RBSE Praveshika Science cheat sheet

Matter is anything that has mass and occupies space; it exists in solid, liquid and gas states, with plasma as a fourth high-energy state.

Density = mass ÷ volume (SI unit kg m⁻³); relative density has no unit because it is a ratio of two densities.

Temperature stays constant during melting and boiling because the heat supplied becomes latent heat used to change state, not to raise kinetic energy.

Latent heat of fusion of ice = 3.34 × 10⁵ J kg⁻¹; latent heat of vaporisation of water = 22.6 × 10⁵ J kg⁻¹.

Evaporation is faster at higher temperature, larger surface area and stronger wind, and slower in humid air; it always cools the surface left behind.

Sublimation is direct solid-to-gas change without melting, seen in camphor, naphthalene, iodine and dry ice (solid CO₂); the reverse is deposition.

Mixtures are separated by physical methods such as filtration, distillation, sublimation and chromatography; compounds need chemical decomposition.

Law of conservation of mass: mass is neither created nor destroyed in a chemical reaction. Law of constant proportions: a compound always has elements in a fixed mass ratio.

Particles of matter are about 10⁻⁹ m in size; diffusion is fastest in gases and slowest in solids because of spacing and motion of particles.

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as.

Speed = distance ÷ time (scalar); velocity = displacement ÷ time (vector); acceleration = change in velocity ÷ time, SI unit m s⁻².

Newton's first law: a body remains at rest or in uniform motion unless an external unbalanced force acts on it; this property is inertia.

Newton's second law: F = ma, equivalently force = rate of change of momentum; 1 N = 1 kg m s⁻².

Newton's third law: every action has an equal and opposite reaction, and the two forces act on different bodies.

Momentum p = mv; when no external force acts, the total momentum of an isolated system is conserved in collisions and explosions.

Weight = mg and varies with g, while mass is constant. On Earth g ≈ 9.8 m s⁻²; on the Moon it is about one-sixth of that value.

Newton's law of gravitation: F = G m₁m₂/r² with G = 6.67 × 10⁻¹¹ N m² kg⁻²; the force is mutual and acts along the line joining the centres.

Friction opposes relative motion and produces heat; static friction is greater than sliding friction, and rolling friction is the smallest of the three.

Work W = F s cos θ, measured in joules; 1 J = 1 N m. Work is zero when force is perpendicular to displacement and negative when θ = 180° (as with friction).

Kinetic energy = ½mv²; gravitational potential energy near Earth's surface = mgh.

Power = work ÷ time = energy ÷ time; SI unit watt, 1 W = 1 J s⁻¹.

1 kWh = 3.6 × 10⁶ J is the commercial unit of electrical energy, called one 'unit' on a household bill.

Sound is a longitudinal mechanical wave and needs a material medium; it cannot travel through a vacuum.

Speed of sound is greatest in solids, less in liquids and least in gases (about 340 m s⁻¹ in air at 20 °C); it increases with temperature.

Human audible range is 20 Hz to 20 000 Hz; below is infrasonic and above is ultrasonic, used in sonar and medical scanning.

Loudness depends on amplitude, pitch on frequency and quality (timbre) on the waveform of overtones present.

An echo needs a gap of at least 0.1 s, so the reflector must be roughly 17 m away in air; distance = v × t ÷ 2.

Laws of reflection: angle of incidence = angle of reflection, and the incident ray, reflected ray and normal lie in one plane.

A plane mirror forms a virtual, erect, same-size, laterally inverted image as far behind the mirror as the object is in front; its focal length is infinite.

Mirror formula 1/v + 1/u = 1/f; magnification m = −v/u = h′/h; focal length f = R/2.

A concave mirror converges light and forms real or virtual images; a convex mirror diverges light and always gives a virtual, diminished, erect image with a wide field of view.

Snell's law: n = sin i / sin r. Refractive index is 1.33 for water, about 1.5 for glass and 2.42 for diamond.

Lens formula 1/v − 1/u = 1/f; magnification m = v/u; power P = 1/f with f in metres, unit dioptre (D).

Total internal reflection occurs when light moves from a denser to a rarer medium beyond the critical angle; it is the basis of optical fibres and mirages.

Dispersion by a prism splits white light into seven colours, red bending least and violet most.

Eye defects: myopia corrected by a concave lens, hypermetropia by a convex lens, presbyopia by bifocals; the normal near point is 25 cm.

Current I = Q/t with SI unit ampere; conventional current flows opposite to the drift of electrons.

Ohm's law: V = IR at constant temperature. Resistance R = ρL/A, so it doubles with length and halves when area is doubled; unit ohm (Ω).

Series combination: R = R₁ + R₂ + … with the same current through each. Parallel: 1/R = 1/R₁ + 1/R₂ + …, and the equivalent is less than the smallest resistor.

Electrical power P = VI = I²R = V²/R; energy in kWh = power in kW × time in hours.

Joule's law of heating: H = I²Rt. A fuse works on this principle, has a low melting point and is fitted in the live wire.

Magnetic field lines form closed loops, never intersect each other and are closer together where the field is stronger.

Right-hand thumb rule gives the field direction around a straight conductor; Fleming's left-hand rule gives the force on a current-carrying conductor (electric motor).

Fleming's right-hand rule gives the direction of induced current in a generator; AC reverses direction periodically while DC does not.

Indian domestic supply is 220 V at 50 Hz; live wire is red or brown, neutral black or blue, and the earth wire green for safety.

Observable signs of a chemical reaction: gas evolution, precipitate formation, colour change, temperature change or a new smell.

A balanced equation has equal numbers of atoms of each element on both sides, satisfying the law of conservation of mass.

Types: combination (A + B → AB), decomposition (AB → A + B), displacement by a more reactive metal, and double displacement with exchange of ions.

Oxidation is gain of oxygen or loss of electrons; reduction is loss of oxygen or gain of electrons; both occur together in a redox reaction.

Exothermic reactions release heat (combustion, respiration, neutralisation); endothermic reactions absorb heat (photosynthesis, thermal decomposition of CaCO₃).

Rate of reaction rises with concentration, temperature and surface area, and can be altered by a catalyst, which is not consumed.

Corrosion (iron + oxygen + moisture → rust) and rancidity (oxidation of fats and oils) are oxidation processes; antioxidants and airtight packing slow rancidity.

Electrolysis uses direct current to decompose a molten or dissolved compound, as in electroplating and refining of metals.

Acids release H⁺ ions in water and turn blue litmus red; bases release OH⁻ ions and turn red litmus blue.

pH scale runs from 0 to 14: below 7 acidic, exactly 7 neutral, above 7 basic; each unit is a tenfold change in H⁺ concentration.

Indicators: litmus, methyl orange (red in acid, yellow in base), phenolphthalein (colourless in acid, pink in base) and universal indicator for full pH.

Neutralisation: acid + base → salt + water. Acid + metal → salt + hydrogen. Acid + carbonate or bicarbonate → salt + water + carbon dioxide.

Strong acids (HCl, H₂SO₄, HNO₃) ionise completely; weak acids (ethanoic, carbonic) ionise partly. Dilution releases heat, so acid is added to water, never water to acid.

Common salts: baking soda NaHCO₃, washing soda Na₂CO₃·10H₂O, bleaching powder Ca(OCl)Cl, plaster of Paris CaSO₄·½H₂O, gypsum CaSO₄·2H₂O.

Tooth decay begins below pH 5.5, acid rain has pH under 5.6, and antacids neutralise excess stomach hydrochloric acid.

Salt of strong acid + strong base is neutral; strong acid + weak base is acidic; weak acid + strong base is basic.

Metals are lustrous, malleable, ductile, sonorous and good conductors; non-metals are generally the opposite, except graphite which conducts electricity.

Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > H > Cu > Hg > Ag > Au; a metal above displaces one below from its salt solution.

Metals give salt + hydrogen with acids and basic oxides with oxygen; amphoteric oxides such as Al₂O₃ and ZnO react with both acids and bases.

Ionic bonding involves transfer of electrons from metal to non-metal; such compounds have high melting points and conduct when molten or in solution.

Alloys: brass = copper + zinc; bronze = copper + tin; steel = iron + carbon; solder = lead + tin with a low melting point.

Carbon is tetravalent and shows catenation, giving a huge number of compounds; allotropes are diamond (hard, non-conducting), graphite (soft, conducting) and fullerene.

Members of a homologous series differ by CH₂. Functional groups: –OH alcohol, –CHO aldehyde, –CO– ketone, –COOH carboxylic acid.

Ethanol C₂H₅OH is oxidised to ethanoic acid CH₃COOH by acidified potassium permanganate or acidified dichromate.

Soap is a sodium or potassium salt of a long-chain fatty acid; it forms micelles that trap oily dirt, and it gives scum in hard water.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in chloroplasts using chlorophyll and light; stomata allow gas exchange and transpiration.

Aerobic respiration in mitochondria releases far more energy than anaerobic respiration; muscle cells give lactic acid, yeast gives ethanol and CO₂.

Human circulation is double with a four-chambered heart; arteries carry blood away from the heart, veins towards it and capillaries allow exchange.

Blood contains plasma, RBCs with haemoglobin for oxygen transport, WBCs for defence and platelets for clotting.

Xylem carries water and minerals upward through dead lignified cells; phloem carries food in both directions through living cells.

The nephron is the functional unit of the kidney; urine forms by filtration and selective reabsorption, and dialysis removes wastes artificially.

Nervous control involves neurons and synapses; a reflex arc passes through the spinal cord. CNS = brain + spinal cord; PNS = cranial and spinal nerves.

Hormones: insulin from the pancreas lowers blood glucose; thyroxine controls metabolism; adrenaline prepares the body for emergencies; auxin and gibberellin control plant growth.

Tropisms are directional growth responses: phototropism to light, geotropism to gravity, hydrotropism to water and chemotropism to chemicals.

Asexual methods: binary fission (Amoeba), budding (yeast, Hydra), fragmentation (Spirogyra), regeneration (Planaria), spore formation (Rhizopus), vegetative propagation (sugarcane, potato).

Sexual reproduction requires gametes and fertilisation and produces variation, which is the raw material of evolution.

Testes produce sperm and testosterone; ovaries produce ova and oestrogen/progesterone; fertilisation normally occurs in the fallopian tube.

The placenta exchanges nutrients, oxygen and wastes between mother and embryo; human gestation is about nine months.

In flowers pollination is transfer of pollen to the stigma, while fertilisation is fusion of gametes; angiosperms show double fertilisation.

Mendel's monohybrid F₂ phenotypic ratio is 3:1 with genotypic ratio 1:2:1; the dihybrid F₂ phenotypic ratio is 9:3:3:1.

Genotype is the allele makeup and phenotype the visible trait; homozygous means identical alleles, heterozygous different alleles; the dominant allele masks the recessive.

Human sex determination: XX is female and XY is male, so the father's sperm decides the child's sex.

Evolution by natural selection (Darwin): homologous organs share basic structure (forelimbs), analogous organs share function (insect and bird wings); fossils give direct evidence.

An ecosystem is the biotic community plus abiotic factors; producers, consumers and decomposers are linked through food chains and food webs.

Only about 10% of energy passes to the next trophic level, so food chains are short and top carnivores are few.

Biogeochemical cycles include the carbon, nitrogen, oxygen and water cycles; decomposers return nutrients to the soil.

Ozone (O₃) in the stratosphere absorbs harmful ultraviolet radiation; CFCs and halons deplete it and create the ozone hole.

Greenhouse gases such as CO₂, CH₄, N₂O and water vapour trap infrared radiation, causing global warming and climate change.

Pollution types: air (SO₂ and NOₓ leading to acid rain), water (sewage raises BOD, fertilisers cause eutrophication) and soil (pesticides, plastics).

Renewable resources (sun, wind, water, biomass) replenish naturally; non-renewable ones (coal, petroleum, minerals) do not, so follow the 3Rs: reduce, reuse, recycle.

Soil conservation uses contour ploughing, terracing, afforestation and check dams; watershed management harvests rainwater.

Biodiversity is protected by national parks, sanctuaries, biosphere reserves and seed banks; the Chipko movement saved Himalayan forests.