Comprehensive Interdisciplinary Study Notes Biology Plant Biology (Botany) Angiosperms 2 n 2n 2 n 3 n 3n 3 n H 2 O \text{H}_2\text{O} H 2 O Gymnosperms Pteridophytes Bryophytes Classification of Plants Root & Stem ⇒ \Rightarrow ⇒ Leaf Photosynthesis 6 CO < e m > 2 + 6 H < / e m > 2 O → l i g h t c h l o r o p h y l l C < e m > 6 H < / e m > 12 O < e m > 6 + 6 O < / e m > 2 6\,\text{CO}<em>2 + 6\,\text{H}</em>2\text{O} \xrightarrow[light]{chlorophyll} C<em>6H</em>{12}O<em>6 + 6\,\text{O}</em>2 6 CO < e m > 2 + 6 H < / e m > 2 O c h l or o p h y l l l i g h t C < e m > 6 H < / e m > 12 O < e m > 6 + 6 O < / e m > 2 ATP \text{ATP} ATP NADPH \text{NADPH} NADPH Transpiration Conduction of Sap Flowers, Fruits & Seeds Plant Hormones Plant Movements Supporting Tissues Cell Biology & Biochemistry Nucleic Acids : DNA (double helix, antiparallel 5 ′ → 3 ′ 5'\rightarrow3' 5 ′ → 3 ′ Genetic Code & Protein Synthesis : codon table; transcription → translation. Cell Membrane : fluid-mosaic; transport (diffusion, osmosis, active). Cytoplasm & Organelles : ER, Golgi, mitochondria (ATP via C < e m > 6 H < / e m > 12 O < e m > 6 + 6 O < / e m > 2 → 6 CO < e m > 2 + 6 H < / e m > 2 O + 38 ATP \text{C}<em>6\text{H}</em>{12}O<em>6 + 6\,\text{O}</em>2 \rightarrow 6\,\text{CO}<em>2 + 6\,\text{H}</em>2\text{O}+38\,\text{ATP} C < e m > 6 H < / e m > 12 O < e m > 6 + 6 O < / e m > 2 → 6 CO < e m > 2 + 6 H < / e m > 2 O + 38 ATP Cell Division : mitosis (2n → two 2n); meiosis (2n → four n, crossing-over). Proteins & Enzymes : structure levels; E + S ⇆ E S → E + P E+S\leftrightarrows ES \rightarrow E+P E + S ⇆ E S → E + P Vitamins : fat- vs water-soluble roles.Ecology Biomes of Brazil : Amazon, Cerrado, Caatinga, Pampa, Pantanal, Mata Atlântica; key flora/fauna and climate. Abiotic Factors & Succession : primary vs secondary succession. Energy Pyramids & Biogeochemical Cycles : C \text{C} C N \text{N} N P \text{P} P Population Ecology : growth models (exponential N ( t ) = N 0 e r t N(t)=N_0e^{rt} N ( t ) = N 0 e r t N ( t ) = K 1 + A e − r t N(t)=\frac{K}{1+Ae^{-rt}} N ( t ) = 1 + A e − r t K Pollution & Human Impact : greenhouse gases, eutrophication. Species Interactions : predation, competition, mutualism, commensalism, parasitism.Human Physiology (selected systems) Circulatory : heart anatomy, double circulation, blood pressure P = F / A P = F/A P = F / A Respiratory : mechanics (Boyle’s Law P < e m > 1 V < / e m > 1 = P < e m > 2 V < / e m > 2 P<em>1V</em>1=P<em>2V</em>2 P < e m > 1 V < / e m > 1 = P < e m > 2 V < / e m > 2 Nervous : CNS, PNS; autonomic (sympathetic vs parasympathetic). Endocrine : hormone pathways; feedback loops. Digestive, Excretory, Sensory overviews.Genetics & Evolution Mendelian laws, linkage, multiple alleles, gene interactions, lethal genes. Population genetics (Hardy–Weinberg p 2 + 2 p q + q 2 = 1 p^2+2pq+q^2=1 p 2 + 2 pq + q 2 = 1 Mutations, biotechnology techniques (PCR, cloning). Evolutionary mechanisms, origin-of-life hypotheses. Chemistry General Chemistry Atomic Structure : particles, quantum numbers n , l , m < e m > l , m < / e m > s n, l, m<em>l, m</em>s n , l , m < e m > l , m < / e m > s Periodic Properties : radius, ionisation energy, electronegativity. Chemical Bonding : ionic, covalent (sigma/π), metallic; molecular geometry (VSEPR). Intermolecular Forces : H-bond, dipole-dipole, London; influence on bp/mp. States of Matter & Phase Changes : phase diagrams, Δ H < e m > f u s , Δ H < / e m > v a p \Delta H<em>{fus}, \Delta H</em>{vap} Δ H < e m > f u s , Δ H < / e m > v a p Stoichiometry : molar concepts, limiting reagent, yield % = exp theor × 100 \% = \frac{\text{exp}}{\text{theor}}\times100 % = theor exp × 100 Solutions : concentration units (M, m, %), dilutions, colligative props (ebullioscopy Δ T < e m > b = K < / e m > b ⋅ m \Delta T<em>b=K</em>b\cdot m Δ T < e m > b = K < / e m > b ⋅ m Acid–Base (Arrhenius/Bronsted/Lewis) : p H = − log [ H + ] pH=-\log[H^+] p H = − log [ H + ] p H = p K a + log [ A − ] [ H A ] pH=pK_a+\log\frac{[A^-]}{[HA]} p H = p K a + log [ H A ] [ A − ] Redox : oxidation numbers; E 0 E^0 E 0 m = M I t n F m=\frac{MIt}{nF} m = n F M I t Radioactivity : α , β , γ \alpha,\beta,\gamma α , β , γ t 1 / 2 t_{1/2} t 1/2 Physical Chemistry Thermochemistry : Δ H = ∑ Δ H < e m > f p r o d u c t s − ∑ Δ H < / e m > f r e a c t a n t s \Delta H=\sum\Delta H<em>f^{products}-\sum\Delta H</em>f^{reactants} Δ H = ∑ Δ H < e m > f p r o d u c t s − ∑ Δ H < / e m > f r e a c t an t s Kinetics : rate laws r = k [ A ] m [ B ] n r=k[A]^m[B]^n r = k [ A ] m [ B ] n Chemical Equilibrium : K c = [ p r o d u c t s ] [ r e a c t a n t s ] K_c=\frac{[products]}{[reactants]} K c = [ r e a c t an t s ] [ p r o d u c t s ] Gibbs Free Energy : Δ G = Δ H − T Δ S \Delta G=\Delta H-T\Delta S Δ G = Δ H − T Δ S Organic Chemistry Hydrocarbon Nomenclature : alkanes, alkenes, alkynes, aromatics. Isomerism : constitutional, geometric (cis/trans), optical (chiral C ∗ C^* C ∗ Reactions : addition (HX to alkenes), elimination (E1/E2), substitution (SN1/SN2), oxidation/reduction (KMnO$4$, LiAlH$ 4$), polymerisation (addition vs condensation). Functional Groups : alcohols, aldehydes, ketones, carboxylic acids, esters, amines, amides. Biomolecules : amino acids (zwitterions, p I pI p I Physics Mechanics Kinematics : 1-D s = s < e m > 0 + v < / e m > 0 t + 1 2 a t 2 s=s<em>0+v</em>0t+\frac12at^2 s = s < e m > 0 + v < / e m > 0 t + 2 1 a t 2 R = v 0 2 sin 2 θ g R=\frac{v_0^2\sin2\theta}{g} R = g v 0 2 s i n 2 θ Dynamics : Newton’s laws; friction f = μ N f=\mu N f = μ N W = Δ K W=\Delta K W = Δ K P = d W d t P=\frac{dW}{dt} P = d t d W J = Δ p J=\Delta p J = Δ p Circular Motion : a c = v 2 r a_c=\frac{v^2}{r} a c = r v 2 Gravitation : Newton F = G m < e m > 1 m < / e m > 2 r 2 F=G\frac{m<em>1m</em>2}{r^2} F = G r 2 m < e m > 1 m < / e m > 2 T 2 ∝ r 3 T^2\propto r^3 T 2 ∝ r 3 Electromagnetism Electrostatics : Coulomb F = k q < e m > 1 q < / e m > 2 r 2 F=k\frac{q<em>1q</em>2}{r^2} F = k r 2 q < e m > 1 q < / e m > 2 E = F q E=\frac{F}{q} E = q F V = k q r V=\frac{kq}{r} V = r k q C = ε A d C=\frac{\varepsilon A}{d} C = d ε A DC Circuits : Ohm V = R I V=RI V = R I Magnetism : F < e m > B = q v B sin θ F<em>B=qvB\sin\theta F < e m > B = q v B sin θ ε = − d Φ < / e m > B d t \varepsilon = -\frac{d\Phi</em>B}{dt} ε = − d t d Φ < / e m > B AC Circuits : RMS values I < e m > r m s = I < / e m > 0 2 I<em>{rms}=\frac{I</em>{0}}{\sqrt2} I < e m > r m s = 2 I < / e m > 0 Waves & Optics Wave Equation : v = f λ v=f\lambda v = f λ Δ x = λ D d \Delta x=\frac{\lambda D}{d} Δ x = d λ D Sound : Doppler f ′ = f ( v ± v < e m > o v ∓ v < / e m > s ) f'=f\left(\frac{v\pm v<em>o}{v\mp v</em>s}\right) f ′ = f ( v ∓ v < / e m > s v ± v < e m > o ) EM Waves : spectrum, polarisation. Geometric Optics : mirrors/lenses (thin-lens 1 f = 1 p + 1 q \frac1f=\frac1p+\frac1q f 1 = p 1 + q 1 m = − q p m=-\frac{q}{p} m = − p q Optical Instruments : microscopes, telescopes; human eye defects (myopia, hyperopia). Thermodynamics Temperature Scales : C 5 = F − 32 9 = K − 273 5 \frac{C}{5}=\frac{F-32}{9}=\frac{K-273}{5} 5 C = 9 F − 32 = 5 K − 273 Heat : Q = m c Δ T Q=mc\Delta T Q = m c Δ T Q = m L Q=mL Q = m L Ideal Gas : P V = n R T PV=nRT P V = n R T P V = const PV=\text{const} P V = const P V γ = const PV^{\gamma}=\text{const} P V γ = const 1st Law : Δ U = Q − W \Delta U=Q-W Δ U = Q − W η = 1 − T < e m > c T < / e m > h \eta=1-\frac{T<em>c}{T</em>h} η = 1 − T < / e m > h T < e m > c Modern Physics Relativity (SR) : time dilation Δ t = γ Δ t < e m > 0 \Delta t=\gamma \Delta t<em>0 Δ t = γ Δ t < e m > 0 L = L < / e m > 0 / γ L=L</em>0/\gamma L = L < / e m > 0/ γ Quantum : photon E = h f E=hf E = h f λ = h p \lambda=\frac{h}{p} λ = p h Nuclear : binding energy E = Δ m c 2 E=\Delta m c^2 E = Δ m c 2 N = N 0 e − λ t N=N_0e^{-\lambda t} N = N 0 e − λ t Geography Physical Geography Cartography basics (latitude/longitude, projections). Climatology: atmospheric dynamics, global/climatic anomalies (El Niño, La Niña). Geomorphology: internal/external processes; plate tectonics; Brazilian morphoclimatic domains. Hydrology: drainage basins; water budget. Pedology & Natural Resources: soil profiles, erosion, mineral/energy resources. Human & Economic Geography Demography (growth rates, demographic transition). Urbanisation & Industrialisation (Brazil & world). Agriculture & Technology; transport networks; global trade. Energy geography (oil, renewables, geopolitics). Regional studies: China, India, Africa, Pacific Basin; Brazilian economy. Geopolitics Cold-War bipolarity, contemporary multipolarity. Blocs (EU, NAFTA, MERCOSUR, ASEAN). Conflicts (Middle East, Asia, Africa, Europe, Americas). Globalisation & neoliberalism; international organisations (UN, WTO). Mathematics Algebra & Functions Basic Arithmetic : factors, multiples, MDC \text{MDC} MDC Polynomials : division, factor theorem, roots; remainder theorem P ( a ) = r P(a)=r P ( a ) = r Functions : linear y = a x + b y=ax+b y = a x + b y = a x 2 + b x + c y=ax^2+bx+c y = a x 2 + b x + c y = a ⋅ b x y=a\cdot b^x y = a ⋅ b x log b a = ln a ln b \log_b a=\frac{\ln a}{\ln b} log b a = l n b l n a Inequalities & Modular Graphs .Sequences & Series Arithmetic Progression : a < e m > n = a < / e m > 1 + ( n − 1 ) d a<em>n=a</em>1+(n-1)d a < e m > n = a < / e m > 1 + ( n − 1 ) d S < e m > n = n 2 ( a < / e m > 1 + a n ) S<em>n=\frac{n}{2}(a</em>1+a_n) S < e m > n = 2 n ( a < / e m > 1 + a n ) Geometric Progression : a < e m > n = a < / e m > 1 q n − 1 a<em>n=a</em>1q^{n-1} a < e m > n = a < / e m > 1 q n − 1 S < e m > n = a < / e m > 1 q n − 1 q − 1 S<em>n=a</em>1\frac{q^n-1}{q-1} S < e m > n = a < / e m > 1 q − 1 q n − 1 Combinatorics & Probability Factorial n ! n! n ! P ( n ) = n ! P(n)=n! P ( n ) = n ! C < e m > n p = n ! p ! ( n − p ) ! C<em>n^p=\frac{n!}{p!(n-p)!} C < e m > n p = p ! ( n − p )! n ! ( a + b ) n = ∑ C < / e m > n k a n − k b k (a+b)^n=\sum C</em>n^k a^{n-k}b^k ( a + b ) n = ∑ C < / e m > n k a n − k b k Probability P ( E ) = favourable total P(E)=\frac{\text{favourable}}{\text{total}} P ( E ) = total favourable P ( A ∣ B ) = P ( A ∩ B ) P ( B ) P(A|B)=\frac{P(A\cap B)}{P(B)} P ( A ∣ B ) = P ( B ) P ( A ∩ B ) Linear Algebra Determinants (Sarrus, Laplace); systems (Cramer’s rule). Matrices : operations, inverses.Geometry Analytic : distance point–line, slope, conic sections (circle ( x − h ) 2 + ( y − k ) 2 = r 2 (x-h)^2+(y-k)^2=r^2 ( x − h ) 2 + ( y − k ) 2 = r 2 Plane Geometry : triangles (law of sines a sin A = b sin B = c sin C \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} s i n A a = s i n B b = s i n C c c 2 = a 2 + b 2 − 2 a b cos C c^2=a^2+b^2-2ab\cos C c 2 = a 2 + b 2 − 2 ab cos C Solid Geometry : prisms, cylinders V = π r 2 h V=\pi r^2h V = π r 2 h V = 1 3 B h V=\frac{1}{3}Bh V = 3 1 B h V = 4 3 π r 3 V=\frac{4}{3}\pi r^3 V = 3 4 π r 3 Trigonometry Unit Circle , radian measure; basic identities sin 2 x + cos 2 x = 1 \sin^2x+\cos^2x=1 sin 2 x + cos 2 x = 1 sin , cos \sin,\cos sin , cos Triangles : right-triangle ratios, area A = 1 2 a b sin C A=\frac12ab\sin C A = 2 1 ab sin C Equations/Inequalities : solving sin x = k \sin x = k sin x = k Complex Numbers Algebraic form z = a + b i z=a+bi z = a + bi ∣ z ∣ = a 2 + b 2 |z|=\sqrt{a^2+b^2} ∣ z ∣ = a 2 + b 2 z = r ( cos θ + i sin θ ) z=r(\cos\theta + i\sin\theta) z = r ( cos θ + i sin θ ) z n = r n ( cos n θ + i sin n θ ) z^n=r^n(\cos n\theta + i\sin n\theta) z n = r n ( cos n θ + i sin n θ ) Study Tips & Connections Integrate concepts across disciplines (e.g., thermodynamics in Biology—enzyme kinetics; in Physics—heat engines; in Chemistry—enthalpy). Utilise mnemonic devices (e.g., “LEO the lion says GER” for oxidation/reduction). Practise problems: derivations, graph interpretation, real-world applications (ecological data, physics experiments). Ethical/Philosophical angles: biotech (GMOs), nuclear energy, environmental stewardship, geopolitical conflicts.