Key Formulas | Class 9 — Science

01

Exploration

SI unit of length: metre (m) | SI unit of mass: kilogram (kg)

SI unit of time: second (s) | SI unit of temperature: kelvin (K)

Density = Mass / Volume | Speed = Distance / Time

1 km = 1000 m | 1 m = 100 cm | 1 cm = 10 mm

02

Cell

Magnification = Image size / Object size

Diffusion: movement of particles from high to low concentration

Osmosis: movement of solvent through semi-permeable membrane from low to high solute concentration

Plasmolysis: shrinkage of plant cell in hypertonic solution

Cell wall: present in plant cells, made of cellulose | Cell membrane: selectively permeable

03

Tissues in Action

Xylem: transports water and minerals from roots to leaves

Phloem: transports food from leaves to other parts

Neuron: cell body + dendrites + axon

Blood = plasma + RBC + WBC + platelets

04

Describing Motion

Speed = Distance / Time | Velocity = Displacement / Time

Acceleration: a = (v - u) / t

First equation: v = u + at

Second equation: s = ut + (1/2)at^2

Third equation: v^2 = u^2 + 2as

Uniform circular motion: v = 2πr / T

SI unit of speed/velocity: m/s | SI unit of acceleration: m/s^2

05

Exploring Mixtures and their Separation

Mass percent of solute = (mass of solute / mass of solution) × 100

Volume percent = (volume of solute / volume of solution) × 100

Density = mass / volume

Solubility = grams of solute per 100 g of solvent at a given temperature

06

How Forces Affect Motion

Newton's second law: F = m × a | Unit of force: newton (N)

Momentum: p = m × v | Unit of momentum: kg m/s

Conservation of momentum: m1u1 + m2u2 = m1v1 + m2v2

Weight: W = m × g, where g = 9.8 m/s²

Gravitational force: F = G m1 m2 / r² (G = 6.67×10^-11 N m²/kg²)

Pressure: P = F / A

07

Work, Energy and Simple Machines

Work: W = F × s × cos θ | Unit: joule (J)

Kinetic energy: KE = (1/2)mv^2

Potential energy: PE = mgh

Conservation of energy: Total energy = constant

Power: P = W / t | Unit: watt (W) | 1 kW = 1000 W

1 kWh = 3.6 × 10^6 J

Mechanical advantage = Load / Effort

08

Journey Inside the Atom

Atomic number (Z) = number of protons

Mass number (A) = protons + neutrons | Neutrons = A - Z

Isotopes: same Z, different A | Isobars: different Z, same A

Maximum electrons in shell n: 2n^2 | K(n=1): 2 | L(n=2): 8 | M(n=3): 18

Valency = electrons gained, lost or shared

09

Atomic Foundations of Matter

Avogadro number N_A = 6.022 × 10^23

Moles n = Mass of substance / Molar mass

Number of particles = n × N_A

Molar mass of H2O = 18 g/mol

1 mole of any gas at STP = 22.4 L

Molecular mass = sum of atomic masses in the molecule

10

Sound Waves: Characteristics and Applications

Speed of wave: v = f × λ | Time period: T = 1/f

Unit of frequency: hertz (Hz)

Speed of sound in air at 20°C ≈ 343 m/s

For echo: minimum distance from reflector = 17.2 m

SONAR: d = (v × t) / 2

Audible range for humans: 20 Hz to 20,000 Hz | Ultrasound: > 20,000 Hz

11

Reproduction: How Life Continues

Chromosome number in human gametes: 23 (haploid)

Chromosome number in human zygote: 46 (diploid)

Gestation period in humans: about 9 months

Fertilisation: fusion of male and female gametes to form zygote

12

Patterns in Life: Diversity and Classification

Hierarchy: Kingdom > Phylum (Division in plants) > Class > Order > Family > Genus > Species

Binomial nomenclature by Carolus Linnaeus: Genus species (e.g., Homo sapiens)

Five kingdoms proposed by R.H. Whittaker (1969)

13

Earth as a System: Energy, Matter and Life

Greenhouse gases: CO2, CH4, N2O, water vapour

Atmosphere composition: N2 (78%), O2 (21%), others (1%)

Major cycles: water, carbon, nitrogen, oxygen

Class 9 — Science — Formulas