NSEJS cheat sheet

Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as apply only for constant acceleration; average velocity = (u+v)/2 in that case.

Newton's second law: net force F = ma; weight = mg with g ≈ 9.8 m/s² (often 10 in NSEJS numericals). Friction f = μN opposes relative motion.

Work-energy: W = Fs cosθ, kinetic energy = ½mv², gravitational PE = mgh; mechanical energy conserved when only conservative forces act.

Momentum p = mv is conserved in all collisions; kinetic energy conserved only in elastic collisions. Impulse = FΔt = Δp.

Pressure in fluids: P = P₀ + ρgh; buoyant force = ρ_fluid·V_displaced·g. A floating body displaces fluid equal to its own weight.

Ohm's law V = IR; series R = R₁+R₂+…, parallel 1/R = 1/R₁+1/R₂+…; electrical power P = VI = I²R = V²/R.

Light: for mirrors and thin lenses 1/v − 1/u = 1/f (mirror) and 1/v − 1/u = 1/f with sign convention; refraction index n = c/v, Snell's law n₁sinθ₁ = n₂sinθ₂.

Wave relation v = fλ; sound speed in air rises with temperature; echo distance = v·t/2. Heat: Q = mcΔT, latent heat Q = mL.

Mole concept: 1 mol = 6.022×10²³ particles; moles n = mass/molar mass; at STP 1 mol of ideal gas occupies 22.4 L.

Empirical formula from percentage composition: divide each % by atomic mass, then divide by the smallest ratio; molecular formula = (empirical formula)ₙ where n = molar mass/empirical formula mass.

Periodic trends: atomic radius decreases left→right across a period and increases down a group; ionisation energy and electronegativity increase left→right and up a group.

Acid-base: pH = −log[H⁺]; strong acid fully dissociates; neutralisation H⁺ + OH⁻ → H₂O. Moles of acid × basicity = moles of base × acidity at equivalence.

Oxidation = loss of electrons (increase in oxidation number); reduction = gain. In a redox reaction, total electrons lost equals total electrons gained.

Gas laws: PV = nRT; Boyle PV = constant at fixed T; Charles V/T = constant at fixed P; combined P₁V₁/T₁ = P₂V₂/T₂.

Bonding: ionic bonds form between metal and nonmetal with large electronegativity difference; covalent bonds share electrons; metallic bonding involves delocalised electrons.

Reaction types and balancing: conservation of atoms and charge; combustion of hydrocarbons gives CO₂ + H₂O; displacement occurs when a more reactive metal displaces a less reactive one.

Cell organelles: mitochondria (ATP via aerobic respiration), chloroplasts (photosynthesis, contain chlorophyll), ribosomes (protein synthesis), lysosomes (hydrolytic enzymes), nucleus (DNA).

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ in the presence of light and chlorophyll; light reactions in thylakoids, Calvin cycle in the stroma.

Respiration: aerobic yields ~36–38 ATP per glucose; anaerobic in muscle gives lactic acid, in yeast gives ethanol + CO₂.

Blood: arteries carry blood away from the heart (thick elastic walls), veins toward the heart (valves), capillaries are one-cell thick for exchange. Human heart has four chambers.

Mendelian genetics: monohybrid F₂ phenotypic ratio 3:1, genotypic 1:2:1; dihybrid F₂ 9:3:3:1; test cross distinguishes homozygous dominant from heterozygous.

Human digestive enzymes: salivary amylase digests starch, pepsin (stomach, acidic) digests protein, lipase digests fats, trypsin acts in the small intestine.

Plant transport: xylem carries water and minerals upward (transpiration pull), phloem carries sugars bidirectionally; stomata regulate gas exchange and water loss.

Excretion and homeostasis: nephron is the functional unit of the kidney (filtration, reabsorption, secretion); negative feedback maintains internal conditions such as temperature and blood glucose.