CBSE · Class 10 · Science

Science Formula Sheet

101 formulas across 13 chapters — with variables explained and exam tips where needed.

Ch 9Light — Reflection and Refraction(8 formulas)

Mirror formula

1/v + 1/u = 1/f

v = image distance, u = object distance, f = focal length

💡

Use Cartesian sign convention: distances measured from pole, +ve in direction of incident light

Focal length and radius

f = R/2

R = radius of curvature

Magnification (mirror)

m = −v/u = h'/h

h' = image height, h = object height

💡

m negative → real inverted image; m positive → virtual erect image

Lens formula

1/v − 1/u = 1/f

Magnification (lens)

m = v/u = h'/h

Refractive index

n = c/v = sin i / sin r

c = speed in vacuum, v = speed in medium, i = angle of incidence, r = angle of refraction

Power of lens

D (dioptre)

P = 1/f

f in metres

💡

Convex lens: +ve power; Concave lens: −ve power

Combined power

P = P₁ + P₂ + P₃ + ...

Ch 10The Human Eye and the Colourful World(8 formulas)

Near point (normal eye)

25 cm (least distance of distinct vision)

💡

Closer than 25 cm and the eye cannot focus — ciliary muscles at maximum strain

Far point (normal eye)

Infinity (eye can see clearly)

💡

Relaxed eye focuses parallel rays on retina

Myopia (short-sightedness)

Far point < ∞; image forms in front of retina | Corrected by: concave lens (diverging)

💡

Power of corrective lens = negative; use P = 1/f (f in metres)

Hypermetropia (long-sightedness)

Near point > 25 cm; image forms behind retina | Corrected by: convex lens (converging)

💡

Power of corrective lens = positive

Presbyopia

Both near and far vision affected (age-related) | Corrected by: bifocal lens

💡

Ciliary muscles weaken with age; near point recedes and far point may also shift

Angle of deviation (prism)

d = (i₁ + i₂) − A

i₁ = angle of incidence, i₂ = angle of emergence, A = angle of prism

💡

At minimum deviation: i₁ = i₂ and the ray passes symmetrically through the prism

Dispersion of white light

White light → VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red)

💡

Violet deviates most (highest refractive index); Red deviates least (lowest refractive index)

Scattering of light (Tyndall effect)

Shorter wavelength (blue) scattered more than longer wavelength (red)

💡

Blue colour of sky: sunlight scattered by atmosphere. Red colour of danger signals: least scattered, travels farthest

Ch 11Electricity(7 formulas)

Ohm's Law

V = IR

V = potential difference (V), I = current (A), R = resistance (Ω)

Resistance

R = ρL/A

ρ = resistivity, L = length, A = cross-section area

Resistors in series

R_total = R₁ + R₂ + R₃

Resistors in parallel

1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Electric power

W (watt)

P = VI = I²R = V²/R

Electrical energy

J or kWh

E = Pt = VIt

💡

1 kWh = 3.6 × 10⁶ J = 1 unit on electricity bill

Joule's law of heating

H = I²Rt

Ch 1Chemical Reactions and Equations(10 formulas)

Law of conservation of mass

Total mass of reactants = Total mass of products

💡

Reason why chemical equations must be balanced

Combination reaction

A + B → AB

💡

e.g. CaO + H₂O → Ca(OH)₂; always exothermic

Decomposition reaction

AB → A + B

💡

e.g. 2H₂O₂ → 2H₂O + O₂; requires heat, light, or electricity

Displacement reaction

A + BC → AC + B

💡

e.g. Fe + CuSO₄ → FeSO₄ + Cu; more reactive metal displaces less reactive

Double displacement reaction

AB + CD → AD + CB

💡

e.g. Na₂SO₄ + BaCl₂ → BaSO₄↓ + 2NaCl; one product usually precipitates

Precipitation reaction

Reactants (aq) → Insoluble precipitate (s) + Soluble product (aq)

💡

↓ symbol denotes precipitate; e.g. AgNO₃ + NaCl → AgCl↓ + NaNO₃

Exothermic reaction

Reactants → Products + Heat (energy released)

💡

e.g. Respiration, combustion, neutralisation; temperature of surroundings increases

Endothermic reaction

Reactants + Heat → Products (energy absorbed)

💡

e.g. Photosynthesis, decomposition of CaCO₃; temperature of surroundings decreases

Oxidation

Gain of oxygen OR loss of hydrogen OR loss of electrons

💡

OIL — Oxidation Is Loss (of electrons)

Reduction

Loss of oxygen OR gain of hydrogen OR gain of electrons

💡

RIG — Reduction Is Gain (of electrons); oxidation and reduction always occur together (redox)

Ch 2Acids, Bases and Salts(14 formulas)

Acid definition (Arrhenius)

Acid furnishes H⁺ ions in solution | e.g. HCl → H⁺ + Cl⁻

💡

Arrhenius definition — used in Class 10

Base definition (Arrhenius)

Base furnishes OH⁻ ions in solution | e.g. NaOH → Na⁺ + OH⁻

pH scale

pH < 7 = acidic | pH = 7 = neutral | pH > 7 = basic

💡

Gastric juice ~2; blood ~7.4; sea water ~8.4; strong acid pH ~0; strong base pH ~14

Neutralisation

Acid + Base → Salt + Water | HCl + NaOH → NaCl + H₂O

Acid + Metal

Zn + H₂SO₄ → ZnSO₄ + H₂↑

💡

H₂ gas produced — burns with pop sound. Cu, Ag, Au don't react.

Acid + Metal oxide

CuO + H₂SO₄ → CuSO₄ + H₂O

💡

Metal oxide is basic; reacts with acid to form salt + water

Acid + Metal carbonate

Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂↑

💡

CO₂ turns lime water milky — standard test for CO₂

Acid + Metal hydrogen carbonate

NaHCO₃ + HCl → NaCl + H₂O + CO₂↑

Action of base on non-metal oxide

Ca(OH)₂ + CO₂ → CaCO₃ + H₂O

💡

Non-metal oxides are acidic; react with base to form salt + water

Chlor-alkali process (NaOH)

2NaCl(aq) + 2H₂O(l) → 2NaOH(aq) + Cl₂(g) + H₂(g)

💡

Electrolysis of brine; Cl₂ at anode, H₂ at cathode, NaOH in solution

Bleaching powder

Ca(OH)₂ + Cl₂ → CaOCl₂ + H₂O

💡

Chemical name: Calcium oxychloride; used for disinfecting water and bleaching

Baking soda

NaHCO₃ (Sodium hydrogen carbonate) | On heating: 2NaHCO₃ → Na₂CO₃ + H₂O + CO₂

💡

Used in baking (CO₂ makes dough rise), antacids, soda-acid fire extinguisher

Washing soda

Na₂CO₃·10H₂O (Sodium carbonate decahydrate)

💡

Used as cleaning agent and for removing permanent hardness of water

Plaster of Paris

CaSO₄·½H₂O | Setting: CaSO₄·½H₂O + 1½H₂O → CaSO₄·2H₂O (gypsum)

💡

Made from gypsum by heating at 100°C; expands on setting — used in casts

Ch 3Metals and Non-Metals(12 formulas)

Metal + Oxygen

2Mg + O₂ → 2MgO

💡

Most metals form basic oxides; non-metals form acidic oxides

Metal + Water (very reactive)

2Na + 2H₂O → 2NaOH + H₂↑

💡

K, Na, Ca react vigorously with cold water

Metal + Steam

3Fe + 4H₂O → Fe₃O₄ + 4H₂↑

💡

Iron reacts only with steam, not cold water

Metal + Acid

Zn + H₂SO₄ → ZnSO₄ + H₂↑

💡

Cu, Ag, Au do not react with dilute acids — below H in reactivity series

Metal + Salt solution (displacement)

Fe + CuSO₄ → FeSO₄ + Cu

💡

More reactive metal displaces less reactive metal from its salt solution

Reactivity series (high → low)

K > Na > Ca > Mg > Al > Zn > Fe > Pb > H > Cu > Ag > Au

💡

Metals above H displace hydrogen from dilute acids

Thermite reaction

Fe₂O₃ + 2Al → Al₂O₃ + 2Fe

💡

Used in welding railway tracks; Al acts as reducing agent

Corrosion of iron (rusting)

4Fe + 3O₂ + xH₂O → 2Fe₂O₃·xH₂O

💡

Both O₂ and moisture are required; prevented by painting, galvanising, alloying

Ionic compound formation

Na → Na⁺ + e⁻ | Cl + e⁻ → Cl⁻ → NaCl

💡

Metals lose electrons (oxidation); non-metals gain electrons (reduction)

Non-metal + Oxygen (acidic oxide)

S + O₂ → SO₂ | C + O₂ → CO₂ | 4P + 5O₂ → 2P₂O₅

💡

Non-metal oxides dissolve in water to form acids; opposite of metal oxides (basic)

Amphoteric oxide

Al₂O₃ + 2NaOH → 2NaAlO₂ + H₂O (with base) | Al₂O₃ + 6HCl → 2AlCl₃ + 3H₂O (with acid)

💡

Reacts with both acids and bases; Al₂O₃ and ZnO are amphoteric

Basic metallurgical processes

Ore → (Concentration) → (Roasting/Calcination) → (Reduction/Smelting) → Crude metal → (Refining) → Pure metal

💡

Calcination: heating without air (carbonates). Roasting: heating in air (sulphides). Reduction: using C, CO, or electrolysis

Ch 4Carbon and its Compounds(13 formulas)

Alkane general formula

CₙH₂ₙ₊₂

💡

Saturated hydrocarbons; e.g. methane CH₄, ethane C₂H₆

Alkene general formula

CₙH₂ₙ

💡

One C=C double bond; unsaturated; e.g. ethene C₂H₄

Alkyne general formula

CₙH₂ₙ₋₂

💡

One C≡C triple bond; unsaturated; e.g. ethyne C₂H₂

Combustion (complete)

CH₄ + 2O₂ → CO₂ + 2H₂O + heat

💡

Complete combustion gives blue flame; incomplete gives sooty yellow flame

Combustion of ethanol

C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O

💡

Ethanol burns with a clean blue flame

Esterification

CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O

conc. H₂SO₄, heat

💡

Acid + Alcohol → Ester + Water; sweet smell; reversible reaction

Saponification

Ester + NaOH → RCOONa (soap) + Alcohol

💡

Soap molecules have hydrophilic head (−COO⁻Na⁺) and hydrophobic tail (carbon chain)

Addition reaction (alkene + Cl₂)

CH₂=CH₂ + Cl₂ → CH₂Cl−CH₂Cl

💡

Unsaturated compounds undergo addition; Br₂ water turns colourless — test for unsaturation

Substitution reaction (alkane + Cl₂)

CH₄ + Cl₂ → CH₃Cl + HCl

sunlight

💡

Saturated compounds undergo substitution in presence of sunlight

Oxidation of ethanol

C₂H₅OH → CH₃COOH (alkaline KMnO₄ or acidic K₂Cr₂O₇)

💡

Ethanol oxidised to ethanoic acid; oxidising agents act as oxygen suppliers

Dehydration of ethanol

C₂H₅OH → C₂H₄ + H₂O

conc. H₂SO₄, 170°C

💡

Produces ethene (unsaturated); H₂SO₄ acts as dehydrating agent

Ethanoic acid + Na₂CO₃

2CH₃COOH + Na₂CO₃ → 2CH₃COONa + H₂O + CO₂↑

💡

Ethanoic acid reacts with carbonates/bicarbonates to give CO₂ — used to identify carboxylic acids

Ethanoic acid properties

Boiling point 118°C | Glacial acetic acid: pure CH₃COOH (freezes at 16.6°C) | Vinegar: 5–8% solution

💡

Glacial = no water; called acetic acid in older nomenclature

Ch 5Life Processes(5 formulas)

Photosynthesis

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

sunlight, chlorophyll

💡

CO₂ enters through stomata; water absorbed by roots; O₂ is byproduct

Aerobic respiration

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy (ATP)

💡

Occurs in mitochondria; releases ~38 ATP molecules per glucose

Anaerobic respiration (yeast)

C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂ + Energy

💡

Used in fermentation; occurs without oxygen

Anaerobic respiration (muscles)

Glucose → Lactic acid + Energy

💡

Causes muscle cramps; lactic acid removed by increased blood supply after exercise

Excretion (kidney filtration)

Blood → Glomerulus filtration → Tubular reabsorption → Urine

💡

Nephron is the structural and functional unit of kidney; urea is the main nitrogenous waste

Ch 6Control and Coordination(4 formulas)

Reflex arc path

Stimulus → Receptor → Sensory nerve → Spinal cord → Motor nerve → Effector → Response

💡

Reflex actions are controlled by spinal cord, not brain — faster response

Synapse

Electrical signal → Chemical neurotransmitter → Electrical signal (next neuron)

💡

Neurotransmitters released at synapse bridge the gap between two neurons

Plant hormones

Auxin (growth/phototropism) | Gibberellin (stem elongation) | Cytokinin (cell division) | Abscisic acid (growth inhibitor)

💡

Auxin accumulates on shaded side → cell elongation → bending towards light

Tropic movements

Phototropism (light) | Geotropism (gravity) | Hydrotropism (water) | Thigmotropism (touch)

💡

Positive tropism = towards stimulus; negative = away from stimulus

Ch 7How do Organisms Reproduce?(5 formulas)

Asexual reproduction types

Binary fission (Amoeba) | Budding (Hydra, Yeast) | Fragmentation (Spirogyra) | Spore formation (Rhizopus)

💡

Asexual reproduction produces genetically identical offspring (clones)

Vegetative propagation

Stem cutting (Rose) | Tuber (Potato) | Leaf (Bryophyllum) | Layering (Jasmine)

💡

Useful for propagating plants that do not produce seeds or produce sterile seeds

Pollination types

Self-pollination (same flower) | Cross-pollination (different flower/plant)

💡

Cross-pollination introduces genetic variation; aided by wind, insects, water

Double fertilisation (plants)

1 sperm + egg → zygote (embryo) | 1 sperm + 2 polar nuclei → endosperm

💡

Unique to angiosperms; endosperm provides nutrition to developing embryo

Gestation period (humans)

~9 months (38–40 weeks) from fertilisation to birth

💡

Placenta provides nutrients and O₂ to foetus; removes CO₂ and waste

Ch 8Heredity(4 formulas)

Monohybrid cross F₂ ratio

3 : 1 (dominant : recessive) phenotype | 1 : 2 : 1 (TT : Tt : tt) genotype

💡

Law of Segregation: alleles separate during gamete formation

Dihybrid cross F₂ ratio

9 : 3 : 3 : 1 (four phenotype classes)

💡

Law of Independent Assortment: genes for different traits assort independently

Sex determination (humans)

XX = Female | XY = Male

💡

Father determines sex of child — Y chromosome from sperm decides male; X from sperm gives female

Inherited vs acquired traits

Inherited: controlled by genes, passed to offspring | Acquired: caused by environment, NOT passed to offspring

💡

Acquired traits (e.g. muscle built by exercise) do not change DNA and cannot be inherited

Ch 12Magnetic Effects of Electric Current(7 formulas)

Force on current-carrying conductor

F = BIL sinθ

B = magnetic field (T), I = current (A), L = length (m), θ = angle between B and L

💡

Maximum force when conductor is perpendicular to field (θ = 90°)

Right-hand thumb rule

Thumb → direction of current; curled fingers → direction of magnetic field lines around wire

💡

Used to find direction of B around a straight current-carrying conductor

Fleming's Left-Hand Rule (motor)

Forefinger → B field | Middle finger → Current | Thumb → Force (motion)

💡

Used for electric motors (converts electrical energy to mechanical energy)

Fleming's Right-Hand Rule (generator)

Forefinger → B field | Middle finger → Induced current | Thumb → Motion

💡

Used for electric generators (converts mechanical energy to electrical energy)

AC frequency (India)

f = 50 Hz | T = 1/f = 0.02 s

💡

AC reverses direction 50 times per second in India; USA uses 60 Hz

Advantage of AC over DC

AC voltage can be stepped up/down using transformer; DC cannot

💡

High voltage AC used for long-distance transmission to reduce energy loss (P = I²R)

Domestic circuit

Live (red/brown, 220V) | Neutral (black/blue, 0V) | Earth (green, safety)

💡

Fuse and switch always connected in live wire; earth wire prevents electric shock

Ch 13Our Environment(4 formulas)

10% energy law (Lindemann)

Only 10% of energy transfers from one trophic level to the next

💡

90% lost as heat; reason food chains are short (usually 3–4 levels)

Trophic levels

T1: Producers (plants) → T2: Primary consumers (herbivores) → T3: Secondary consumers → T4: Tertiary consumers

💡

Energy and biomass decrease at each level; toxins (DDT) accumulate — biological magnification

Ozone layer reaction (depletion)

CFC → Cl | Cl + O₃ → ClO + O₂ (chain reaction depletes ozone)

💡

CFCs from refrigerants and aerosols cause ozone depletion; UV-B radiation increases

Biodegradable vs non-biodegradable

Biodegradable: broken down by microbes (paper, food) | Non-biodegradable: persist in environment (plastic, DDT)

💡

Non-biodegradable substances accumulate in food chains (biological magnification)

More for CBSE Class 10

All Formula Sheets →Important Derivations →Named Reactions →Important Diagrams →Previous Year Papers →

Science Formula Sheet — Class 10