OMIM

## Notes

The information in this outline was last updated in 2002/
# Handbook of Genetic Counseling/Sanfilippo syndrome

Sanfilippo syndrome

## Other names: Mucopolysacchardosis III, Type A, B, C, and D

* So, it is a syndrome in which the large saccharides are not broken down properly in the lysosomes. It's a lysosomal storage deficiency.

## Characteristics

* Most common of the MPS diseases
* Normal to fast growth 1-3 years. Slow growth after that.
* Slow development by 1-3 years then deterioration
* Short stature
* Hearing loss
* Poor gait
* Poor speech
* Poor behavior
* Synophrys (joined eyebrows)
* Mild cardiac involvement
* Clear corneas
* Sleep disturbances
* Upper respiratory tract infections
* Many die of pneumonia (10-20 years)

## Genetics

* Autosomal recessive in all types
* Sanfilippo A = defect in heparan N-sulfatase
* Sanfilippo B = deficiency in N-acetyl-alpha-delta glucosaminidase
* Sanfilippo C = deficiency of acetyl-CoA: alpha-glucosaminide-N-acetyltransferase
* Sanfilippo D = deficiency of N-acetyl-alpha-delta glucosaminide-6-sulfatase

## Diagnosis

* By clinical features mentioned above (same for all four types except type D)
** Overactivity
** Destructive tendencies
** Weakness in all extremities
* Presence of excess heparan sulfate in the urine

## Resources

* National MPS Society
    102 Aspen Drive
* Downingtown, PA 19335
* (610) 942-0100
* http://mpssociety.org/index.htm

## Notes

The information in this outline was last updated in 2000.
# HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/HSC/Applications of calculus to the physical world
## Exponential Growth and Decay

2 unit course
The exponential function can be used to show the growth or decay of a given variable, including the growth or decay of population in a city, the heating or cooling of a body, radioactive decay of radioisotopes in nuclear chemistry, and amount of bacteria in a culture.
The exponential growth and decay formula is $N=N$$_0$e$^{kt}$
where: $N$$_0$ is the first value of N (where $t=0$) $t$ represents time in given units (seconds, hours, days, years, etc.) $e$ is the exponential constant ($e=2.718281828...$), and $k$ is the growth ($k+ve$) or decay($k-ve$) constant.
Differentiation can be used to show that the rate of change (with respect to time, $t$) of $N$ is proportional (∞) to $N$. if: $N=N$$_0$e$^{kt}$, then the derivative of $N$ can be shown as: dN $=kN$$_0$e$^{kt}$ dt $=kN$, substituting $N=N$$_0$e$^{kt}$.
(note the derivative of e is the variable $k$ of the power of e times $e^{kx}$ and $N,t$ are constant.)

## 3 Unit applications

not yet complete
The variable of a given application can be proportionate to the difference between the variable and a constant. An example of this is the internal cooling of a body as it adjusts to the external room temperature.
dN = $k(N-P)$ dt $=kN$$_0$e$^{kt}$$-kP$
where $P$ = the external constant (e.g., the external room temperature)
using natural logarithms, $log$$_e$$x$, we can find any variable when given certain information. Example: A cup of boiling water is initially $100$$^o$C. The external room temperature is $24$$^o$C. after 10 minutes, the temperature of the water is $74$$^o$C. find (i) k (ii)how many minutes it takes for the temperature to equal 30 degrees.
(i)$74=24-100$e$^{10k}$ $50=-100$e$^{10k}$
${\frac {50}{-100}}=e^{10k}$
$log$$_e$$1-log$$_e$$(-2)=10k$
$k={\frac {log_{e}1-log_{e}(-2)}{2}}$
= .34567359... (store in memory)
(ii) 30=24-100e^(.34657359t)
incomplete 10th august '08
# HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/HSC/Harder 2-Unit

Some Harder 2 unit Problems:
See HSC 1998 Q 10 b James Ruse 2003 Trial Paper Q 9 and 10 James Ruse 2006 Trial Paper Question 10 HSC 2001-2005 Q 10 HSC 2013 Q 10b Sydney Grammar 2012,2013,2014 2 unit trial Q 16
# HSC Information Processing and Technology/Exam Work
## Key Words used in HSC Exam Questions

Account: Account for, state reasons for, report on. Give an account of: narrate a series of events or transactions
Example Question:
Analyse: Identify components and the relationship between them: draw out and relate implications
Example Question:
Apply: Use, utilise, employ in a particular situation
Example Question:
Appreciate: Make a judgement about the value of
Example Question:
Asses: Make a judgement of value, quality, outcomes, results or size
Example Question:
Calculate: Ascertain/determine from given facts, figures or information
Example Question:
Clarify: Make clear or plain
Example Question:
Classify: Arrange or include in classes/categories
Example Question:
Compare: Show how things are similar or different
Example Question:
Construct: Make; build; put together items or arguments
Example Question:
Contrast: Show how things are different or opposite
Example Question:
Critically (Analyse/Evaluate): Add a degree or level of accuracy, depth, knowledge and understanding, logic, questioning, reflection and quality to (analysis/evaluation)
Example Question:
Deduce: Draw conclusions
Example Question:
Define: State meaning and identify essential qualities
Example Question:
Demonstrate: Show by example
Example Question:
Describe: Provide characteristics and features
Example Question:
Discuss: Identify issues and provide points for and/or against
Example Question:
Distinguish: Recognise or note/indicate as being distinct or different from; to note differences between
Example Question:
Evaluate: Make a judgement based on criteria; determine the valuof
Example Question:
Examine: Inquire into
Example Question:
Explain: Relate cause and effect; make the relationships betweethings evident; provide why and/or how
Example Question:
Extract: Choose relevant and/or appropriate details
Example Question:
Extrapolate: Infer from what is known
Example Question:
Identify: Recognise and name
Example Question:
Interpret: Draw meaning from
Example Question:
Investigate: Plan, inquire into and draw conclusions about
Example Question:
Justify: Support an argument or conclusion
Example Question:
Outline: Sketch in general terms; indicate the main features of
Example Question:
Predict: Suggest what may happen based on available information
Example Question:
Propose: Put forward (for example a point of view, idea, argument or suggestion) for consideration or action
Example Question:
Recall: Present remembered ideas, facts or experiences
Example Question:
Recommend: Provide reasons in favour
Example Question:
Recount: Retell a series of events
Example Question:
Summarise: Express concisely the relevant details
Example Question:
Synthesise: Putting together various elements to make a whole
Example Question:

### References

http://www.curriculumsupport.education.nsw.gov.au/policies/gats/assets/pdf/usci6keywords.pdf
# HSC Mathematics Advanced, Extension 1, and Extension 2

This book covers the New South Wales mathematics syllabi for Advanced, Extension 1 and Extension 2 levels. This aims to be a comprehensive guide to the course and heavily encourages contributions to improve its usefulness and keep it current in the face of more syllabus changes.

## Outline
### Advanced course (assumed knowledge for both Extensions)
#### Preliminary

* Basic arithmetic and algebra
* Real functions
* Trigonometric ratios
* Linear functions
* The quadratic polynomial and the parabola
* Plane geometry — geometrical properties
* Tangent to a curve and derivative of a function

#### HSC

* Coordinate methods in geometry
* Applications of geometrical properties
* Geometrical applications of differentiation
* Integration
* Trigonometric functions (including applications of trigonometric ratios)
* Exponential and logarithmic functions
* Applications of calculus to the physical world
* Probability
* Series and series applications

### Extension 1 course

* Graphs
* Complex numbers
* Conics
* Integration
* Volumes
* Mechanics
* Polynomials
* Harder 3-Unit Topics
* /4-Unit/Mathematical inductions

#### Preliminary

* Other inequalities
* Circle geometry
* Further trigonometry (sums and differences, t-formulae, identities and equations)
* Lines and linear functions
* Internal and external division of lines into given ratios
* Parametric representation
* Permutations and combinations
* Polynomials
* Harder applications of the Preliminary 2-Unit course

#### HSC

* Methods of integration
* Primitive of sin²α and cos²α
* Equation dN / dt = k(N - P)
* Projectile motion
* Further probability
* Iterative methods for numerical estimation of the roots of a polynomial equation
* Harder applications of HSC 2-Unit topics
# What you need to know

(d) explain why data is represented in computer systems in binary form (e) understand and produce simple logic diagrams using the operations NOT, AND and OR (f) produce a truth table from a given logic diagram.

# These items are covered on the following pages

* Introduction to Binary
* Logic Diagrams
* Truth Tables