Lebanese University Faculty of Agronomy Entrance Examination cheat sheet

Cell theory: all living organisms are made of cells; cells are the basic structural and functional unit; new cells arise from pre-existing cells by division.

Prokaryotic cells lack a membrane-bound nucleus and mitochondria; eukaryotic cells have a nucleus, endoplasmic reticulum, Golgi, mitochondria, and in plants chloroplasts and a cell wall.

Photosynthesis: 6CO2 + 6H2O + light → C6H12O6 + 6O2; light reactions occur in thylakoid membranes and the Calvin cycle in the stroma.

Cellular respiration: C6H12O6 + 6O2 → 6CO2 + 6H2O + ATP; glycolysis occurs in cytoplasm, Krebs cycle in mitochondrial matrix, oxidative phosphorylation on inner membrane.

Mendel monohybrid cross of heterozygotes gives 3:1 phenotype and 1:2:1 genotype; dihybrid cross with independent assortment gives 9:3:3:1.

DNA is antiparallel double helix; A pairs with T by two hydrogen bonds, G with C by three; replication is semiconservative.

Plant transport: xylem carries water and minerals upward under cohesion-tension; phloem carries sucrose from source to sink; stomata regulated by guard cells.

Taxonomy hierarchy: domain, kingdom, phylum, class, order, family, genus, species; binomial name = capitalized genus + lowercase species epithet, italicized.

Mole: n = m/M; one mole contains 6.022×10^23 entities; molar volume of an ideal gas is 22.4 L at STP (273.15 K, 1 atm).

Ideal gas law: PV = nRT with R = 8.314 J mol^-1 K^-1; at constant T and n, P1V1 = P2V2.

pH = -log[H3O+]; pOH = -log[OH-]; at 25°C pH + pOH = 14 and Kw = Ka × Kb = 1.0×10^-14.

Redox: oxidation is loss of electrons, reduction is gain; balance by separating half-reactions and equalizing electron transfer.

Functional groups: alcohol -OH, aldehyde -CHO, ketone C=O, carboxylic acid -COOH, amine -NH2, ester -COO-, amide -CONH2.

Isomers have same molecular formula but different structures; enantiomers are non-superimposable mirror images; cis-trans isomers differ around a double bond or ring.

Beer-Lambert law: A = εlc; absorbance is proportional to concentration for dilute colored solutions at a fixed wavelength and path length.

Arrhenius equation: k = A e^(-Ea/RT); catalysts lower activation energy Ea without changing equilibrium constant; increasing temperature increases k.

Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity increases across a period and decreases down a group.

Quadratic equation ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/(2a); discriminant D = b² - 4ac; D>0 two real roots, D=0 one double root, D<0 no real roots.

Logarithms: log(ab) = log a + log b; log(a/b) = log a - log b; log(a^n) = n log a; change of base logb a = ln a / ln b.

Derivatives: (x^n)' = n x^(n-1); (e^x)' = e^x; (ln x)' = 1/x; product rule (uv)' = u'v + uv'; chain rule d/dx f(g(x)) = f'(g(x))g'(x).

Integral: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ -1; ∫ 1/x dx = ln|x| + C; definite integral equals F(b) - F(a).

Limits: lim x→0 (sin x)/x = 1; lim n→∞ (1 + 1/n)^n = e; a function is continuous at a if limit equals function value.

Probability: P(A∪B) = P(A) + P(B) - P(A∩B); P(A|B) = P(A∩B)/P(B); independent events satisfy P(A∩B) = P(A)P(B).

Statistics: mean μ = Σx/n; variance σ² = Σ(x-μ)²/n for population; standard deviation σ = √σ²; normal distribution follows 68-95-99.7 rule.

Combinatorics: nPr = n!/(n-r)!; nCr = n!/[r!(n-r)!]; arithmetic sequence an = a1 + (n-1)d; geometric sequence an = a1 r^(n-1).

Newton's laws: Fnet = ma; inertia keeps velocity constant without net force; action-reaction forces are equal, opposite, on different bodies.

Kinematics with constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.

Work-energy: W = Fd cosθ; kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; mechanical energy conserved without friction.

Fluids: pressure P = F/A; hydrostatic P = P0 + ρgh; buoyancy Fb = ρfluid V g; continuity A1v1 = A2v2 for incompressible flow.

Electricity: Ohm V = IR; power P = VI = I²R = V²/R; series resistances add; parallel 1/R = Σ1/Ri; Coulomb F = kq1q2/r².

Optics: Snell n1 sinθ1 = n2 sinθ2; thin lens 1/f = 1/do + 1/di; magnification m = -di/do; total internal reflection when angle exceeds critical angle.

Thermodynamics: ΔU = Q - W; W = PΔV at constant pressure; Carnot efficiency η = 1 - Tc/Th; entropy of isolated system does not decrease.

Waves: v = fλ; frequency determined by source, speed by medium; sound needs a medium; light travels in vacuum at c ≈ 3×10^8 m/s.

Soil profile horizons: O organic layer, A topsoil, E eluviated layer, B subsoil accumulation, C parent material, R bedrock.

Soil texture triangle classifies sand, silt, clay; clay and humus increase water retention and cation exchange capacity; sandy soils drain faster.

Soil pH controls nutrient availability; lime (CaCO3) raises pH, elemental sulfur lowers pH; most crops grow best near pH 6-7.

Water cycle: evaporation, transpiration, condensation, precipitation, infiltration, runoff, groundwater flow; watersheds collect runoff.

Climate vs weather: weather is short-term atmospheric state; climate is long-term average and variability, often over 30 years.

Greenhouse gases include CO2, CH4, N2O, and water vapor; they absorb outgoing infrared radiation and warm the lower atmosphere.

Ecology: energy flows through trophic levels with about 10% transfer; nutrients cycle; carrying capacity limits population growth.

Nitrogen cycle: fixation converts N2 to ammonia; nitrification forms nitrite then nitrate; denitrification returns N2 to atmosphere.

Natural resources: renewable resources replenish naturally; nonrenewable resources such as fossil fuels and minerals are finite; sustainable use matches consumption to replenishment.

Scientific report structure IMRaD: Introduction states question and hypothesis; Methods gives procedure; Results reports data; Discussion interprets and limits conclusions.

Citation: APA uses author-date in text; Vancouver uses numbered references; every borrowed idea, figure, or dataset needs a citation.

Plagiarism: presenting others' words, ideas, data, or images as one's own; avoid by quoting, paraphrasing, and citing the original source.

SI units: length meter (m), mass kilogram (kg), time second (s), amount mole (mol), temperature kelvin (K); prefixes kilo 10^3, milli 10^-3, micro 10^-6.

Significant figures: all nonzero digits significant; zeros between significant digits are significant; leading zeros not significant; trailing zeros after decimal are significant.

Graph conventions: independent variable on x-axis, dependent variable on y-axis; label axes with quantity and unit; include a descriptive caption and legend.

Technical terms: photosynthesis = photosynthèse (French) = التمثيل الضوئي (Arabic); cell = cellule = خلية; DNA = ADN = الحمض النووي.

Abstract: concise summary of objective, methods, key results, and conclusion, usually 150-250 words; it should stand alone without citations or undefined abbreviations.

Precision vs accuracy: precision is closeness of repeated measurements; accuracy is closeness to true value; random errors affect precision, systematic errors affect accuracy.