Class 10 Science Formula Sheet (CBSE 2026-27)

General reactions

• Acid + Metal \(\to\) Salt + Hydrogen gas
• Base + Metal: \(\ce{2NaOH(aq) + Zn(s) -> Na2ZnO2(s) + H2(g)}\)
• Metal carbonate / hydrogencarbonate + Acid \(\to\) Salt + CO\(_2\) + Water
• Neutralisation: Acid + Base \(\to\) Salt + Water, e.g. \(\ce{NaOH + HCl -> NaCl + H2O}\)
• Metal oxide + Acid \(\to\) Salt + Water (metal oxides are basic)
• Non-metal oxide + Base \(\to\) Salt + Water (non-metal oxides are acidic)

Ions in water

• Acids give \(\ce{H+}\) (as \(\ce{H3O+}\)): \(\ce{HCl + H2O -> H3O+ + Cl-}\)
• Bases give \(\ce{OH-}\): \(\ce{NaOH(s) ->[H2O] Na+(aq) + OH-(aq)}\)
• Neutralisation core: \(\ce{H+(aq) + OH-(aq) -> H2O(l)}\)
• Water-soluble bases are alkalis. Always add acid to water, never water to acid (highly exothermic).

pH scale

• pH 7: neutral; below 7: acidic; above 7: basic (scale 0 to 14)
• Higher \(\ce{H+}\) concentration means lower pH
• Tooth decay starts below pH 5.5
• Strong acids give many \(\ce{H+}\) ions, weak acids give few

Indicators

Olfactory indicators: onion and vanilla lose their smell in a base.

Reactions of metals

• With oxygen: \(\ce{2Cu + O2 -> 2CuO}\); \(\ce{4Al + 3O2 -> 2Al2O3}\)
• Amphoteric oxides (Al\(_2\)O\(_3\), ZnO) react with both acids and bases
• Soluble metal oxides give alkalis: \(\ce{Na2O(s) + H2O(l) -> 2NaOH(aq)}\)
• With water: \(\ce{2Na(s) + 2H2O(l) -> 2NaOH(aq) + H2(g)}\) + heat; \(\ce{Ca(s) + 2H2O(l) -> Ca(OH)2(aq) + H2(g)}\)
• With steam: \(\ce{3Fe(s) + 4H2O(g) -> Fe3O4(s) + 4H2(g)}\)

Acids, salts and reactivity

• Metal + dilute acid \(\to\) salt + H\(_2\) (H\(_2\) only with very dilute HNO\(_3\), using Mg or Mn)
• Metal A + salt solution of B \(\to\) salt solution of A + metal B (if A is more reactive)
• Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > [H] > Cu > Hg > Ag > Au
• Aqua regia: conc. HCl and conc. HNO\(_3\) in 3 : 1; dissolves gold and platinum

Ionic compounds

• \(\ce{Na -> Na+ + e-}\); \(\ce{Cl + e- -> Cl-}\); \(\ce{Na+ + Cl- -> NaCl}\)
• \(\ce{Mg -> Mg^2+ + 2e-}\); \(\ce{Mg^2+ + 2Cl- -> MgCl2}\)
• High melting and boiling points; conduct when molten or dissolved; soluble in water

Extracting metals

• Low reactivity (heat alone): \(\ce{2HgS + 3O2 ->[Heat] 2HgO + 2SO2}\); \(\ce{2HgO ->[Heat] 2Hg + O2}\)
• Middle: roasting \(\ce{2ZnS + 3O2 ->[Heat] 2ZnO + 2SO2}\); calcination \(\ce{ZnCO3 ->[Heat] ZnO + CO2}\); then \(\ce{ZnO + C -> Zn + CO}\)
• Thermit reaction: \(\ce{Fe2O3(s) + 2Al(s) -> 2Fe(l) + Al2O3(s)}\) + heat
• High reactivity: electrolysis of molten chloride; cathode \(\ce{Na+ + e- -> Na}\), anode \(\ce{2Cl- -> Cl2 + 2e-}\)

Hydrocarbon formulae

Successive members of a homologous series differ by \(\ce{CH2}\) (14 u).

Functional groups and names

Chemical properties

• Combustion: \(\ce{CH4 + 2O2 -> CO2 + 2H2O}\) + heat and light
• Oxidation: \(\ce{CH3CH2OH ->[alkaline KMnO4 + heat or acidified K2Cr2O7 + heat] CH3COOH}\)
• Addition (hydrogenation, Ni or Pd catalyst): \(\ce{R2C=CR2 + H2 -> R2CH-CHR2}\) (vegetable oils)
• Substitution: \(\ce{CH4 + Cl2 ->[sunlight] CH3Cl + HCl}\)

Ethanol

• With sodium: \(\ce{2Na + 2CH3CH2OH -> 2CH3CH2O^-Na+ + H2}\)
• Dehydration: \(\ce{CH3CH2OH ->[hot conc. H2SO4, 443 K] CH2=CH2 + H2O}\)

Photosynthesis

• Carbon dioxide + water \(\xrightarrow{\text{sunlight, chlorophyll}}\) carbohydrates (stored as starch)
• Steps: light energy absorbed by chlorophyll; water split into hydrogen and oxygen; CO\(_2\) reduced to carbohydrates
• Gas exchange through stomata

Respiration pathways

• Glucose (6C) \(\xrightarrow{\text{cytoplasm}}\) pyruvate (3C) + energy
• Yeast, no oxygen: pyruvate \(\to\) ethanol + CO\(_2\) + energy (anaerobic)
• Muscle, lack of oxygen: pyruvate \(\to\) lactic acid + energy (causes cramps)
• Mitochondria, with oxygen: pyruvate \(\to\) CO\(_2\) + H\(_2\)O + energy (aerobic, most energy)
• Energy currency: ATP

Spherical mirrors

• Focal length: \(f = \dfrac{R}{2}\), i.e. \(R = 2f\)
• Mirror formula: $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
• Magnification: \(m = \dfrac{h'}{h} = -\dfrac{v}{u}\)
• Negative \(m\): real, inverted image. Positive \(m\): virtual, erect image.

Sign convention (New Cartesian)

• Distances measured from the pole (mirror) or optical centre (lens)
• Along the incident light: +; against it: \(-\)
• Heights above the principal axis: +; below: \(-\)
• Object distance \(u\) is always negative. Concave mirror and concave lens: \(f < 0\). Convex mirror and convex lens: \(f > 0\).

Refraction

• Snell's law: \(\dfrac{\sin i}{\sin r} = n_{21}\) (constant)
• Absolute refractive index: \(n_m = \dfrac{c}{v}\)
• Relative: \(n_{21} = \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}\)
• Values: air 1.0003, water 1.33, kerosene 1.44, crown glass 1.52, diamond 2.42
• Optical density is not mass density: kerosene is optically denser than water but lighter.

Spherical lenses

• Lens formula: $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
• Magnification: \(m = \dfrac{h'}{h} = \dfrac{v}{u}\)
• Power: \(P = \dfrac{1}{f}\) (\(f\) in metres), unit dioptre (D). Convex: + ; concave: \(-\)
• Lenses in contact: \(P = P_1 + P_2 + P_3 + \dots\)

The eye

• Near point (least distance of distinct vision): 25 cm. Far point: infinity
• Accommodation: ciliary muscles change the focal length of the eye lens
• Myopia (near-sightedness): image before retina; corrected by a concave lens
• Hypermetropia (far-sightedness): image behind retina; corrected by a convex lens
• Presbyopia: accommodation weakens with age

Prism and atmosphere

• Dispersion: white light splits into VIBGYOR; violet bends most, red least
• Rainbow: dispersion + refraction + internal reflection in raindrops (Sun behind you)
• Atmospheric refraction: twinkling of stars; advance sunrise and delayed sunset (about 2 minutes)
• Scattering: blue sky (fine particles scatter blue most); Tyndall effect

Current and potential difference

• \(I = \dfrac{Q}{t}\); 1 A = 1 C s\(^{-1}\)
• 1 C is the charge of nearly \(6 \times 10^{18}\) electrons; \(e = 1.6 \times 10^{-19}\,\text{C}\)
• \(V = \dfrac{W}{Q}\); 1 V = 1 J C\(^{-1}\)
• Ammeter in series; voltmeter in parallel

Ohm's law and resistivity

• Ohm's law: \(V = IR\) (at constant temperature)
• $$R = \rho\,\frac{l}{A}$$ (\(\rho\) in \(\Omega\) m)
• Metals and alloys: \(\rho\) from \(10^{-8}\) to \(10^{-6}\,\Omega\,\text{m}\); insulators: \(10^{12}\) to \(10^{17}\,\Omega\,\text{m}\)
• Alloys (nichrome) have higher \(\rho\) and do not oxidise: used in heaters

Resistors in combination

• Series: \(R_s = R_1 + R_2 + R_3\) (same current)
• Parallel: \(\dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}\) (same voltage)
• Home appliances are wired in parallel so each gets full voltage and can be switched separately.

Heating effect and power

• Joule's law: \(H = I^2Rt\) (also \(H = VIt\))
• Power: \(P = VI = I^2R = \dfrac{V^2}{R}\); 1 W = 1 V \(\times\) 1 A
• Energy: \(E = Pt\); 1 kW h = \(3.6 \times 10^{6}\) J (1 "unit")
• Uses: heater, iron, bulb filament (tungsten), fuse (low melting point)

Field from a current

• Right-hand thumb rule: thumb along current, fingers curl along field lines
• Straight wire: concentric circles; field \(\propto I\), weaker farther away
• Circular loop: field \(\propto\) current and number of turns
• Solenoid: uniform field inside, like a bar magnet; with soft iron core it makes an electromagnet

Force on a conductor

• Fleming's left-hand rule: forefinger = field, middle finger = current, thumb = force (motion)
• Force is greatest when current \(\perp\) field
• Field lines never cross; they run N to S outside a magnet and S to N inside.

Energy flow

• 10% law: only about 10% of the energy at one trophic level passes to the next
• Producers \(\to\) herbivores \(\to\) carnivores (energy flow is one-way)
• Biological magnification: pesticides build up along the food chain (highest at top)

Ozone

• \(\ce{O2 ->[UV] O + O}\)
• \(\ce{O + O2 -> O3}\)
• Ozone layer shields Earth from UV; depleted by CFCs
• Biodegradable vs non-biodegradable waste