🔬 CBSE 2026–27 · Subject Code 086 · 80 Marks

Science Syllabus Tracker

Physics · Chemistry · Biology · Earth Science. Sub-topics with key concepts, formulas & reverse formulas.

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Unit I — BiologyWorld of Living4 ch · Ch 2–12 · 27 marks · 50 periods
Ch 2The Cell — Structure and Function
Discovery of cell, plant vs animal cell, organelles, osmosis, cell division
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2.1Discovery of cell and cell theory
  • Robert Hooke (1665) first observed cells in cork using a microscope — saw box-like chambers.
  • Anton van Leeuwenhoek discovered living cells (bacteria and protists) — called them "animalcules".
  • Cell Theory (Schleiden, Schwann, Virchow): (1) all living things are made of cells; (2) cell is the basic unit; (3) cells arise from pre-existing cells.
  • Exceptions to cell theory: viruses (non-cellular), RBCs (no nucleus in humans).
Formulas & Key Relations
Cell size range1–100 μm typically
MagnificationM = Image size / Object size
Reverse — object sizeObject size = Image size / M
2.2Prokaryotic vs Eukaryotic cells
  • Prokaryotic: no membrane-bound nucleus; DNA is naked in the nucleoid region; no membrane-bound organelles. Examples: bacteria, blue-green algae.
  • Eukaryotic: true membrane-bound nucleus; complex organelles. Examples: plant, animal, fungal cells.
  • Key distinction: nuclear membrane present in eukaryotes; absent in prokaryotes.
  • Prokaryotes are generally smaller (1–10 μm) than eukaryotes (10–100 μm).
2.3Plant cell vs Animal cell
  • Plant cell has: cell wall (cellulose), chloroplasts, large central vacuole, plasmodesmata.
  • Animal cell has: centrioles (for cell division), lysosomes prominent, no cell wall or chloroplasts.
  • Both have: cell membrane, nucleus, mitochondria, ER, ribosomes, Golgi apparatus.
  • Vacuoles: large and permanent in plant cells; small and temporary in animal cells.
2.4Cell organelles — structure and function
  • Nucleus: control centre; contains DNA; bounded by double nuclear membrane with nuclear pores; nucleolus makes rRNA.
  • Mitochondria: "powerhouse of the cell"; site of aerobic respiration; has its own DNA; double membrane (outer smooth, inner folded into cristae).
  • Chloroplast: site of photosynthesis; has thylakoids (where light reactions occur) stacked into grana; stroma for dark reactions; contains chlorophyll.
  • Endoplasmic Reticulum (ER): Rough ER has ribosomes — makes proteins; Smooth ER makes lipids, detoxification.
  • Golgi apparatus: sorts, packages and dispatches proteins and lipids; makes lysosomes.
  • Lysosomes: "suicide bags"; contain digestive enzymes; destroy worn-out organelles and pathogens.
  • Vacuoles: storage organelles; maintain turgor pressure in plants.
  • Ribosomes: site of protein synthesis; found free in cytoplasm and on rough ER; no membrane.
Formulas & Key Relations
Photosynthesis (overall)6CO2 + 6H2O →(light) C6H12O6 + 6O2
Aerobic respirationC6H12O6 + 6O2 → 6CO2 + 6H2O + Energy
2.5Cell membrane — semi-permeability and osmosis
  • Cell membrane is selectively (semi-) permeable — allows small molecules (water, O₂) but blocks large ones.
  • Osmosis: movement of water molecules through a semi-permeable membrane from a region of higher water concentration (lower solute) to lower water concentration (higher solute).
  • Turgor pressure: pressure exerted by water inside a plant cell against its cell wall — keeps plants rigid.
  • Plasmolysis: when a plant cell is placed in hypertonic solution, water leaves and cell membrane shrinks away from cell wall.
  • Turgid cell: hypotonic solution → water enters → cell swells (plant stays firm). Flaccid cell: hypertonic → water leaves → cell wilts.
Formulas & Key Relations
Osmotic pressureHigher solute conc → higher osmotic pressure
Water potentialWater moves: high water potential → low water potential
Turgor pressureTurgor = Osmotic pressure − Wall pressure— In turgid cell
2.6Cell division — Mitosis and Meiosis
  • Mitosis: division producing 2 identical daughter cells (same chromosome number); for growth and repair. Phases: Prophase, Metaphase, Anaphase, Telophase + Cytokinesis.
  • Meiosis: reduction division producing 4 genetically diverse cells with half the chromosome number; for sexual reproduction (gamete formation).
  • Interphase (S phase): DNA replication occurs; chromosomes duplicate.
  • Meiosis I separates homologous chromosomes; Meiosis II separates sister chromatids.
  • Crossing over during Meiosis I (Prophase I) creates genetic variation.
  • Cancer: uncontrolled mitosis due to mutations in cell cycle control genes (proto-oncogenes → oncogenes).
Formulas & Key Relations
Chromosome number after mitosis2n → 2n (unchanged)
Chromosome number after meiosis2n → n (halved)
Reverse — zygoten + n → 2n (fertilisation restores)
Ch 3Tissues
Plant tissues (meristematic, permanent), animal tissues (epithelial, connective, muscular, nervous)
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3.1Introduction to tissues and levels of organisation
  • Tissue: a group of cells with similar structure and function working together.
  • Levels of organisation: cell → tissue → organ → organ system → organism.
  • Division of labour: multicellular organisms have specialised tissues — allows efficiency.
  • Plants have two main tissue types: meristematic (dividing) and permanent (non-dividing).
  • Animals have four main tissue types: epithelial, connective, muscular, nervous.
3.2Meristematic tissues
  • Meristematic tissue: actively dividing cells with large nuclei, thin walls, no vacuoles.
  • Apical meristem: at tips of roots and shoots → causes increase in length (primary growth).
  • Lateral meristem (cambium): in the cylinder of stems → causes increase in girth (secondary growth).
  • Intercalary meristem: at the base of leaves/internodes → regrowth after grazing.
3.3Permanent plant tissues
  • Simple permanent tissues: parenchyma (thin-walled, loosely packed, photosynthesis and storage), collenchyma (thickened corners, flexibility), sclerenchyma (thick lignified walls, dead at maturity, support).
  • Complex permanent tissues — Xylem: conducts water and minerals upward; consists of tracheids, vessels, xylem parenchyma, xylem fibres.
  • Phloem: conducts food (sugars) from leaves to all parts; consists of sieve tubes, companion cells, phloem parenchyma, phloem fibres.
  • Epidermis: outermost protective layer; stomata for gas exchange; root hair cells for water absorption.
3.4Animal tissues — Epithelial
  • Epithelial tissue: covers body surfaces and lines cavities; cells tightly packed with little intercellular space; basement membrane below.
  • Simple squamous: flat, thin; forms lining of blood vessels, alveoli; allows diffusion.
  • Cuboidal: cube-shaped; found in kidney tubules, glands; secretion and absorption.
  • Columnar: tall; lines intestines; absorption and secretion.
  • Ciliated columnar: has cilia (hair-like); lines respiratory tract; sweeps mucus and dust.
  • Stratified squamous: multiple layers; skin epidermis; protection against wear and tear.
3.5Animal tissues — Connective
  • Connective tissue: cells embedded in an intercellular matrix (ground substance + fibres).
  • Areolar: loose connective tissue; fills spaces between organs; contains collagen and elastic fibres.
  • Dense (tendon, ligament): collagen fibres tightly packed; tendons join muscle to bone; ligaments join bone to bone.
  • Adipose (fat): stores fat; insulation and energy reserve.
  • Bone: hard matrix (calcium phosphate + collagen); Haversian system; bone cells = osteocytes.
  • Cartilage: flexible matrix (chondroitin sulphate); cartilage cells = chondrocytes; found in ear pinna, nose tip, larynx, between bones.
  • Blood: liquid connective tissue; plasma + RBCs + WBCs + platelets.
3.6Animal tissues — Muscular and Nervous
  • Striated (skeletal) muscle: voluntary; attached to bones; multinucleated; dark and light bands (striations) due to actin and myosin arrangement.
  • Smooth (unstriated) muscle: involuntary; walls of hollow organs (stomach, intestine, blood vessels); spindle-shaped, single nucleus.
  • Cardiac muscle: involuntary, striated; heart only; never fatigues; intercalated discs for synchronised contraction.
  • Nervous tissue: neurons (nerve cells) — have cell body (cyton), dendrites (receive signals), axon (transmit signals); covered by myelin sheath.
  • Nerve impulse travels along axon by electrochemical signals at ~100 m/s in myelinated neurons.
Formulas & Key Relations
Nerve impulse speed (myelinated)≈ 70–120 m/s
Nerve impulse speed (unmyelinated)≈ 0.5–2 m/s
Ch 11Reproduction
Asexual and sexual reproduction, flowering plant reproduction, human reproductive systems
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11.1Introduction to reproduction
  • Reproduction: biological process by which organisms produce offspring to continue their species.
  • Asexual reproduction: single parent; no fertilisation; offspring genetically identical (clones); faster.
  • Sexual reproduction: two parents; gametes fuse; genetic variation in offspring; slower but more adaptable.
  • Asexual types: fission (Amoeba — binary; Plasmodium — multiple), budding (Hydra, yeast), spore formation (Rhizopus/bread mould), fragmentation (Spirogyra), regeneration (Planaria), vegetative propagation (plants).
11.2Sexual reproduction in flowering plants
  • Flower: reproductive organ of angiosperms. Parts: sepals (calyx), petals (corolla), stamens (androecium = male), carpels/pistil (gynoecium = female).
  • Stamen: filament + anther (produces pollen grains — male gametes).
  • Pistil: stigma (receives pollen) + style + ovary (contains ovules with egg cells).
  • Pollination: transfer of pollen from anther to stigma. Self-pollination (same flower) vs Cross-pollination (different flower, by wind/insects/water).
  • Fertilisation: pollen germinates on stigma; pollen tube grows down style to ovule; male nucleus fuses with egg cell → zygote.
  • Double fertilisation (unique to angiosperms): one nucleus fertilises egg (→ zygote → embryo); other fuses with polar nuclei (→ endosperm = food for embryo).
  • After fertilisation: ovule → seed; ovary → fruit; zygote → embryo.
  • Seed dispersal: by wind (dandelion — light, feathery), water (coconut — buoyant), animals (bur — hooks), explosion (touch-me-not).
11.3Human male reproductive system
  • Testes: produce sperm (spermatogenesis) and testosterone; kept in scrotum (2–3°C below body temp for sperm viability).
  • Epididymis: sperm storage and maturation.
  • Vas deferens: carries sperm from epididymis to urethra.
  • Seminal vesicles + prostate gland: secrete fluids forming semen (nourish sperm, provide medium).
  • Urethra: common passage for urine and semen (not simultaneously).
  • Sperm structure: head (nucleus with 23 chromosomes + acrosome to penetrate egg), midpiece (mitochondria for energy), tail (flagellum for movement).
Formulas & Key Relations
Sperm count (normal)≥ 15 million/mL
Duration of spermatogenesis≈ 74 days
11.4Human female reproductive system
  • Ovaries: produce eggs (oogenesis) and hormones (oestrogen, progesterone); one egg released per month (ovulation).
  • Fallopian tubes (oviducts): carry egg from ovary to uterus; site of fertilisation.
  • Uterus: site of implantation and fetal development; muscular wall (myometrium), inner lining (endometrium).
  • Cervix: lower narrow end of uterus.
  • Vagina: birth canal and passage for menstrual flow.
  • Menstrual cycle: 28-day cycle; Day 1–5 = menstruation; Day 6–13 = follicular phase; Day 14 = ovulation; Day 15–28 = luteal phase.
Formulas & Key Relations
Menstrual cycle≈ 28 days
Ovulation day≈ Day 14 of cycle
Gestation period (human)≈ 280 days (40 weeks)
11.5Reproductive health and birth control
  • Sexually transmitted infections (STIs): HIV/AIDS, gonorrhoea, syphilis — prevent by safe sex practices.
  • Contraception methods: barrier (condom — also prevents STIs, diaphragm), hormonal (oral pills — oestrogen/progesterone), intrauterine devices (IUDs), surgical (vasectomy, tubectomy).
  • Importance of family planning: population control, maternal health, child welfare.
  • Natural method: calendar method (avoid sex during fertile days around ovulation).
Ch 12Diversity in Living Organisms
Five kingdoms, classification, binomial nomenclature, major groups of plants and animals
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12.1Need for and basis of classification
  • Classification organises the vast diversity of life into manageable groups based on similarities.
  • Aristotle (first classifier): divided animals into those with and without red blood.
  • Whittaker (1969): proposed Five Kingdom classification based on cell structure, nutrition, body organisation.
  • Three-domain system (modern): Bacteria, Archaea, Eukarya — based on molecular (rRNA) evidence.
  • Taxonomy: science of classification. Taxonomic hierarchy: Kingdom → Phylum → Class → Order → Family → Genus → Species.
Formulas & Key Relations
Hierarchy mnemonicKing Phillip Came Over For Good Spaghetti
12.2Five kingdoms and their key features
  • Monera: prokaryotic; unicellular; no nuclear membrane. Examples: Bacteria (Lactobacillus, Vibrio), Cyanobacteria (blue-green algae).
  • Protista: eukaryotic; mostly unicellular; some multicellular; diverse nutrition. Examples: Amoeba, Paramecium, Euglena, Plasmodium, diatoms, Spirogyra.
  • Fungi: eukaryotic; mostly multicellular (except yeast); heterotrophic (saprophytic or parasitic); cell wall of chitin; reproduce by spores. Examples: Rhizopus, mushrooms, Penicillium, Aspergillus.
  • Plantae: eukaryotic; multicellular; autotrophic (photosynthetic); cell wall of cellulose; embryo development inside female organ.
  • Animalia: eukaryotic; multicellular; heterotrophic; no cell wall; motile; embryonic development.
12.3Major plant groups (Plant Kingdom)
  • Thallophyta (Algae): no distinct root, stem, leaf; live in water; e.g. Spirogyra, Chara, Ulothrix.
  • Bryophyta (Mosses and Liverworts): first land plants; no vascular tissue; need water for reproduction; e.g. Moss (Funaria), Marchantia.
  • Pteridophyta (Ferns): vascular tissue (xylem and phloem); no seeds; reproduce by spores; e.g. Fern, Horsetail (Equisetum).
  • Gymnosperms: vascular; seeds not enclosed in fruit (naked seeds); conifer trees; e.g. Pine (Pinus), Cycas, Deodar.
  • Angiosperms: vascular; seeds enclosed in fruit (flowering plants); divided into Monocots (one cotyledon, parallel venation) and Dicots (two cotyledons, reticulate venation).
12.4Major animal groups (Animal Kingdom)
  • Porifera (sponges): pores all over body; non-motile; water canal system; e.g. Sycon, Spongilla.
  • Coelenterata (Cnidaria): radial symmetry; body cavity (coelenteron); stinging cells (nematocysts); e.g. Hydra, jellyfish, sea anemone, coral.
  • Platyhelminthes: flat worms; bilaterally symmetric; no body cavity (acoelomate); parasitic mostly; e.g. tapeworm, Planaria.
  • Nematoda: round worms; pseudocoelom; parasites causing diseases; e.g. Ascaris (roundworm), filarial worm.
  • Annelida: segmented body (metameres); true coelom; e.g. earthworm, leech, Nereis.
  • Arthropoda: exoskeleton (chitin); jointed appendages; largest phylum; e.g. insects (butterfly, cockroach), crustaceans (prawn), arachnids (spider), myriapods (centipede).
  • Mollusca: soft body; mantle; most have shell; e.g. snail, octopus, squid, clam.
  • Echinodermata: spiny skin; water vascular system; radial symmetry in adults; e.g. starfish, sea urchin, sea cucumber.
  • Chordata: notochord at some stage; dorsal nerve cord; pharyngeal slits. Vertebrata: backbone; fish (bony/cartilaginous), amphibia, reptilia, aves (birds), mammalia.
12.5Binomial nomenclature
  • Binomial nomenclature: every species given two-part Latin name. Proposed by Carl Linnaeus (1753).
  • Format: Genus species (Genus capitalised, species lowercase, both italicised when typed, underlined when handwritten).
  • Examples: Homo sapiens (human), Mangifera indica (mango), Felis catus (cat), Rana tigrina (frog).
  • Rules: ICBN (plants), ICZN (animals) govern nomenclature.
12.6Viruses — acellular entities
  • Viruses are not cellular — they are on the boundary between living and non-living.
  • Structure: nucleic acid core (DNA or RNA, never both) + protein coat (capsid). Some have lipid envelope.
  • Reproduce only inside a living host cell (obligate intracellular parasites).
  • Diseases: common cold (rhinovirus), influenza, HIV/AIDS, rabies, polio, COVID-19, hepatitis.
  • Bacteriophage: virus that infects bacteria — used in molecular biology research.
Unit II — ChemistryMatter — Its Nature and Behaviour3 ch · Ch 5–9 · 25 marks · 40 periods
Ch 5Exploring Mixtures and their Separation
Mixtures, solutions, colloids, suspensions, separation techniques, concentration
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5.1Pure substances vs Mixtures
  • Pure substance: fixed composition; definite properties; either element or compound.
  • Mixture: two or more substances combined in any proportion; no chemical change; properties of components retained.
  • Homogeneous mixture (solution): uniform composition throughout; single phase; e.g. saltwater, alloy, air.
  • Heterogeneous mixture: non-uniform composition; two or more visible phases; e.g. sand + water, oil + water.
Formulas & Key Relations
Mass fractionwA = mA / (mA + mB)
Mole fractionXA = nA / (nA + nB)
5.2Solutions, suspensions, and colloids
  • Solution: particle size < 1 nm; transparent; does not scatter light; particles do not settle; e.g. sugar solution, copper sulphate solution.
  • Suspension: particle size > 100 nm; opaque; particles settle on standing; can be filtered; e.g. muddy water, chalk in water.
  • Colloid: particle size 1–100 nm; appears homogeneous; shows Tyndall effect; particles do not settle; cannot be filtered; e.g. milk, fog, blood, starch solution.
  • Tyndall effect: scattering of light by colloidal particles — visible as a beam of light through a colloid (e.g. sunlight through fog).
  • Types of colloids: sol (solid in liquid), gel (liquid in solid), aerosol (solid/liquid in gas), emulsion (liquid in liquid), foam (gas in liquid/solid).
Formulas & Key Relations
Particle sizeSolution < 1 nm < Colloid < 100 nm < Suspension
5.3Concentration of solutions
  • Mass by mass percentage: mass of solute per 100 g of solution × 100.
  • Mass by volume percentage: mass of solute (g) per 100 mL of solution × 100.
  • Volume by volume percentage: volume of solute per 100 mL of solution × 100.
  • Solubility: maximum amount of solute that dissolves in 100 g of solvent at a given temperature.
  • Saturated solution: contains maximum dissolved solute at that temperature. Unsaturated: can dissolve more.
Formulas & Key Relations
Mass/mass %w/w% = (msolute / msolution) × 100
Reverse — find m_solutemsolute = (w/w% × msolution) / 100
Mass/volume %w/v% = (msolute (g) / Vsolution (mL)) × 100
Volume/volume %v/v% = (Vsolute / Vsolution) × 100
Reverse — find V_soluteVsolute = (v/v% × Vsolution) / 100
5.4Separation techniques
  • Evaporation: separate soluble solid from liquid (e.g. salt from seawater); liquid evaporates, solid remains.
  • Filtration: separate insoluble solid from liquid using filter paper; retains particles > 0.1 μm.
  • Distillation: separate miscible liquids with different boiling points; liquid vaporises then condenses.
  • Fractional distillation: separates liquids with close boiling points (e.g. crude oil refining, liquid air separation).
  • Paper chromatography: separates solutes based on their differential solubility in a solvent; Rf value = distance travelled by solute / distance travelled by solvent.
  • Crystallisation: purify solids by dissolving in hot water then cooling; impurities stay in solution.
  • Centrifugation: separates by density using rapid spinning (e.g. separating cream from milk, blood cells from plasma).
  • Sublimation: directly converts solid to vapour (and back), bypassing liquid stage; e.g. separate ammonium chloride from salt.
  • Coagulation: adding alum to muddy water — alum neutralises charge on clay particles, they clump and settle.
Formulas & Key Relations
Rf value (chromatography)Rf = Distance moved by solute / Distance moved by solvent
Reverse — find distanceDistance by solute = Rf × Distance by solvent
Ch 9Atoms and Molecules
Laws of chemical combination, Dalton's theory, chemical formulae, molecular mass
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9.1Laws of chemical combination
  • Law of Conservation of Mass (Lavoisier, 1789): in a chemical reaction, total mass of reactants = total mass of products; matter is neither created nor destroyed.
  • Law of Constant (Definite) Proportions (Proust, 1799): a pure chemical compound always contains same elements in the same ratio by mass.
  • Example: water is always 1:8 by mass (H:O), regardless of the source.
Formulas & Key Relations
Conservation of massmreactants = mproducts
Constant proportion (water)H : O = 1 : 8 by mass
VerificationMass before reaction = Mass after reaction
9.2Dalton's Atomic Theory
  • All matter is made of tiny, indivisible particles called atoms.
  • Atoms of the same element are identical in mass and properties; atoms of different elements differ.
  • Compounds are formed by combining atoms of different elements in fixed whole-number ratios.
  • Atoms cannot be created, destroyed, or transformed in chemical reactions — only rearranged.
  • Limitations: atoms are divisible (protons, neutrons, electrons); atoms of same element can have different masses (isotopes); atoms of different elements can have same mass (isobars).
9.3Atoms — symbols and atomic masses
  • Symbol: one or two letters representing an element (first letter capitalised).
  • Atomic mass unit (amu or u): 1 u = 1/12 the mass of a carbon-12 atom = 1.66 × 10-27 kg.
  • Relative atomic mass: average mass of atom compared to 1/12 of C-12.
  • IUPAC symbols for first 18 elements: H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar.
Formulas & Key Relations
1 amu= 1.66 × 10-27 kg
Avogadro numberNA = 6.022 × 1023 mol-1
Molar massMolar mass (g/mol) = Relative atomic/molecular mass in grams
9.4Molecules and chemical formulae
  • Molecule: smallest particle of an element or compound that can exist independently and shows all properties of that substance.
  • Atomicity: number of atoms in one molecule. Monoatomic (noble gases: He, Ne); Diatomic (H₂, O₂, N₂, Cl₂, Br₂, I₂, F₂); Polyatomic (O₃, P₄, S₈).
  • Valency: combining capacity of an element. H = 1; O = 2; N = 3; C = 4; Na = 1; Cl = 1; Ca = 2; Fe = 2,3.
  • Writing formulae: crisscross valencies. Example: Calcium chloride — Ca²⁺, Cl⁻ → CaCl₂.
  • Ionic compounds: formed by transfer of electrons; strong electrostatic attraction; high mp/bp; conduct electricity when dissolved.
  • Covalent compounds: formed by sharing electrons; low mp/bp; do not conduct electricity usually.
Formulas & Key Relations
Formula writing (criss-cross)Am Bn → An Bm (criss-cross valencies)
9.5Molecular mass and molar concept
  • Molecular mass: sum of atomic masses of all atoms in one molecule (in amu).
  • Formula unit mass: used for ionic compounds (e.g. NaCl, 23+35.5=58.5 u).
  • Mole: amount of substance containing 6.022 × 10²³ entities (Avogadro's number NA).
  • 1 mole of any substance has mass equal to its molar mass in grams.
  • 1 mole of any gas at STP occupies 22.4 L (molar volume).
Formulas & Key Relations
Number of molesn = m / M (m=mass given, M=molar mass)
Reverse — find massm = n × M
Number of particlesN = n × NA = (m/M) × 6.022 × 1023
Reverse — find moles from Nn = N / NA
At STP: volumeV = n × 22.4 L
Reverse — find n from Vn = V / 22.4
Ch 8Structure of an Atom
Subatomic particles, atomic models (Thomson, Rutherford, Bohr), electron configuration, valency
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8.1Subatomic particles
  • Electron: discovered by J.J. Thomson (cathode ray experiment, 1897); charge = −1.6 × 10-19 C; mass ≈ 1/1837 u; located in shells around nucleus.
  • Proton: discovered by Goldstein (canal/anode rays, 1886); charge = +1.6 × 10-19 C; mass ≈ 1 u; located in nucleus.
  • Neutron: discovered by James Chadwick (1932); no charge; mass ≈ 1 u; located in nucleus.
  • Atom is electrically neutral: number of protons = number of electrons.
Formulas & Key Relations
Charge of electron−1.6 × 10-19 C
Mass of electron9.11 × 10-31 kg ≈ 1/1837 u
Mass of proton1.673 × 10-27 kg ≈ 1 u
Neutron countN = A − Z (A=mass number, Z=atomic number)
Reverse — find AA = Z + N
8.2Atomic models
  • Thomson's Plum Pudding Model (1904): atom is a sphere of positive charge with electrons embedded in it like plums in a pudding.
  • Rutherford's Nuclear Model (Gold Foil Experiment, 1909–11): most of atom is empty space; tiny, dense, positively charged nucleus at centre; electrons revolve around nucleus.
  • Drawbacks of Rutherford's model: accelerating electrons should emit radiation and spiral into nucleus (unstable); couldn't explain discrete line spectra.
  • Bohr's Model (1913): electrons move in fixed circular orbits (shells) of definite energy; electrons do not radiate energy while in orbit; they absorb or emit energy only when jumping between orbits.
  • Energy of shell increases with shell number: K < L < M < N.
Formulas & Key Relations
Energy of orbit (Bohr)En = −13.6/n2 eV (for hydrogen)
Energy emitted/absorbedΔE = E2 − E1 = hν
Radius of orbit (Bohr)rn = 0.529 × n2 Å (for hydrogen)
8.3Electron distribution in shells
  • Maximum electrons in a shell: given by 2n² (n = shell number). K(n=1): 2; L(n=2): 8; M(n=3): 18; N(n=4): 32.
  • Aufbau principle: electrons fill lower energy shells first.
  • Outermost shell can hold maximum 8 electrons (octet rule).
  • Valence electrons: electrons in the outermost shell — determine chemical properties and valency.
  • Example configurations: Na (2,8,1) → 1 valence electron, valency 1; Cl (2,8,7) → 7 valence electrons, valency 1 (gains 1).
Formulas & Key Relations
Max electrons in shell n2n2
K shell (n=1)2 × 12 = 2
L shell (n=2)2 × 22 = 8
M shell (n=3)2 × 32 = 18
Valency from configValency = 8 − valence electrons (if > 4)
8.4Atomic number, mass number, isotopes, isobars
  • Atomic number (Z): number of protons in nucleus; determines the element.
  • Mass number (A): total number of protons + neutrons in nucleus.
  • Isotopes: atoms of same element with same Z but different A (different neutron numbers). Example: ¹H, ²H (deuterium), ³H (tritium); ¹²C, ¹³C, ¹⁴C.
  • Isobars: atoms of different elements with same A but different Z. Example: ⁴⁰Ca (Z=20) and ⁴⁰Ar (Z=18).
  • Applications of isotopes: ¹⁴C dating (archaeology), ¹³¹I (thyroid cancer treatment), ⁶⁰Co (cancer radiation therapy), ²³⁵U (nuclear fuel).
Formulas & Key Relations
Atomic numberZ = number of protons = number of electrons (neutral atom)
Mass numberA = Z + N (N = neutrons)
Isotope notationAZ X e.g. 126 C
Reverse — find neutronsN = A − Z
8.5Valency and chemical bonding (introduction)
  • Valency: combining capacity; number of electrons an atom loses, gains, or shares to achieve stable octet.
  • Noble gases (He:2, Ne:8, Ar:8) have full outermost shells — chemically inert, valency = 0.
  • Electrovalent (ionic) bonding: electron transfer between metals and non-metals. Metal loses electrons (forms cation), non-metal gains (forms anion).
  • Covalent bonding: electron sharing between two non-metals.
  • Electron dot (Lewis) structures: represent valence electrons as dots around element symbol.
Formulas & Key Relations
Charge on ionCharge = p − e (p=protons, e=electrons remaining)
Ionic formulaMetal cation charge = Non-metal anion charge (balance)
Unit III — PhysicsMotion, Force, Work and Sound4 ch · Ch 4–10 · 23 marks · 50 periods
Ch 4Motion
Displacement, velocity, acceleration, kinematic equations, graphs, uniform circular motion
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4.1Distance and displacement
  • Distance: total path length travelled; scalar quantity; always positive; SI unit = metre (m).
  • Displacement: shortest straight-line distance from initial to final position, with direction; vector quantity; can be positive, negative, or zero.
  • An object can have non-zero distance but zero displacement (e.g. circular path returning to start).
  • Distance ≥ |displacement| always.
Formulas & Key Relations
No formulaDistance is path length; displacement is straight-line vector from start to end
4.2Speed and velocity
  • Speed: distance covered per unit time; scalar; always ≥ 0; unit = m/s.
  • Velocity: displacement per unit time; vector; can be negative; unit = m/s.
  • Average speed = total distance / total time. Average velocity = total displacement / total time.
  • Uniform speed: equal distances in equal time intervals. Non-uniform (variable) speed: unequal distances.
  • Instantaneous velocity: velocity at a specific instant = slope of tangent to position-time graph.
Formulas & Key Relations
Average speedvavg = Total distance / Total time
Average velocityvavg = Total displacement / Total time = Δx / Δt
Reverse — find distanceDistance = Speed × Time
Reverse — find timet = Distance / Speed
4.3Acceleration
  • Acceleration: rate of change of velocity; vector; SI unit = m/s².
  • Positive acceleration: velocity increasing in positive direction (or slowing in negative).
  • Negative acceleration (deceleration/retardation): velocity decreasing.
  • Uniform acceleration: equal changes in velocity in equal time intervals.
  • Zero acceleration: constant velocity (uniform motion).
Formulas & Key Relations
Accelerationa = (v − u) / t (v=final, u=initial velocity)
Reverse — find vv = u + at
Reverse — find uu = v − at
Reverse — find tt = (v − u) / a
4.4Graphical representation of motion
  • Position-time (s-t) graph: slope = velocity. Straight line → uniform velocity; curve → changing velocity; horizontal line → at rest.
  • Velocity-time (v-t) graph: slope = acceleration; area under graph = displacement.
  • Straight line in v-t graph → uniform acceleration; horizontal line → constant velocity.
  • Area of v-t graph: rectangle (uniform velocity) or trapezium/triangle (uniform acceleration).
Formulas & Key Relations
Slope of s-t graphv = Δs / Δt
Slope of v-t grapha = Δv / Δt
Displacement from v-t graphs = Area under v-t graph
Displacement (trapezium)s = (1/2)(u + v) × t
4.5Kinematic equations (derived by graphical method)
  • These three equations describe uniformly accelerated motion in a straight line.
  • First equation: v = u + at — derived from the definition of acceleration.
  • Second equation: s = ut + ½at² — derived from area of v-t graph (triangle + rectangle).
  • Third equation: v² = u² + 2as — derived by eliminating t from first two equations.
  • Conditions: constant acceleration, straight-line motion.
Formulas & Key Relations
First equationv = u + at
Second equations = ut + (1/2)at2
Third equationv2 = u2 + 2as
Reverse — find s (1st+2nd)s = ((u+v)/2) × t
Reverse — find a from v,u,sa = (v2 − u2) / (2s)
Reverse — find t from s,u,at = (−u + √(u2 + 2as)) / a
4.6Uniform circular motion
  • Uniform circular motion: speed is constant but velocity is changing (direction always changes) → there IS acceleration (centripetal acceleration, directed towards centre).
  • The object moves in a circle of radius r with constant speed v.
  • Time period T: time taken for one complete revolution.
  • Frequency f: number of revolutions per second = 1/T.
Formulas & Key Relations
Speed in UCMv = 2πr / T (circumference / period)
Centripetal accelerationac = v2 / r
Frequencyf = 1 / T
Angular velocityω = 2π / T = 2πf
Reverse — find r from v,Tr = vT / (2π)
Ch 6Force and Laws of Motion
Force, Newton's three laws, friction, momentum, conservation of momentum
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6.1Force and its effects
  • Force: push or pull on an object; vector quantity; SI unit = Newton (N) = kg⋅m/s².
  • Effects of force: change speed, change direction, change shape of an object.
  • Balanced forces: net force = 0; object remains at rest or in uniform motion.
  • Unbalanced forces: net force ≠ 0; object accelerates.
  • Types of forces: contact (friction, normal, tension, spring) and non-contact (gravitational, magnetic, electrostatic).
Formulas & Key Relations
Net forceFnet = F1 + F2 + ... (vector sum)
SI unit of force1 N = 1 kg × 1 m/s2
6.2Newton's First Law — Inertia
  • Newton's First Law: an object at rest stays at rest, and an object in motion stays in uniform motion, unless acted upon by an unbalanced external force.
  • This is also called the Law of Inertia.
  • Inertia: tendency of an object to resist changes in its state of motion; directly proportional to mass.
  • Examples: passengers jerk forward when bus stops suddenly; coin falls into glass when card is flicked.
  • Galileo's thought experiment (frictionless inclined plane) led to this law.
Formulas & Key Relations
Condition for equilibriumΣ F = 0 (sum of all forces = 0)
6.3Newton's Second Law and Momentum
  • Momentum (p): quantity of motion = mass × velocity; vector; SI unit = kg⋅m/s.
  • Newton's Second Law: the rate of change of momentum of an object is directly proportional to the net external force applied on it, in the direction of the force.
  • F = ma: force equals mass times acceleration (when mass is constant).
  • Impulse: force × time = change in momentum; J = FΔt = Δp.
Formulas & Key Relations
Momentump = m × v
Newton's Second LawF = ma = m(v−u)/t = Δp/Δt
Reverse — find aa = F / m
Reverse — find mm = F / a
ImpulseJ = F × t = Δp = m(v − u)
Reverse — find F from impulseF = m(v − u) / t
6.4Newton's Third Law
  • Newton's Third Law: for every action, there is an equal and opposite reaction. Forces always come in pairs.
  • Action and reaction forces act on DIFFERENT objects — they do not cancel each other.
  • Examples: rocket propulsion (exhaust gas pushed back, rocket goes forward); swimming (push water back, move forward); gun recoil (bullet forward, gun backward).
  • Walking: foot pushes ground backward (action), ground pushes foot forward (reaction) → we walk.
Formulas & Key Relations
Third LawFAB = −FBA (equal magnitude, opposite direction)
6.5Law of Conservation of Momentum
  • Conservation of momentum: in the absence of external forces, total momentum of a system remains constant.
  • In collisions: total momentum before = total momentum after.
  • Elastic collision: both momentum AND kinetic energy are conserved.
  • Inelastic collision: momentum conserved but kinetic energy is NOT fully conserved (some converted to heat/sound/deformation).
Formulas & Key Relations
Conservation of momentumm1 u1 + m2 u2 = m1 v1 + m2 v2
For equal masses, elasticu1 = v2 and u2 = v1 (velocities exchange)
Perfectly inelastic(m1 + m2) v = m1 u1 + m2 u2
Reverse — find v after collisionv = (m1 u1 + m2 u2) / (m1 + m2)
6.6Friction
  • Friction: force that opposes relative motion between two surfaces in contact.
  • Static friction: prevents motion from starting; can be as large as needed up to a maximum (limiting friction).
  • Kinetic (sliding) friction: acts when surfaces slide over each other; slightly less than static friction.
  • Rolling friction: when one surface rolls over another; much less than sliding friction.
  • Coefficient of friction (μ): ratio of friction force to normal force. Typical values: rubber on concrete ≈ 0.7; steel on steel ≈ 0.6.
  • Friction can be increased (tread on tyres, gripping surfaces) or reduced (lubricants, ball bearings, streamlining).
Formulas & Key Relations
Friction forcef = μN (μ=coefficient, N=normal force)
Normal force (horizontal surface)N = mg
Friction on slopef = μ mg cosθ
Reverse — find μμ = f / N
Ch 7Work, Energy and Simple Machines
Work, kinetic and potential energy, conservation of energy, power, simple machines
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7.1Work done by a force
  • Work is done when a force causes displacement in the direction of (or component along) the force.
  • Work is a scalar quantity; SI unit = Joule (J) = N⋅m.
  • Positive work: force and displacement in the same direction (e.g. pushing a box forward).
  • Negative work: force opposes displacement (e.g. friction when object moves).
  • Zero work: force perpendicular to displacement (e.g. carrying a bag horizontally — gravity does no work).
Formulas & Key Relations
Work doneW = F × d × cosθ (θ = angle between F and d)
When θ=0°W = F × d (force and displacement in same direction)
When θ=90°W = 0 (force perpendicular to displacement)
Reverse — find F from W,dF = W / (d cosθ)
Reverse — find d from W,Fd = W / (F cosθ)
7.2Kinetic energy
  • Kinetic energy (KE): energy possessed by an object due to its motion.
  • Depends on both mass and velocity; KE is always positive (scalar).
  • Work-Energy Theorem: net work done on an object = change in its kinetic energy.
  • When a body decelerates, KE decreases (negative work done on it).
Formulas & Key Relations
Kinetic energyKE = (1/2) m v2
Work-Energy theoremWnet = ΔKE = KEf − KEi
Reverse — find v from KEv = √(2KE / m)
Reverse — find m from KE,vm = 2KE / v2
Derivation checkW = Fs; F=ma; v2=u2+2as → W=(1/2)mv2−(1/2)μ2
7.3Potential energy and conservation of energy
  • Potential energy (PE): energy stored due to position or configuration.
  • Gravitational PE: energy due to height above a reference level.
  • Elastic PE: energy stored in a stretched/compressed spring.
  • Law of Conservation of Energy: energy cannot be created or destroyed; it only transforms from one form to another.
  • Free fall example: at height h → all PE; at ground → all KE; in between → PE + KE = constant.
  • Total mechanical energy E = KE + PE = constant (no friction).
Formulas & Key Relations
Gravitational PEPE = mgh (m=mass, g=9.8 m/s2, h=height)
Conservation of energyKE + PE = constant (no friction)
At height h: PEPE = mgh, KE = 0
At ground: KEKE = (1/2)mv2 = mgh → v = √(2gh)
Reverse — find h from vh = v2 / (2g)
Elastic PE (spring)PE = (1/2)kx2 (k=spring constant, x=extension)
7.4Power
  • Power: rate of doing work or rate of energy transfer; scalar quantity.
  • SI unit = Watt (W) = J/s. Commercial unit = kilowatt-hour (kWh).
  • 1 kWh = 3.6 × 10⁶ J (energy consumed by 1 kW device in 1 hour).
  • 1 horsepower (hp) = 746 W (used for motors/engines).
  • Average power = total work done / total time. Instantaneous power = F⋅v.
Formulas & Key Relations
PowerP = W / t = Energy / t
Power from force and velocityP = F × v
Reverse — find W from P,tW = P × t
Reverse — find t from W,Pt = W / P
1 kWh= 1000 W × 3600 s = 3.6 × 106 J
Electricity billUnits consumed = Power (kW) × Time (h)
7.5Simple machines and mechanical advantage
  • Simple machine: device that does work with one applied force. Examples: lever, pulley, inclined plane, wheel and axle, wedge, screw.
  • Mechanical Advantage (MA): ratio of load to effort. MA > 1 means machine multiplies force.
  • Velocity ratio (VR): ratio of distance moved by effort to distance moved by load.
  • Efficiency: ratio of useful work output to total work input × 100%.
  • Lever: rigid rod pivoting on fulcrum. Classes: 1st (fulcrum between load and effort: scissors), 2nd (load between fulcrum and effort: wheelbarrow), 3rd (effort between fulcrum and load: tweezers).
  • Pulley: single fixed pulley — changes direction of effort (MA=1); movable pulley — doubles mechanical advantage; block and tackle — multiple pulleys.
  • Inclined plane: sloped surface reduces effort needed to raise a load at the cost of increased distance.
Formulas & Key Relations
Mechanical advantage (MA)MA = Load / Effort
Velocity ratio (VR)VR = Distance by effort / Distance by load
Efficiencyη = (MA / VR) × 100% = (Work out / Work in) × 100%
For ideal machineMA = VR (efficiency = 100%)
Lever principleLoad × Load arm = Effort × Effort arm
Reverse — find EffortEffort = (Load × Load arm) / Effort arm
Inclined plane MAMA = Length of plane / Height
Ch 10Sound
Production and propagation, longitudinal waves, characteristics, echo, sonar, hearing
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10.1Production and propagation of sound
  • Sound is produced by vibrating objects (e.g. guitar string, vocal cords, tuning fork).
  • Sound requires a material medium to travel — cannot travel through vacuum (demonstrated by bell in evacuated jar experiment).
  • Sound travels as a longitudinal wave: compressions (high pressure) and rarefactions (low pressure) travel through the medium.
  • Speed of sound in air at 0°C ≈ 332 m/s; at 20°C ≈ 344 m/s; in water ≈ 1500 m/s; in steel ≈ 5100 m/s.
  • Speed order: vsolid > vliquid > vgas (sound travels faster in denser, more elastic materials).
Formulas & Key Relations
Speed of sound in air (0°C)v ≈ 332 m/s
Speed of sound in air (20°C)v ≈ 344 m/s
Effect of temperaturev increases with temperature (≈ 0.6 m/s per °C rise)
10.2Characteristics of sound waves
  • Wavelength (λ): distance between two consecutive compressions or rarefactions; unit = m.
  • Frequency (f): number of compressions passing a point per second; unit = Hertz (Hz).
  • Time period (T): time for one complete oscillation = 1/f.
  • Amplitude (A): maximum displacement of the medium particles from mean position; determines loudness.
  • Speed (v): distance travelled by the wave per second.
  • Intensity: power per unit area of the wave; related to amplitude squared; unit = W/m².
  • Pitch: perceived frequency; high frequency → high pitch. Loudness: perceived intensity; large amplitude → louder.
Formulas & Key Relations
Wave speedv = f × λ
Frequency and periodf = 1 / T
Reverse — find λ from v,fλ = v / f
Reverse — find f from v,λf = v / λ
Reverse — find T from fT = 1 / f
Intensity ∝A2 (A = amplitude)
Loudness (dB)L = 10 log10(I / I0) (I0 = 10-12 W/m2)
10.3Human hearing and audible range
  • Audible range for humans: 20 Hz to 20,000 Hz (20 kHz).
  • Infrasound: < 20 Hz; produced by earthquakes, ocean waves; detected by some animals (elephants, dogs).
  • Ultrasound: > 20,000 Hz; used in sonar, medical imaging (sonography), industrial flaw detection.
  • Hearing mechanism: sound → eardrum (tympanic membrane) vibrates → ossicles (hammer, anvil, stirrup) amplify → cochlea converts to electrical signals → auditory nerve → brain.
Formulas & Key Relations
Audible range20 Hz ≤ f ≤ 20,000 Hz
Infrasoundf < 20 Hz
Ultrasoundf > 20,000 Hz
10.4Reflection of sound — Echo and Reverberation
  • Reflection of sound: sound bounces off a hard surface at the same angle (just like light reflection).
  • Echo: distinct reflected sound heard after the original sound has ended. Minimum distance for echo: 17.2 m (at 20°C) — ear needs 0.1 s to distinguish two sounds.
  • Reverberation: multiple reflections of sound in a closed space causing prolonged sound; undesirable in rooms but helpful for musicians.
  • Acoustic design: sound-absorbing materials (soft furnishings, curtains) reduce reverberation; curved surfaces focus sound.
  • SONAR: Sound Navigation And Ranging; uses ultrasound pulses to detect objects underwater; calculates distance from time taken for echo to return.
Formulas & Key Relations
Minimum distance for echod = v × tmin / 2 = 344 × 0.1 / 2 = 17.2 m
SONAR distanced = v × t / 2 (t = time for echo to return)
Reverse — find t from dt = 2d / v
Speed of sound from echov = 2d / t
Unit IV — Earth ScienceEarth as a System1 ch · Ch 13 · 5 marks · 12 periods
Ch 13Earth as a System: Energy, Matter and Life
Earth's spheres, solar radiation, differential heating, biogeochemical cycles, human impact
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13.1Earth as an interconnected system
  • Earth consists of four interconnected spheres that constantly interact: Geosphere (solid Earth — rocks, minerals), Hydrosphere (all water — oceans, rivers, ice, groundwater), Atmosphere (layers of gases surrounding Earth), Biosphere (all living organisms and their environments).
  • Cryosphere: all frozen water (polar ice caps, glaciers, permafrost) — part of hydrosphere.
  • Energy and matter flow between these spheres — no sphere operates in isolation.
  • Examples of interactions: rain from atmosphere (hydrosphere) erodes geosphere; plants (biosphere) affect atmosphere through photosynthesis and respiration.
13.2Solar radiation and the electromagnetic spectrum
  • Sun is Earth's primary energy source. Solar radiation travels as electromagnetic waves at the speed of light: c = 3 × 10⁸ m/s.
  • Electromagnetic spectrum (short to long wavelength): gamma rays → X-rays → UV → visible → infrared → microwaves → radio waves.
  • Solar radiation: mostly visible light (43%) + infrared (49%) + UV (8%).
  • Earth absorbs solar radiation and re-emits it as longer-wavelength infrared (heat) radiation.
  • Albedo: fraction of incoming solar radiation reflected by a surface. Snow: 80–90%; ocean: 6%; forest: 10–15%.
Formulas & Key Relations
Speed of lightc = 3 × 108 m/s
Wave equationc = f × λ
Reverse — find f from λf = c / λ
AlbedoAlbedo = Reflected radiation / Incoming radiation
13.3Differential heating of the Earth
  • Different parts of Earth receive different amounts of solar energy, causing temperature differences.
  • Equator receives more direct sunlight (less area, more concentrated energy); poles receive slanted rays (more spread, less energy per area).
  • Land heats up and cools down faster than water (lower specific heat capacity of land).
  • Differential heating drives: sea breeze (day: land hot → air rises → sea air moves in), land breeze (night: sea warmer → sea air rises → land air moves in), monsoons, global wind patterns.
  • Mountain and valley breezes are also caused by differential heating (slopes vs valleys).
Formulas & Key Relations
Solar intensity vs latitudeI = I0 cosθ (θ = angle from vertical)
Specific heat capacity (water)cw = 4200 J/(kg⋅K) (much higher than land)
Heat absorbedQ = mcΔT
Reverse — find ΔTΔT = Q / (mc)
13.4Biogeochemical cycles
  • Water cycle: evaporation → condensation → precipitation → runoff → groundwater → evaporation. Driven by solar energy and gravity.
  • Carbon cycle: CO₂ absorbed by plants (photosynthesis) → carbon enters food chain → released by respiration, decomposition, combustion; ocean absorbs CO₂.
  • Nitrogen cycle: N₂ fixed by bacteria (Rhizobium, Azotobacter) → nitrates in soil → absorbed by plants → eaten by animals → returned by decomposers.
  • Oxygen cycle: O₂ released by photosynthesis → consumed by respiration and combustion → returned to atmosphere.
  • Phosphorus cycle: no gaseous phase; rock → soil (weathering) → plants → animals → decomposers → soil.
Formulas & Key Relations
Photosynthesis (carbon cycle)6CO2 + 6H2O + light → C6H12O6 + 6O2
Respiration (carbon cycle)C6H12O6 + 6O2 → 6CO2 + 6H2O + Energy
Nitrogen fixationN2 → NH3 → NO2− → NO3− (nitrification)
13.5Human impact on Earth's system
  • Greenhouse effect: CO₂, CH₄, N₂O trap outgoing infrared radiation → global warming. Enhanced by burning fossil fuels, deforestation.
  • Ozone depletion: CFCs (chlorofluorocarbons) break down O₃ in stratosphere → more UV reaches Earth → skin cancer, cataracts, ecosystem damage.
  • Acid rain: SO₂ and NOx from burning fossil fuels react with water → H₂SO₄, HNO₃ → acid rain → damages forests, aquatic life, buildings.
  • Deforestation: reduces CO₂ absorption, increases runoff (flooding), causes soil erosion, reduces biodiversity.
  • Water pollution: industrial effluents, agricultural runoff (fertilizers → eutrophication), sewage → affects aquatic ecosystems.
Formulas & Key Relations
Greenhouse gas effectTrapped heat → ΔT increase ≈ 1.1°C since 1880
Ozone reaction (CFCs)CF2Cl2 + UV → CF2Cl + Cl; Cl + O3 → ClO + O2
Acid rain (SO2)SO2 + H2O → H2SO3; 2H2SO3 + O2 → 2H2SO4
Class 9 Science (086) · CBSE Syllabus 2026–27 · GEMS New Millennium School Dubai
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