EJU Science cheat sheet

Newton's second law: net force = mass × acceleration (F = ma); action–reaction pairs act on different bodies, so they never cancel inside one body's equation of motion.

Momentum p = mv is conserved when the net external impulse is zero; for two-body collisions the coefficient of restitution e = (v₂′ − v₁′)/(v₁ − v₂), with e = 1 elastic and e = 0 perfectly inelastic (bodies move together).

Work–energy: work by all forces equals the change in kinetic energy; friction removes mechanical energy as heat, while gravity and spring forces are conservative and have potentials mgh and ½kx².

Uniform circular motion: v = rω, centripetal acceleration a = v²/r = rω² directed to the centre; period T = 2πr/v; on a banked or frictional track the inward force is provided by a component of normal force or static friction.

Ideal gas: pV = nRT with T in kelvin, R = 8.31 J/(mol·K); monatomic internal energy U = (3/2)nRT; first law ΔU = Q + W, where W is work done on the gas (isothermal ΔU = 0, isochoric W = 0, adiabatic Q = 0).

Waves: v = fλ; string wave speed v = √(T/μ) with tension T and linear density μ; a pipe open at both ends has antinodes at both ends (λ = 2L for the fundamental), a pipe closed at one end has a node there (λ = 4L).

Geometric optics: n₁ sin θ₁ = n₂ sin θ₂; total internal reflection occurs only when light goes from higher to lower n and θ exceeds θc with sin θc = n₂/n₁; thin lens/mirror 1/f = 1/a + 1/b.

Electrostatics and circuits: Coulomb F = kq₁q₂/r², uniform field E = V/d, capacitor C = εS/d storing ½CV²; magnetic force F = qvB sin θ or F = BIL sin θ; induced emf = −ΔΦ/Δt (Faraday–Lenz).

Atomic physics: photoelectric effect hν = W + K_max, so no emission below the threshold frequency ν₀ = W/h; hydrogen levels E_n = −13.6/n² eV, and a photon's energy equals the level difference.

Amount of substance n = m/M = N/N_A, with N_A = 6.02×10²³ mol⁻¹; molar volume of an ideal gas is 22.4 L at 0 °C and 1 atm, about 24.5 L at 25 °C and 1 atm.

Concentration c = n/V (mol/L); dilution keeps moles constant so c₁V₁ = c₂V₂; mass percent = (solute mass/solution mass)×100, and molality uses solvent mass in kg.

Acid–base: pH = −log[H₃O⁺], pOH = −log[OH⁻], pH + pOH = 14 at 25 °C; strong acids dissociate completely, weak acids follow Ka = [H⁺][A⁻]/[HA]; buffer pH = pKa + log([A⁻]/[HA]).

Equilibrium: Kc = [products]^coeff/[reactants]^coeff depends only on temperature; Le Châtelier shifts: raising pressure favours the side with fewer gas moles, raising temperature favours the endothermic direction, catalysts change rate only.

Redox bookkeeping: oxidation number of O is −2 (except peroxides), H is +1 (except hydrides), free elements 0, sum equals the ion charge; balance half-reactions with H₂O/H⁺ in acid and H₂O/OH⁻ in base.

Electrochemistry: cell emf = E°(cathode) − E°(anode), and a positive emf means spontaneity; ΔG° = −nFE°; electrolysis charge Q = It with F = 96,500 C/mol of electrons.

Organic formulas: alkanes CnH2n+2, alkenes CnH2n, alkynes CnH2n−2, benzene rings C6H6; functional groups −OH alcohol, −CHO aldehyde, −CO− ketone, −COOH carboxylic acid, −COO− ester.

Reaction patterns: alkanes give radical substitution with halogens under UV; alkenes give electrophilic addition of H₂, X₂, HX; alcohols dehydrate to alkenes and oxidise to aldehydes/ketones or acids depending on the alcohol class.

Esterification (acid + alcohol, concentrated H₂SO₄ catalyst) is reversible; ester hydrolysis under base is saponification and goes to completion because the carboxylate salt is formed.

Prokaryotes lack a nucleus and membrane-bound organelles and keep DNA in a nucleoid; both prokaryotes and eukaryotes have ribosomes, but only eukaryotes have mitochondria, chloroplasts and a nuclear envelope.

Organelle functions: mitochondria (oxidative phosphorylation, cristae), chloroplasts (light reactions in thylakoids, Calvin cycle in stroma), rough ER (protein synthesis and transport), Golgi (modification and secretion), lysosomes (hydrolytic digestion).

Cell cycle order: G1 → S (DNA replication) → G2 → M; mitosis stages prophase, metaphase, anaphase, telophase give two diploid, genetically identical cells, while meiosis gives four haploid cells after two divisions.

Photosynthesis summary: light reactions split water to give O₂, ATP and NADPH; the Calvin cycle uses rubisco to fix CO₂ into triose phosphate, which builds glucose and starch.

Respiration summary: glycolysis (cytosol, 2 ATP, 2 NADH) → pyruvate oxidation and Krebs cycle (matrix, CO₂ and reduced coenzymes) → electron transport chain on the inner membrane, giving about 36–38 ATP per glucose aerobically.

Genetics: alleles segregate so each gamete carries one per gene, and different gene pairs assort independently when on different chromosomes; a test cross with a homozygous recessive reveals an unknown genotype.

Molecular genetics: DNA is antiparallel with A–T and G–C pairing, replicates semiconservatively, is transcribed to mRNA, and is translated at ribosomes by codon–anticodon matching with tRNA-delivered amino acids.

Circulation in mammals: double circulation with left ventricle → aorta → body → vena cava → right atrium → right ventricle → pulmonary artery → lungs → pulmonary vein → left atrium; mammalian red blood cells lack a nucleus and carry haemoglobin.

Ecology: energy flows through trophic levels with roughly ten percent transfer efficiency, so food chains are short; matter such as carbon and nitrogen cycles, with nitrogen fixation by rhizobia and nitrification by soil bacteria.