Math Functions and Proportions Quiz

Functions

• A function relates two sets of numbers or variables
• Each input is linked to exactly one output
• Example: y = 2x + 3, input x, get specific y

Proportion

• Proportion describes relationship between two quantities
• Their ratio is constant
• Example: y is directly proportional to x, written as y = kx (k is constant)
• If x doubles, y also doubles

Inverse Proportion

• Inverse proportion shows one quantity increasing as the other decreases
• Example: y is inversely proportional to x, written as y = k/x (k is constant)
• If x doubles, y is halved

Applying Proportion and Inverse Proportion

• Direct Proportion: Quantities increase/decrease together (e.g., more apples, higher cost)
• Inverse Proportion: One quantity decreases as the other increases (e.g., speed and time to travel a fixed distance)
• Proportional: y=ax a=x/y x=y/a
• Inverse Proportional: y=a/x a=xy x=a/y

Light and Reflection

• Light travels in straight lines; can be reflected, refracted, or absorbed
• Reflection: Light bounces off a surface; angle of incidence equals angle of reflection
• Mirrors: Create virtual images of same size, behind the mirror

Refraction and Total Internal Reflection

• Refraction: Light bends passing from one medium to another (e.g., air to water)
• Speed changes in different media
• Total Internal Reflection: Light reflects entirely within a medium; hits the boundary at an angle greater than the critical angle

Colours of Light

• White light is a spectrum of colours
• Prism splits white light into component colours (red, orange, yellow, green, blue, indigo, violet)

Lenses, Focal Point, and Focal Length

• Lenses: Transparent objects that refract light to converge or diverge light rays
• Focal Point: Point where light rays converge after passing through a lens
• Focal Length: Distance between lens and focal point

Convex Lens and Optical Drawings

• Convex lens: Thicker in the middle than at edges; converges light rays to a focal point
• Optical drawings: Diagrams illustrating light ray interaction with lenses and mirrors

Waves and Sound

• Waves: Transfer energy from one place to another
• Sound: travels as waves through a medium (air, water, solids)
• Speed of Sound: Faster in solids than liquids/gases
• Volume (Amplitude): Sound's loudness (height of wave)
• Pitch (Frequency): Sound's highness/lowness (number of waves per second)

Oscilloscopes and Sound Experiments

• Oscilloscopes: Visualize sound waves (amplitude and frequency)
• Sound Experiments: Investigate sound wave behavior (tuning forks, measuring sound speed)

Applications of Sound

• Uses of sound in technology and everyday life (ultrasound in medicine, sonar)

Forces and Representation

• Forces: Pushes or pulls causing motion change (gravity, friction, magnetism)
• Diagrams: Show force direction and magnitude (arrows)

Refraction

• Bending of light when passing from one medium to another.
• Speed of light changes in different mediums.
• Angle of incidence and refraction are important factors.
• Snell's Law describes the relationship between angles of incidence and refraction.

Practical Applications of Refraction

• Lenses in glasses, cameras, microscopes.
• Prisms for splitting light into spectrum.
• Optical fibers for communication

History of Early China

• Agriculture, Philosophy, Religion, Art, and Architecture played a role in early Chinese life.
• Qin and Han Dynasties had significant developments.

Geography and History of South Asia

• Indus Valley Civilization and Aryan Migration were early developments.
• Notable empires like Maurya and Gupta shaped South Asia's development

Islamic Influence

• Islamic Empires impacted South Asian culture, architecture, and society during the medieval period.

Life in South Asia

• Geography (mountains, rivers, plains) influenced agriculture, daily life, and cultural diversity
• Agriculture (monsoon rains crucial).
• Cultural diversity (multiple languages, religions - Hinduism, Buddhism, Islam, Sikhism).

Analysis: Compare and Contrast Confucianism and Daoism

• Confucianism: Emphasizes moral virtues, social harmony, filial piety, humaneness, and education. Focus is on social roles and responsibilities, striving for ethical behavior for societal order.
• Daoism: Emphasizes living in harmony with the Dao (the Way), a fundamental principle underlaying the universe. Wu Wei (non-action), simplicity and spontaneity are key. Focus is on aligning oneself with the natural order.

Evaluation of Philosophies

• Confucianism emphasizes social order and ethical behavior, potentially creating stable society.
• Daoism emphasizes harmony and simplicity. Integrating Daoist principles with strong central authority and maintaining order (Legalism) could create effective governance.

Education and Meritocracy

• Establishing a system where officials are chosen based on knowledge/moral integrity.
• Promoting ethical behavior and moral education among citizens.
• Daoism's simplicity and non-interference also influence governance policies promoting harmony/simplicity and reducing bureaucracy

Legalism

• Clear laws and consistent enforcement for order.
• Strong central authority for effectively implementing policies.

Major Chinese Thinkers

• Confucius, Laozi, Han Feizi influenced society's and governance structure.
• Confucianism: Morality, social relations, justice.
• Daoism: Simplicity, harmony with the Dao.
• Legalism: Strict laws and order.

Confucianism and Society

• Confucius advocated for accessible education to foster virtue and civic responsibility
• Overview explores early Chinese society's structure, social classes, gender roles, and developments during the Qin and Han dynasties.