Odisha BSE HSC General Science cheat sheet

Mirror formula: 1/v + 1/u = 1/f, with linear magnification m = -v/u; all distances are measured from the pole and are positive in the direction of the incident light (New Cartesian sign convention).

Lens formula: 1/v - 1/u = 1/f; power of a lens P = 1/f with f in metres, so a convex lens of focal length 50 cm has power +2 D and a concave lens of the same focal length has -2 D.

Refractive index n = c/v = sin i / sin r; for glass n = 1.5 means light slows to 2 x 10^8 m/s inside the glass and the ray bends towards the normal on entering.

Ohm's law: V = IR at constant temperature; series combination R = R1 + R2 + R3, parallel combination 1/R = 1/R1 + 1/R2 + 1/R3, and parallel resistance is always smaller than the least branch.

Electric power P = VI = I^2R = V^2/R; commercial energy consumed in kWh = power in kW multiplied by time in hours, and 1 kWh = 3.6 x 10^6 J.

Right-hand thumb rule: hold a straight current-carrying conductor with the right thumb pointing along the current; the curled fingers give the direction of the magnetic field, whose lines are concentric circles around the wire.

Fleming's left-hand rule gives the direction of force on a current-carrying conductor placed in a magnetic field (electric motor); Fleming's right-hand rule gives the direction of induced current (generator).

Plane mirror: focal length is infinite, the image is virtual, erect, of the same size as the object and laterally inverted, and it lies as far behind the mirror as the object is in front.

Human eye: near point 25 cm and far point infinity for a normal adult eye; myopia is corrected with a concave lens, hypermetropia with a convex lens and presbyopia with bifocal lenses.

pH scale runs from 0 to 14: pH below 7 is acidic, pH equal to 7 is neutral, pH above 7 is basic; acids turn blue litmus red and bases turn red litmus blue.

Neutralisation: acid + base gives salt + water, for example HCl + NaOH gives NaCl + H2O; the reaction is exothermic and is used in treating acidity and soil acidity.

Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > Cu > Hg > Ag > Au; a metal higher in the series displaces a metal lower in the series from its salt solution.

Rusting of iron requires both oxygen and moisture and forms hydrated iron(III) oxide Fe2O3.xH2O; it is prevented by painting, oiling, greasing, galvanising or making stainless steel.

Metals above hydrogen in the reactivity series (Mg, Zn, Fe) react with dilute HCl or dilute H2SO4 to liberate hydrogen gas; copper, silver and gold do not react with these dilute acids.

Carbon is tetravalent and shows catenation, forming long chains and rings; its allotropes include diamond (tetrahedral network, hardest natural substance, non-conductor) and graphite (hexagonal layers, soft, good conductor).

Plaster of Paris is CaSO4.1/2H2O, prepared by heating gypsum to 373 K; when mixed with water it sets into hard CaSO4.2H2O and is used for casts and moulds.

Ionic bonding involves transfer of electrons from a metal to a non-metal (NaCl), whereas covalent bonding involves sharing of electron pairs (H2, O2, CH4, H2O).

Common salts to recall: baking soda NaHCO3, washing soda Na2CO3.10H2O, bleaching powder Ca(OCl)Cl, common salt NaCl, and quicklime CaO obtained by heating limestone.

Photosynthesis: 6CO2 + 6H2O gives C6H12O6 + 6O2, occurring in chloroplasts containing chlorophyll in the presence of sunlight; the oxygen released comes from water.

Stomata are pores in the leaf epidermis guarded by two guard cells; they allow carbon dioxide intake and escape of oxygen and water vapour as transpiration.

Human digestion: salivary amylase digests starch to maltose, pepsin digests protein in the acidic stomach, and trypsin, lipase and intestinal juice act in the small intestine.

Blood: red blood cells carry oxygen bound to haemoglobin, white blood cells provide immunity, platelets help clotting, and plasma transports food, hormones and nitrogenous wastes.

The nephron is the functional unit of the kidney; it carries out glomerular filtration followed by selective reabsorption of glucose, amino acids, salts and water, and tubular secretion.

A reflex action follows the reflex arc: receptor, sensory neuron, spinal cord (relay), motor neuron and effector, giving a rapid response without waiting for the brain to decide.

Mendel's monohybrid cross gave all tall plants in F1 and a 3 tall : 1 dwarf phenotypic ratio in F2; the genotypic ratio is 1 TT : 2 Tt : 1 tt.

Human sex determination: the mother contributes an X chromosome and the father contributes X or Y; XX is female and XY is male, so the father determines the sex of the child.

Plant hormones: auxin promotes cell elongation and phototropism, gibberellin promotes stem elongation, cytokinin promotes cell division, and abscisic acid closes stomata and induces dormancy.

Ten per cent law: only about 10 per cent of the energy at one trophic level is transferred to the next, the remainder being lost mainly as heat, so food chains rarely exceed four or five links.

Ozone O3 in the stratosphere absorbs harmful ultraviolet-B radiation; it is depleted by chlorofluorocarbons and halons, whose chlorine and bromine atoms destroy ozone catalytically.

Greenhouse gases include carbon dioxide, methane, nitrous oxide and water vapour; they absorb infrared radiation re-radiated by the Earth and cause global warming.

Biodegradable wastes such as paper, food and cotton are broken down by micro-organisms; non-biodegradable wastes such as polythene, glass, plastics and DDT persist and accumulate.

Eutrophication: excess nitrates and phosphates from fertilisers and sewage cause algal blooms, whose decomposition depletes dissolved oxygen and kills aquatic animals.

Acid rain is rainfall with pH below about 5.6, formed when sulphur dioxide and nitrogen oxides from burning fossil fuels dissolve in atmospheric moisture.

Waste management follows the three Rs: reduce, reuse and recycle; segregation of biodegradable and non-biodegradable waste at source is necessary before recycling or composting.

The Chipko movement (1973) and Joint Forest Management show community participation in forest protection; stakeholders include local villagers, the forest department and industry.