Odisha BSE Madhyama Science cheat sheet

Ohm's law: V = IR, where V is potential difference in volts, I is current in amperes, and R is resistance in ohms; valid for metallic conductors at constant temperature.

Series combination: total resistance R = R1 + R2 + R3; the same current flows through every component and the total voltage divides in proportion to resistance.

Parallel combination: 1/R = 1/R1 + 1/R2 + 1/R3; the voltage is the same across every branch and the total current is the sum of branch currents.

Electrical power: P = VI = I²R = V²/R; energy consumed in kWh equals power in kilowatts multiplied by time in hours.

Mirror formula: 1/v + 1/u = 1/f, with the Cartesian sign convention where distances measured against the incident light are negative; magnification m = -v/u.

Lens formula: 1/v - 1/u = 1/f; power of a lens P = 1/f (in metres), measured in dioptres, and power is positive for a converging convex lens.

Snell's law: n1 sin i = n2 sin r; refractive index n = c/v, so light bends towards the normal when entering a denser medium.

Magnetic field around a straight current-carrying conductor forms concentric circles; the field direction is given by the right-hand thumb rule and reverses when the current reverses.

Fleming's left-hand rule gives the direction of force on a current-carrying conductor in a magnetic field: thumb = force, forefinger = field, middle finger = current.

Balanced chemical equation: number of atoms of each element is equal on both sides; coefficients are adjusted, never subscripts, to balance an equation.

Law of conservation of mass: mass can neither be created nor destroyed in a chemical reaction, so total reactant mass equals total product mass.

Acids turn blue litmus red and have pH below 7; bases turn red litmus blue and have pH above 7; pH 7 is neutral at 25 °C.

Neutralisation: acid + base → salt + water, e.g. HCl + NaOH → NaCl + H2O; this is an exothermic reaction.

Types of reaction: combination (A + B → AB), decomposition (AB → A + B), displacement (A + BC → AC + B), and double displacement (AB + CD → AD + CB).

Oxidation is loss of electrons or gain of oxygen; reduction is gain of electrons or loss of hydrogen; a redox reaction involves both simultaneously.

Molar mass in grams per mole equals the sum of atomic masses; one mole of any substance contains 6.022 × 10²³ particles (Avogadro's number).

Metals are generally malleable, ductile, sonorous and good conductors; non-metals are brittle and poor conductors, with graphite as a conducting exception.

Rusting of iron needs both oxygen and moisture; galvanisation coats iron with zinc to prevent contact with air and water.

Photosynthesis: 6CO2 + 6H2O → C6H12O6 + 6O2 in the presence of chlorophyll and sunlight; occurs in chloroplasts, mainly in palisade mesophyll cells.

Stomata are tiny pores on leaves guarded by guard cells; they allow gas exchange and transpiration, opening when guard cells are turgid.

Xylem transports water and dissolved minerals upward from roots; phloem transports prepared food in both directions.

Human digestive order: mouth → oesophagus → stomach → small intestine → large intestine; most absorption occurs in the small intestine via villi.

Human breathing: inhalation lowers diaphragm and raises ribs, increasing chest volume and lowering pressure so air enters the lungs.

Blood components: plasma, red blood cells (haemoglobin, oxygen transport), white blood cells (defence) and platelets (clotting); RBCs lack a nucleus in mammals.

Nephron is the functional unit of the kidney; it filters blood at the glomerulus and reabsorbs glucose, salts and water in the tubule.

Asexual reproduction modes: binary fission (Amoeba), budding (Hydra, yeast), fragmentation (Spirogyra) and vegetative propagation in plants.

Mendel's law of segregation: alleles separate during gamete formation, so each gamete carries only one allele of a pair; dominant allele masks recessive.

Newton's second law: F = ma; force in newtons equals mass in kilograms times acceleration in metres per second squared.

Equations of motion: v = u + at; s = ut + ½at²; v² = u² + 2as, where u is initial and v is final velocity.

Work W = F·s·cos θ in joules; power P = W/t in watts; one kilowatt-hour equals 3.6 × 10⁶ joules.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh, with g ≈ 9.8 m/s² near Earth's surface.

Law of conservation of energy: energy is neither created nor destroyed but changes form; in a freely falling body potential energy converts to kinetic energy.

Momentum p = mv, measured in kg·m/s; in an isolated system total momentum before collision equals total momentum after collision.

Universal law of gravitation: F = G m1 m2 / r², with G = 6.67 × 10⁻¹¹ N·m²/kg²; weight = mg varies with location while mass is constant.

Sound is a longitudinal mechanical wave needing a medium; it travels fastest in solids and cannot travel through a vacuum.

Frequency is measured in hertz; audible range for humans is about 20 Hz to 20,000 Hz, and ultrasound lies above 20,000 Hz.

Matter has three common states: solid (fixed shape and volume), liquid (fixed volume, no fixed shape) and gas (neither fixed); plasma is a fourth state.

Change of state: melting (solid→liquid), freezing (liquid→solid), evaporation (liquid→gas), condensation (gas→liquid) and sublimation (solid→gas directly).

Latent heat of fusion of ice is about 80 cal/g; during a change of state the temperature stays constant even though heat is absorbed.

Density = mass / volume; objects with density less than water (about 1 g/cm³) float on it.

Dalton's atomic theory states that matter is made of indivisible atoms of a given element identical in mass and properties.

Thomson's model described the atom as a sphere of positive charge with electrons embedded in it; Rutherford's alpha-scattering experiment revealed a small dense nucleus.

Atomic number Z equals the number of protons; mass number A equals protons plus neutrons; isotopes have the same Z but different A.

Valency is the combining capacity of an element; the modern periodic table arranges elements by increasing atomic number into 18 groups and 7 periods.

Ionic bonds form by transfer of electrons between metals and non-metals; covalent bonds form by sharing electrons between non-metals.

Average speed = total distance / total time; velocity is speed in a stated direction, so a body moving uniformly in a circle has changing velocity.

Acceleration = change in velocity / time taken; its SI unit is m/s² and deceleration is negative acceleration.

Distance-time graph: a straight sloping line means uniform speed, a horizontal line means the body is at rest; slope gives speed.

Velocity-time graph: slope gives acceleration and the area under the graph gives the distance travelled.

Uniform circular motion requires a continuous centripetal force directed towards the centre; speed stays constant while direction changes.

Scalars have magnitude only (distance, speed, mass); vectors have magnitude and direction (displacement, velocity, force).

First law of motion (inertia): a body stays at rest or in uniform motion unless acted on by a net external force.

Third law of motion: every action has an equal and opposite reaction acting on a different body, so the two forces never cancel.

Friction opposes relative motion, acts along the surface, and can be reduced by lubricants or ball bearings.

Cell organelles: nucleus (control centre), mitochondria (power house, ATP production), ribosome (protein synthesis), chloroplast (photosynthesis) and vacuole (storage).

Plant cells have a cellulose cell wall, chloroplasts and a large central vacuole; animal cells lack a cell wall and chloroplasts and have centrioles.

Prokaryotic cells lack a true nucleus and membrane-bound organelles (bacteria); eukaryotic cells have a nucleus bounded by a nuclear membrane.

Mitosis produces two genetically identical diploid daughter cells for growth and repair; meiosis produces four haploid gametes with variation.

Tissues: meristematic tissue causes growth in plants; epithelial, connective, muscular and nervous tissues are the four animal tissue types.

Classification hierarchy: kingdom → phylum → class → order → family → genus → species; the binomial name gives genus and species.

Five-kingdom system: Monera, Protista, Fungi, Plantae and Animalia, distinguished by cell type, body organisation and mode of nutrition.

Food chain transfers energy from producers to consumers; only about 10% of energy passes to the next trophic level.

Ecosystem components are biotic (producers, consumers, decomposers) and abiotic (light, temperature, water, soil); decomposers recycle nutrients.

Speed of light in vacuum c ≈ 3 × 10⁸ m/s; light travels in straight lines and shows reflection, refraction, dispersion and scattering.

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

Plane mirror forms a virtual, erect image of the same size, laterally inverted, at the same distance behind the mirror as the object is in front.

Concave mirrors converge light and can form real or virtual images; convex mirrors diverge light and always form a virtual, diminished, erect image.

Concave mirror uses: shaving mirrors and torch reflectors; convex mirror uses: rear-view mirrors in vehicles because of a wide field of view.

Real images are inverted and can be caught on a screen; virtual images are erect and cannot be caught on a screen.

Dispersion splits white light into seven colours (VIBGYOR) because each colour has a different refractive index in glass.

Total internal reflection occurs when light travels from a denser to a rarer medium beyond the critical angle; used in optical fibres.

Human eye: cornea and lens focus light on the retina; myopia is corrected by a concave lens and hypermetropia by a convex lens.

Electric current is the rate of flow of charge: I = Q/t, measured in amperes; conventional current flows opposite to electron flow.

Ammeter measures current and is connected in series; voltmeter measures potential difference and is connected in parallel across a component.

Resistance R = ρL/A; it increases with length, decreases with cross-sectional area, and rises with temperature for metals.

Electric fuse works on the heating effect of current; it melts and breaks the circuit when current exceeds a safe value.

Electric motor converts electrical energy into mechanical energy using the magnetic effect of current on a coil in a magnetic field.

Electric generator converts mechanical energy into electrical energy by electromagnetic induction; a split-ring commutator gives direct current.

Domestic wiring is parallel so each appliance gets full supply voltage and can be switched independently; the earth wire is a safety connection.

Alternating current in Indian domestic supply reverses direction periodically at about 50 Hz and is supplied at about 220 V.

Heating effect: heat produced H = I²Rt joules, which explains working of electric iron, heater and filament bulb.