Lebanese University Faculty of Medical Sciences Entrance Examination - Second Year, General Medicine study materials
Lebanese University Faculty of Medical Sciences Entrance Examination - Second Year, General Medicine study resources

Lebanese University Faculty of Medical Sciences Entrance Examination - Second Year, General Medicine cheat sheet

Lebanese University Faculty of Medical Sciences Entrance Examination - Second Year, General Medicine · Keep the key ideas within reach.

Quick reference

Biology - Cell Biology and Molecular Biology

  • Central dogma: DNA → RNA → protein; transcription occurs in the nucleus (eukaryotes), translation on ribosomes in the cytoplasm or rough ER.

  • Membrane transport decision rule: O2, CO2, steroids cross by simple diffusion; glucose and ions need carriers or channels; macromolecules use vesicular transport.

  • Na+/K+-ATPase pumps 3 Na+ out and 2 K+ in per ATP hydrolyzed, maintaining resting membrane potential and osmotic balance.

  • Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity and inversely reflects enzyme affinity.

  • Competitive inhibitors raise apparent Km with unchanged Vmax; non-competitive inhibitors lower Vmax with unchanged Km.

  • DNA replication is semiconservative and proceeds 5'→3' by DNA polymerase; the leading strand is continuous, the lagging strand is made in Okazaki fragments.

  • Mitochondrial oxidative phosphorylation yields roughly 30–32 ATP per glucose; glycolysis (cytosol) nets 2 ATP and 2 NADH.

  • Cell cycle checkpoints: G1/S (DNA damage, size), G2/M (replication complete), and spindle assembly checkpoint at metaphase.

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Biology - Genetics

  • Mendel's law of segregation: two alleles separate during meiosis I; independent assortment applies only to genes on different chromosomes or far apart on the same chromosome.

  • Monohybrid cross Aa × Aa gives 1:2:1 genotype and 3:1 phenotype; dihybrid AaBb × AaBb gives 9:3:3:1.

  • Test cross with a homozygous recessive reveals the genotype of a dominant-phenotype individual.

  • Hardy–Weinberg: p + q = 1 and p² + 2pq + q² = 1; allele frequencies stay constant without selection, mutation, migration, drift, or non-random mating.

  • X-linked recessive traits affect males more; an affected father cannot pass the allele to sons but transmits it to all daughters (carriers).

  • Codominance (AB blood type) shows both alleles; incomplete dominance (pink snapdragons) gives an intermediate phenotype.

  • Pedigree rule: two affected parents with an unaffected child indicates a dominant trait; unaffected parents with an affected child indicates recessive.

  • Karyotype notation: 47,XX,+21 = female with trisomy 21; 46,XY = normal male karyotype.

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Chemistry - General and Inorganic Chemistry

  • Moles: n = m/M = N/NA = V/22.4 L at STP for gases; NA = 6.022 × 10²³ mol⁻¹.

  • pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 at 25 °C; strong acid pH requires full dissociation.

  • Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); buffer capacity is maximal when pH = pKa.

  • Ideal gas law: PV = nRT with R = 8.314 J·mol⁻¹·K⁻¹; temperature must be in kelvin.

  • Oxidation numbers: O is usually −2, H is +1, sum equals the overall charge; oxidation is loss of electrons, reduction is gain.

  • Periodic trends: atomic radius decreases left→right and increases top→bottom; electronegativity and ionization energy increase left→right and up a group.

  • Solubility rule: most nitrates, acetates, and alkali-metal salts are soluble; AgCl, BaSO4, and PbI2 are sparingly soluble.

  • Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; a catalyst changes rate only, not position.

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Chemistry - Organic Chemistry

  • Functional-group priority for naming: carboxylic acid > ester > amide > nitrile > aldehyde > ketone > alcohol > amine > alkene > alkyne > alkane.

  • Markovnikov's rule: H adds to the carbon with more hydrogens; anti-Markovnikov addition occurs with HBr and peroxides (radical mechanism).

  • SN1 proceeds via carbocation intermediate, favored by tertiary substrates and polar protic solvents; SN2 is concerted and favored by primary substrates and polar aprotic solvents.

  • Elimination (E2) uses a strong base and is anti-periplanar; higher temperature favors elimination over substitution.

  • Nucleophilic acyl substitution on acid chlorides is fastest, then anhydrides, esters, and amides; amides are least reactive due to resonance.

  • Aldehydes are more reactive than ketones toward nucleophilic addition; Tollens' reagent tests aldehydes (silver mirror).

  • Chirality requires a carbon with four different groups; a racemic mixture has zero net optical rotation.

  • Aromaticity (Hückel): cyclic, planar, fully conjugated, 4n + 2 π electrons; benzene has 6 π electrons and undergoes substitution, not addition.

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Physics

  • Kinematics: v = v₀ + at; x = v₀t + ½at²; v² = v₀² + 2ax (constant acceleration only).

  • Newton's second law: ΣF = ma; weight W = mg with g ≈ 9.8 m·s⁻² near Earth's surface.

  • Work–energy theorem: W = ΔKE = ½mv² − ½mv₀²; gravitational potential energy near Earth U = mgh.

  • Conservation of momentum: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' for isolated systems; kinetic energy is conserved only in elastic collisions.

  • Ohm's law V = IR; power P = VI = I²R = V²/R; resistors in series add, in parallel 1/R = Σ1/Rᵢ.

  • Snell's law: n₁sinθ₁ = n₂sinθ₂; total internal reflection occurs when the incidence angle exceeds the critical angle sinθc = n₂/n₁.

  • Ideal gas kinetic theory: average kinetic energy depends only on temperature, KE = (3/2)kBT per molecule.

  • Simple harmonic motion: T = 2π√(m/k) for a spring; T = 2π√(L/g) for a pendulum; period is independent of amplitude.

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Mathematics

  • Quadratic formula: x = (−b ± √(b² − 4ac))/(2a); discriminant Δ = b² − 4ac gives two, one, or no real roots.

  • Derivative rules: (xⁿ)' = nxⁿ⁻¹; (eˣ)' = eˣ; (ln x)' = 1/x; product rule (uv)' = u'v + uv'; chain rule d/dx f(g(x)) = f'(g(x))g'(x).

  • Definite integral as area: ∫ₐᵇ f(x)dx = F(b) − F(a) for an antiderivative F.

  • Limits: lim(x→0) sin x/x = 1; lim(x→0)(1 − cos x)/x = 0; L'Hôpital applies to 0/0 or ∞/∞ forms.

  • Logarithm rules: log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n log a; log_b a = ln a/ln b.

  • Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x.

  • Arithmetic sequence: uₙ = u₁ + (n−1)r; geometric sequence uₙ = u₁qⁿ⁻¹ with sum u₁(1 − qⁿ)/(1 − q) for q ≠ 1.

  • Vector dot product a·b = |a||b|cosθ; perpendicular when a·b = 0; cross product magnitude |a||b|sinθ gives parallelogram area.

Quick reference

Biology - Human Anatomy and Physiology

  • Cardiac output = heart rate × stroke volume; normal resting output is about 5 L·min⁻¹.

  • Blood flow follows the pressure gradient; the largest pressure drop occurs across arterioles, which are the main resistance vessels.

  • Oxygen–hemoglobin dissociation curve shifts right (lower affinity) with increased CO2, H⁺, temperature, and 2,3-BPG (Bohr effect).

  • Nephron order: glomerulus → proximal tubule → loop of Henle → distal tubule → collecting duct; glucose reabsorption occurs mainly in the proximal tubule.

  • Spirometry: tidal volume ≈ 500 mL; vital capacity = inspiratory reserve + tidal + expiratory reserve; residual volume cannot be exhaled.

  • Hormone axes: hypothalamus → anterior pituitary → target gland; insulin lowers blood glucose, glucagon raises it.

  • Action potential phases: depolarization by Na⁺ influx, repolarization by K⁺ efflux, hyperpolarization, then Na+/K+ pump restores gradients.

  • Blood circulation: systemic veins → right atrium → right ventricle → pulmonary artery → lungs → left atrium → left ventricle → aorta.

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Scientific Reasoning and Data Interpretation

  • Hypothesis must be falsifiable and testable; a prediction states an observable outcome if the hypothesis holds.

  • Independent variable is manipulated; dependent variable is measured; controlled variables are held constant to avoid confounding.

  • A control group isolates the effect of the treatment; randomization reduces selection bias; blinding reduces observer bias.

  • Correlation does not imply causation; a plausible confounder can explain an observed association.

  • Sensitivity = true positives/(true positives + false negatives); specificity = true negatives/(true negatives + false positives).

  • Positive predictive value depends on prevalence, so a test's PPV falls when disease prevalence in the tested population is low.

  • Significance: p-value is the probability of data at least as extreme given the null hypothesis; it is not the probability the null is true.

  • Reading a graph: check axis units and scale, note error bars (SD vs SEM), and distinguish absolute from relative changes.

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Scientific Terminology and Communication

  • Prefixes: hyper- (above normal), hypo- (below normal), tachy- (fast), brady- (slow), dys- (disordered), a-/an- (absence).

  • Suffixes: -itis (inflammation), -ectomy (surgical removal), -otomy (incision), -osis (condition/degeneration), -emia (blood condition), -uria (urine condition).

  • Roots: cardio- (heart), nephro- (kidney), hepato- (liver), pulmo- (lung), neuro- (nerve), osteo- (bone), derm- (skin).

  • Anatomical position: standing upright, face forward, palms forward; proximal means closer to the trunk, distal farther away.

  • Directional terms: superior (above), inferior (below), anterior (front), posterior (back), medial (toward midline), lateral (away from midline).

  • SI units: length metre (m), mass kilogram (kg), time second (s), amount mole (mol), temperature kelvin (K); derived unit of force is the newton.

  • Significant figures: multiplication/division keep the least number of sig figs; addition/subtraction keep the least number of decimal places.

  • Scientific writing: report mean ± SD with n, state units, avoid causal language for correlational data, and cite primary sources.

Quick reference

Biology - Cell Biology and Molecular Biology

  • Organelle functions: ribosome synthesizes protein, rough ER folds and modifies protein, Golgi sorts and packages, lysosome degrades, mitochondrion produces ATP.

  • Prokaryotes lack a nucleus and membrane-bound organelles; they have a nucleoid, 70S ribosomes, and a peptidoglycan wall.

  • Cell membrane is a phospholipid bilayer with embedded proteins and cholesterol; it is selectively permeable and described by the fluid mosaic model.

  • DNA structure: antiparallel double helix, A pairs with T (2 H-bonds), G pairs with C (3 H-bonds); purines are A and G, pyrimidines are T and C.

  • Transcription: RNA polymerase reads the template 3'→5' and synthesizes mRNA 5'→3'; in eukaryotes introns are spliced out before translation.

  • Codon table rule: 64 codons encode 20 amino acids; AUG is the start codon and UAA, UAG, UGA are stop codons.

  • Mitosis stages: prophase (chromosomes condense), metaphase (align at equator), anaphase (sister chromatids separate), telophase (nuclei reform).

  • Meiosis produces four haploid cells; crossing over in prophase I and independent assortment in metaphase I generate genetic diversity.

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Biology - Genetics

  • Genotype vs phenotype: genotype is the allele combination; phenotype is the observable trait resulting from genotype and environment.

  • Homozygous means two identical alleles; heterozygous means two different alleles; a carrier is heterozygous for a recessive disease.

  • Punnett square for Aa × aa gives 50% Aa and 50% aa, so half the offspring show the recessive phenotype.

  • Autosomal dominant inheritance: affected individuals appear in every generation; each affected child has a 50% risk if one parent is heterozygous.

  • Blood type inheritance: IA and IB are codominant; i is recessive, so type O is ii and type AB is IAIB.

  • Mutation types: substitution (may be silent, missense, or nonsense), insertion/deletion (frameshift), and chromosomal (deletion, duplication, translocation).

  • Nondisjunction in meiosis causes aneuploidy such as trisomy 21 (Down syndrome) or monosomy X (Turner syndrome).

  • Sex determination: the father's sperm determines sex; an X-bearing sperm yields XX (female), a Y-bearing sperm yields XY (male).

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Chemistry - General and Inorganic Chemistry

  • Atomic structure: atomic number Z = protons; mass number A = protons + neutrons; isotopes differ in neutrons only.

  • Electron configuration follows Aufbau, Pauli exclusion, and Hund's rule; for example, Na is 1s²2s²2p⁶3s¹.

  • Bond type: metal + nonmetal gives ionic; nonmetal + nonmetal gives covalent; metallic bonding occurs among metal atoms.

  • Molarity M = moles of solute/litres of solution; dilution rule M₁V₁ = M₂V₂.

  • Stoichiometry requires a balanced equation; limiting reagent is the reactant that produces the least product.

  • Acid–base: strong acids (HCl, HNO3, H2SO4) dissociate fully; weak acids (CH3COOH) partially dissociate with Ka.

  • Electrochemistry: oxidation at the anode, reduction at the cathode; in a galvanic cell electrons flow from anode to cathode.

  • Bond polarity arises from electronegativity difference; a molecule is polar if bond dipoles do not cancel (H2O polar, CO2 nonpolar).

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Chemistry - Organic Chemistry

  • Alkane general formula CnH2n+2; alkenes CnH2n; alkynes CnH2n−2; each ring or double bond reduces hydrogen count by 2.

  • Isomerism: structural isomers differ in connectivity; stereoisomers (enantiomers, diastereomers) differ only in spatial arrangement.

  • Alcohol oxidation: primary alcohol → aldehyde → carboxylic acid; secondary alcohol → ketone; tertiary alcohol resists oxidation.

  • Esterification: carboxylic acid + alcohol in acid catalyst gives ester + water; hydrolysis reverses this reaction.

  • Grignard reagents (RMgX) are strong nucleophiles that add to carbonyls to form alcohols.

  • Friedel–Crafts acylation attaches an acyl group to an aromatic ring using AlCl3 as Lewis acid catalyst.

  • IR spectroscopy: O–H broad ~3300 cm⁻¹, C=O strong ~1700 cm⁻¹, C–H stretch ~2900 cm⁻¹.

  • NMR: number of signals equals number of chemically distinct proton environments; integration gives relative proton counts.

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Physics

  • Projectile motion: horizontal velocity constant; vertical acceleration = −g; range R = v₀²sin2θ/g for launch and landing at the same height.

  • Circular motion: centripetal acceleration a = v²/r; centripetal force F = mv²/r directed toward the center.

  • Universal gravitation: F = Gm₁m₂/r²; orbital speed v = √(GM/r); period T = 2π√(r³/GM).

  • Pressure in a fluid: P = P₀ + ρgh; buoyant force equals weight of displaced fluid (Archimedes' principle).

  • Thermodynamics: ΔU = Q − W; efficiency of a heat engine η = 1 − Tc/Th.

  • Coulomb's law: F = kq₁q₂/r²; electric field E = F/q; potential energy U = kq₁q₂/r.

  • Magnetic force on a moving charge F = qvB sinθ; on a current-carrying wire F = BIL sinθ.

  • Wave relation: v = fλ; refraction changes speed and wavelength but not frequency.

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Mathematics

  • Function composition: (f∘g)(x) = f(g(x)); inverse function f⁻¹ satisfies f(f⁻¹(x)) = x.

  • Exponential growth/decay: N(t) = N₀e^{kt}; k > 0 growth, k < 0 decay; half-life t½ = ln2/|k|.

  • Integration by parts: ∫u dv = uv − ∫v du; substitution method reverses the chain rule.

  • Conic sections: circle (x−h)² + (y−k)² = r²; parabola y = ax² + bx + c with vertex x = −b/2a.

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

  • Binomial distribution: P(X = k) = C(n,k)p^k(1−p)^{n−k}; mean np; variance np(1−p).

  • Mean, median, mode: mean is sensitive to outliers; median is the middle value; mode is most frequent.

  • Standard deviation σ = √(Σ(xᵢ − μ)²/n); variance is σ²; larger σ means more spread around the mean.

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Biology - Human Anatomy and Physiology

  • Digestive order: mouth → esophagus → stomach → small intestine (duodenum, jejunum, ileum) → large intestine; most absorption occurs in the small intestine.

  • Enzyme sources: salivary amylase (starch), pepsin (protein in stomach), pancreatic lipase (fat), trypsin (protein in small intestine).

  • Homeostasis: negative feedback reverses deviation (e.g., thermoregulation); positive feedback amplifies (e.g., oxytocin in labor).

  • Nervous system: CNS = brain and spinal cord; PNS = somatic and autonomic; autonomic divides into sympathetic (fight/flight) and parasympathetic (rest/digest).

  • Synaptic transmission: action potential → Ca²⁺ influx → neurotransmitter release → receptor binding → postsynaptic potential.

  • Kidney regulation: ADH increases water reabsorption; aldosterone increases Na⁺ reabsorption; both raise blood pressure.

  • Gas exchange occurs in alveoli by simple diffusion; CO2 diffuses out, O2 diffuses in, driven by partial pressure gradients.

  • Bone and muscle: osteoblasts build bone, osteoclasts resorb it; skeletal muscle contraction uses the sliding filament model with actin and myosin.

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Scientific Reasoning and Data Interpretation

  • Experimental design order: observation → question → hypothesis → prediction → experiment → analysis → conclusion.

  • Bias types: selection bias (non-random groups), measurement bias (faulty instrument), and reporting bias (publishing only positive results).

  • Sample size affects precision, not bias; larger n narrows confidence intervals if sampling is random.

  • Confidence interval interpretation: a 95% CI means 95% of such intervals would contain the true parameter, not that 95% of data lie inside.

  • Relative risk = risk in exposed/risk in unexposed; odds ratio approximates it for rare outcomes.

  • Dose–response relationship and temporal sequence strengthen causal inference; reversibility (removing exposure removes effect) also supports causality.

  • Randomized controlled trial is the strongest design for treatment effect; cohort studies measure incidence; case–control studies suit rare diseases.

  • Data presentation: bar charts suit categorical data, histograms suit continuous distributions, scatter plots show correlation between two variables.

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Scientific Terminology and Communication

  • Common abbreviations: BP (blood pressure), HR (heart rate), ECG (electrocardiogram), CNS (central nervous system), DNA (deoxyribonucleic acid).

  • Units and conversions: 1 L = 1000 mL; 1 kg = 1000 g; 1 mmHg ≈ 133.3 Pa; body temperature ≈ 37 °C = 310 K.

  • Medical roots for systems: gastro- (stomach), intestino- (intestine), pulmono- (lung), cardio- (heart), renal/nephro- (kidney), hepato- (liver).

  • Precision vs accuracy: precision is closeness of repeated measurements to each other; accuracy is closeness to the true value.

  • Percent error = |measured − true|/true × 100%; percent change = (new − old)/old × 100%.

  • Scientific notation: 0.0034 = 3.4 × 10⁻³; 25,000 = 2.5 × 10⁴; keep one digit before the decimal point.

  • Abstract structure: background, objective, methods, results, conclusion; methods must allow replication.

  • Ethical communication: report conflicts of interest, avoid plagiarism, obtain informed consent, and do not overstate conclusions beyond the data.

Quick reference

Biology - Cell Biology and Molecular Biology

  • ATP is the universal energy currency; hydrolysis of ATP to ADP + Pi releases about 30.5 kJ·mol⁻¹ under standard conditions.

  • Cellular respiration stages: glycolysis (cytosol), pyruvate oxidation and Krebs cycle (mitochondrial matrix), electron transport chain (inner membrane).

  • Photosynthesis: light reactions in thylakoid membranes produce ATP and NADPH; Calvin cycle in stroma fixes CO2 using RuBisCO.

  • Apoptosis is programmed cell death with controlled packaging; necrosis is uncontrolled cell death with inflammation.

  • Signal transduction order: receptor binding → intracellular cascade → effector response; G-protein-coupled receptors activate second messengers such as cAMP.

  • Cell junctions: tight junctions seal, desmosomes anchor cells, gap junctions allow ion and small-molecule passage.

  • Enzyme activity increases with temperature up to optimum, then denatures; pH also has an optimum specific to each enzyme.

  • PCR steps: denaturation (~95 °C), annealing of primers (~55 °C), extension by Taq polymerase (~72 °C), repeated in cycles.

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Biology - Genetics

  • DNA replication enzymes: helicase unwinds, primase lays RNA primer, DNA polymerase extends, ligase joins Okazaki fragments.

  • Transcription and translation in prokaryotes are coupled; in eukaryotes they are separated by the nuclear envelope.

  • Genetic code is degenerate (multiple codons per amino acid) but unambiguous (each codon specifies one amino acid).

  • Recombination frequency between two genes approximates genetic distance in centimorgans; 1% recombination ≈ 1 cM.

  • Mitochondrial inheritance is maternal; both sons and daughters inherit, but only daughters transmit.

  • Polygenic traits show continuous variation and are influenced by many genes plus environment (e.g., height).

  • Epistasis occurs when one gene masks or modifies the expression of another gene.

  • Genetic screening: a carrier test identifies heterozygotes; prenatal diagnosis (amniocentesis, CVS) detects fetal chromosomal anomalies.

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Chemistry - General and Inorganic Chemistry

  • Balancing redox in acidic solution: balance atoms, balance O with H2O, balance H with H⁺, balance charge with electrons, then equalize electron transfer.

  • Entropy and spontaneity: ΔG = ΔH − TΔS; reaction is spontaneous when ΔG < 0.

  • Equilibrium constant K: large K favors products; K depends on temperature only, not on initial concentrations.

  • Colligative properties depend on particle number: boiling point elevation ΔTb = Kb·m·i; freezing point depression ΔTf = Kf·m·i.

  • Radioactivity: alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay increases atomic number by 1.

  • Coordination compounds: ligand is a Lewis base donating an electron pair; coordination number counts donor atoms bound to the metal.

  • Transition metals show variable oxidation states and form colored complexes due to d–d electronic transitions.

  • Gas laws combined: P₁V₁/T₁ = P₂V₂/T₂ at constant amount; Avogadro's law states equal volumes of gases at same T and P contain equal moles.

Quick reference

Chemistry - Organic Chemistry

  • Hybridization: sp³ tetrahedral (109.5°), sp² trigonal planar (120°), sp linear (180°).

  • Alkene addition reactions: hydrogenation (H2/Pd), halogenation (Br2), hydrohalogenation (HX), hydration (H2O/H⁺).

  • Aromatic substitution: nitration (HNO3/H2SO4), halogenation (X2/FeX3), sulfonation (SO3/H2SO4); activating groups direct ortho/para, deactivating groups direct meta.

  • Amine basicity increases with alkyl groups (electron donating) and decreases with aromatic attachment (resonance delocalization).

  • Carboxylic acid derivatives reactivity order: acid chloride > anhydride > ester > amide; amide is least reactive due to resonance.

  • Chirality: R/S assignment uses Cahn–Ingold–Prelog priority by atomic number; rotate to put lowest priority away, then read 1→2→3.

  • Aldol condensation: enolate attacks a carbonyl to form a β-hydroxy carbonyl, which can dehydrate to an α,β-unsaturated carbonyl.

  • Mass spectrometry: molecular ion peak gives molecular mass; fragmentation pattern helps identify structure.

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Physics

  • Energy units: 1 eV = 1.6 × 10⁻¹⁹ J; work done by a constant force W = Fd cosθ.

  • Rotational motion: torque τ = rF sinθ; moment of inertia depends on mass distribution; angular momentum L = Iω.

  • Fluid flow: continuity equation A₁v₁ = A₂v₂; Bernoulli's equation P + ½ρv² + ρgh = constant along a streamline.

  • Electromagnetic induction: Faraday's law ε = −dΦ/dt; Lenz's law states induced current opposes the change in flux.

  • Photoelectric effect: photon energy E = hf; threshold frequency f₀ = W/h where W is the work function.

  • Atomic spectra: energy levels quantized; photon emitted when electron drops from higher to lower level, E = hf = ΔE.

  • Capacitors in series: 1/C = Σ1/Cᵢ; in parallel C = ΣCᵢ; energy stored U = ½CV².

  • Radioactive decay: N(t) = N₀e^{−λt}; half-life t½ = ln2/λ; activity A = λN.

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Mathematics

  • Polynomial factorization: a² − b² = (a − b)(a + b); a³ ± b³ = (a ± b)(a² ∓ ab + b²).

  • Rational function asymptotes: vertical where denominator = 0 (if numerator ≠ 0); horizontal determined by degree comparison.

  • Matrix multiplication is not commutative; AB ≠ BA in general; determinant of 2×2 [[a,b],[c,d]] = ad − bc.

  • Linear system solution: Cramer's rule uses determinants; unique solution exists when the determinant is nonzero.

  • Sequences: arithmetic mean between a and b is (a + b)/2; geometric mean is √(ab).

  • Trigonometric values: sin 30° = 1/2, cos 30° = √3/2, sin 45° = √2/2, tan 45° = 1.

  • Derivative applications: f'(x) = 0 locates extrema; f''(x) > 0 indicates a local minimum.

  • Integral of 1/x is ln|x| + C; integral of eˣ is eˣ + C; integral of cos x is sin x + C.

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Biology - Human Anatomy and Physiology

  • Blood components: plasma (~55%), red blood cells (erythrocytes, carry O2 via hemoglobin), white blood cells (immunity), platelets (clotting).

  • Heart conduction order: SA node → AV node → bundle of His → Purkinje fibers; SA node sets the resting rhythm (~70 beats/min).

  • ECG waves: P = atrial depolarization, QRS = ventricular depolarization, T = ventricular repolarization.

  • Respiratory control: medulla oblongata sets rhythm; chemoreceptors respond mainly to rising CO2/H⁺ rather than falling O2.

  • Endocrine glands: thyroid (T3, T4, calcitonin), parathyroid (PTH), adrenal cortex (cortisol, aldosterone), pancreas (insulin, glucagon).

  • Immune response: B cells produce antibodies (humoral); T cells mediate cellular immunity; memory cells give long-term protection.

  • Skeletal system functions: support, protection, movement, mineral storage, and blood cell production in bone marrow.

  • Body fluid compartments: intracellular fluid ~2/3 of total body water; extracellular fluid includes plasma and interstitial fluid.

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Scientific Reasoning and Data Interpretation

  • Study types: cross-sectional measures at one time; cohort follows over time; case–control compares past exposures; RCT randomizes intervention.

  • Measurement scales: nominal (categories), ordinal (ordered), interval (equal spacing, arbitrary zero), ratio (true zero).

  • Mean vs median: use median for skewed data; use mean ± SD for approximately symmetric data.

  • Type I error = rejecting a true null (α); type II error = failing to reject a false null (β); power = 1 − β.

  • Effect size measures strength independent of sample size; a very small p-value can reflect a large sample, not a large effect.

  • Confidence interval excluding the null value corresponds to statistical significance at the matching α level.

  • Survival analysis: Kaplan–Meier curves estimate time-to-event; log-rank test compares curves.

  • Graph interpretation: slope gives rate of change; area under a curve often gives total accumulated quantity.

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Scientific Terminology and Communication

  • Diagnostic suffixes: -gram (record/image), -graphy (process of recording), -scopy (visual examination), -pathy (disease), -plasty (surgical repair).

  • Number prefixes: mono- (one), di- (two), tri- (three), tetra- (four), poly- (many); used in chemistry and anatomy.

  • Common lab abbreviations: CBC (complete blood count), Hb (hemoglobin), WBC (white blood cells), RBC (red blood cells), ESR (erythrocyte sedimentation rate).

  • Anatomical planes: sagittal divides left/right; coronal divides front/back; transverse divides upper/lower.

  • Body cavities: cranial, spinal, thoracic (heart, lungs), abdominal, pelvic; diaphragm separates thoracic from abdominal.

  • Statistical notation: x̄ = sample mean, μ = population mean, s = sample SD, σ = population SD, n = sample size.

  • Reporting results: state the test used (t-test, chi-square, ANOVA), the statistic value, degrees of freedom, and p-value.

  • Peer review and reproducibility: describe methods in enough detail for replication, share data when possible, and disclose funding sources.