Notes, summaries, assignments, exams, and problems for Secondary education

MEGA CHEAT SHEET

1. Programming Fundamentals

Software Development Life Cycle (SDLC)

Steps: Requirements → Specifications → Design → Development → Integration → Testing/Debugging → Installation → Maintenance.

Mnemonic: Really Smart Developers In Tech Install Machines.

Algorithms

• Control Structures:
  • Sequence (In Order)
  • Selection (If/Else)
  • Iteration (Loops)
• Design Strategies: Divide and Conquer, Backtracking.
• Representations: Pseudocode, Flowcharts, Structure Charts, Abstraction Diagrams.
• Checking: Identify Input/Output, Purpose, Desk Check with data.

Programming Paradigms

• Imperative: Step-by-step instructions (e.g., Python).
• OOP: Objects and classes (e.g., Java, Python).
• Logic: Facts and rules (e.g., Prolog).
• Functional: Pure functions, no state

You requested the full list of major probability distributions used in computational statistics, machine learning, and data science. Below is a classification with key examples.

Types of Probability Distributions

1. Discrete Distributions (Countable Outcomes)

• Bernoulli Distribution: Binary outcome (0 or 1, e.g., a coin toss).
• Binomial Distribution: Number of successes in n independent trials.
• Negative Binomial Distribution: Number of trials required to achieve k successes.
• Geometric Distribution: Number of trials until the first success.
• Poisson Distribution: Number of events occurring in a fixed interval of time or space.
• Multinomial Distribution: Generalization of the binomial distribution for multiple categories.
• Discrete Uniform Distribution: Each

Properties of Sets

Important Set Formulas

• n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
• If A and B are disjoint: n(A ∪ B) = n(A) + n(B)
• Number of subsets of a set with n elements = 2ⁿ
• Number of proper subsets = 2ⁿ – 1
• n(P(A)) = 2ⁿ

1. Identity Function

f(x) = x

• Graph: Straight line through origin
• Line: y = x
• Domain & Range: ℝ
• Passes through: (0, 0), (1, 1), (-1, -1)

2. Constant Function

f(... Continue reading "Essential Mathematical Formulas: Sets, Functions, and Trigonometry" »

Mammalian Gas Exchange: Lungs and Adaptations

Most mammals live on land, meaning they breathe in oxygen through the air. They are at risk of desiccation; therefore, their gas exchange system, the lungs, is found deep inside their bodies to avoid water loss. Air has a relatively high oxygen concentration of approximately 21% and is easy to ventilate.

Mammalian Respiratory Mechanism

Air enters the lungs through the trachea, which then splits into two bronchi, and further separates into smaller bronchioles. These tubes are held open by rings of cartilage. At the end of the bronchioles are the alveoli, the primary sites of gas exchange. Each alveolus is surrounded by capillaries, facilitating the diffusion of gases between the air and the blood. Mammals... Continue reading "Comparative Gas Exchange: Mammals, Fish, and Insects" »

Electrostatics Fundamentals

This document covers key concepts in electrostatics, including properties of electric charge, Coulomb's Law, and electric fields.

Properties of Electric Charge

Here are four fundamental properties of electric charge:

1. Additivity of Charges: The total charge of a system is the algebraic sum of all individual charges present in the system.
2. Conservation of Charge: The total charge of an isolated system remains unchanged over time. Charge can neither be created nor destroyed, only transferred.
3. Quantization of Charge: The total charge of a body is always an integral multiple of a basic quantum of charge, denoted as 'e'. This means charge q can only exist as q = ±ne, where n is an integer (1, 2, 3, ...).
4. Interaction of Charges:

Decolonization: A Global Transformation

Decolonization was the historical process through which the Asian and African colonies of European Empires gained independence between 1945 and 1975. As a consequence, the Third World appeared, a bloc of former colonies not aligned with the US or the Soviet Union.

Causes of Decolonization

Metropolitan Causes

The causes originated both within the European empires and in the colonies.

• Increasing Awareness: European empires fought against the Axis powers for freedom and democracy and could no longer justify their colonial domination ideologically.
• Economic Factors: After the war, the metropolitan powers lacked sufficient military and economic resources to control their colonies; furthermore, it was no longer profitable.

Chapter 7: Generating Electricity

DC motors convert electrical energy into kinetic energy. Magnetic flux is the amount of magnetic field flowing through a given area, determined by the density of field lines and the surface area. Two factors affect magnetic flux: 1. Area and 2. Magnetic field strength.

Faraday's law states that a changing magnetic flux in a conducting loop or coil induces an electromotive force (EMF) with a magnitude proportional to the rate of change of magnetic flux. Electromagnetic induction occurs when the magnetic flux through a loop changes over time, creating a potential difference. This induces a current in the loop.

The EMF graph is negative when the magnetic flux graph has a positive gradient, and vice versa. Lenz's

1. Tsarist Russia at the Beginning of the 20th Century

• The Russian Empire had about 150 million people, living across a vast and unevenly populated territory with great ethnic and cultural diversity.
• The economy was based on agriculture, with only slow industrial development; most of the population lived in poverty.
• It was an autocratic monarchy: the Tsar held absolute power, supported by the Orthodox Church, the feudal aristocracy, and a corrupt bureaucracy.
• Political opposition developed within the educated elite, inspired by liberal and Marxist ideas. In 1898 the Russian Social Democratic Labour Party was founded.
• 1903: split into Bolsheviks (radical revolutionaries, led by Lenin) and Mensheviks (more moderate, led by Julius Martov).
• Grigory Rasputin,

The Menstrual and Ovarian Cycles

Menstruation: This phase begins on the first day of the cycle and lasts 5 to 7 days. If fertilization does not occur, the corpus luteum breaks down and stops producing progesterone. This causes the endometrium to shed, along with the oocyte, resulting in menstruation. If fertilization occurs, the embryo produces a hormone similar to LH (Luteinizing Hormone) to keep the corpus luteum active. It continues producing hormones, preventing menstruation. The oocyte is fertilized and completes oogenesis.

Proliferative Phase: This starts after menstruation and lasts until ovulation. Estrogens from the ovarian follicle stimulate the thickening of the endometrium and the growth of blood vessels.

Secretory Phase: This occurs... Continue reading "Menstrual and Ovarian Cycle Phases and Hormonal Changes" »

Artistic Masterpieces & Cultural Venues

Famous Paintings of the World

• Mona Lisa by Leonardo da Vinci

  Value: This painting is a symbol of the Renaissance and reflects the genius of da Vinci and the mystery of the female portrait.

• The Starry Night by Vincent van Gogh

  Value: It shows emotional perception of nature and is important for understanding Post-Impressionism.

• Guernica by Pablo Picasso

  Value: This painting symbolizes anti-war protest and reflects the horror of the bombing of Guernica in 1937.

Famous Paintings of Russia

• The Ninth Wave by Ivan Aivazovsky

  Value: This painting shows the beauty of Russian seas and expresses the strong character of the Russian spirit.

• Morning in a Pine Forest by Ivan Shishkin

  Value: It illustrates the beauty of Russian