Cambodia Bac II Science cheat sheet

Derivative rules: (x^n)′ = n x^(n−1); (e^x)′ = e^x; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x.

Product rule: (uv)′ = u′v + uv′; quotient rule: (u/v)′ = (u′v − uv′)/v².

Chain rule: [f(g(x))]′ = f′(g(x))·g′(x).

If F′(x)=f(x), then ∫_a^b f(x) dx = F(b) − F(a).

Standard limits: lim_{x→0} (sin x)/x = 1; lim_{x→0} (e^x − 1)/x = 1; lim_{x→∞} (1 + 1/x)^x = e.

Quadratic equation ax²+bx+c=0 has roots x = [−b ± √(b²−4ac)]/(2a). Discriminant Δ=b²−4ac: Δ>0 two real roots; Δ=0 one repeated root; Δ<0 complex conjugate roots.

Probability: P(A∪B)=P(A)+P(B)−P(A∩B); P(A|B)=P(A∩B)/P(B) when P(B)>0.

Arithmetic sequence: u_n = u_1 + (n−1)d; S_n = n(u_1+u_n)/2. Geometric sequence: u_n = u_1 r^(n−1); S_n = u_1(1−r^n)/(1−r) for r≠1.

Complex number z=a+bi has modulus |z|=√(a²+b²) and argument θ with tan θ=b/a; i²=−1.

Newton's second law: ΣF = ma; weight W = mg, with g ≈ 9.8 m/s² near Earth's surface.

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

Work W = Fd cos θ; kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; power P = W/t.

Ohm's law: V = IR. Resistors in series: R = R₁+R₂+…; in parallel: 1/R = 1/R₁ + 1/R₂ + ….

Electrical power: P = VI = I²R = V²/R. Energy consumed E = Pt.

Wave relation: v = fλ; period T = 1/f. For sound, speed depends on medium and temperature.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂; refractive index n = c/v. Total internal reflection occurs when θ₁ exceeds the critical angle.

Ideal gas: PV = nRT; first law of thermodynamics ΔU = Q − W, where W is work done by the gas.

Radioactive decay: N = N₀ e^(−λt); half-life T½ = ln 2/λ; activity A = λN.

Mole: n = m/M; number of particles N = nN_A, where N_A ≈ 6.02×10²³ mol⁻¹.

Molarity M = n/V(L); dilution C₁V₁ = C₂V₂. At STP (0 °C, 1 atm), 1 mol of ideal gas occupies about 22.4 L.

pH = −log[H⁺]; pOH = −log[OH⁻]; at 25 °C, pH + pOH = 14. pH < 7 acidic; pH = 7 neutral; pH > 7 basic.

Strong acids and bases dissociate completely in water; weak acids and bases dissociate partially and reach equilibrium.

Oxidation is loss of electrons; reduction is gain of electrons. In redox, oxidation numbers change; the oxidizing agent is reduced.

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

Ionic bonds form by electron transfer between metals and nonmetals; covalent bonds form by electron sharing between nonmetals.

Ideal gas law PV = nRT; combine with n = m/M to get PM = dRT for density d.

Organic functional groups: alcohol −OH; aldehyde −CHO; ketone C=O; carboxylic acid −COOH; amine −NH₂.

Cell theory: all living organisms are made of cells; cells arise from pre-existing cells; the cell is the basic unit of life.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts, using chlorophyll.

Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP; glycolysis in cytoplasm, most ATP in mitochondria.

DNA is a double helix with antiparallel strands; base pairing is A–T and G–C; replication is semi-conservative.

Mendel's laws: segregation-alleles separate during gamete formation; independent assortment-different genes assort independently when on different chromosomes.

Mitosis produces two identical diploid cells for growth and repair; meiosis produces four haploid gametes and increases genetic variation.

Human heart has four chambers; arteries carry blood away from the heart, veins carry blood toward it; capillaries allow exchange.

In a food chain, energy transfer between trophic levels is about 10%; decomposers recycle nutrients.

Homeostasis uses negative feedback; insulin lowers blood glucose, glucagon raises it; body temperature and pH are also regulated.

Reamker (រាមកេរ្តិ៍) is the Khmer epic adaptation of the Ramayana; central characters include Preah Ream, Neang Sita, Preah Leak, Krong Reap, and Hanuman.

Chbap (ច្បាប់) are didactic poems teaching moral conduct; Chbap Pros addresses men, Chbap Srei addresses women, and both use aphorism and metaphor.

Tum Teav (ទុំទាវ) is a tragic Khmer love story set in Kampong Cham; the best-known literary version is by Preah Botumthera Som.

Preah Vesandor (ព្រះវេស្សន្តរ) is a Buddhist birth story about the Bodhisattva's generosity (dana); it is one of the most widely known Khmer literary-religious works.

Phka Srabon (ផ្កាស្រពោន, 'Wilted Flower') is a novel by Nou Hach; it examines love, morality, and social constraints in twentieth-century Cambodia.

Khmer classical poetry uses syllable counting and rhyme; common forms include Kbak, Tum, Bat, and Brahm, often with moral or religious content.

Khmer traditional theatre and shadow puppetry often draw on Reamker and Jataka stories for plots and characters.

Khmer literary genres include epic (Reamker), didactic verse (Chbap), romance/tragedy (Tum Teav), and Jataka (Vesandor).

Subject–verb agreement: a singular subject takes a singular verb; indefinite pronouns such as everyone, each, and somebody are singular.

Present perfect: have/has + past participle; use for past actions with present relevance, with time markers since, for, already, yet, ever, never.

Passive voice: be + past participle; the object becomes subject, and the agent is introduced by 'by' only when relevant.

Conditionals: first conditional if + present, will + base verb; second conditional if + past, would + base verb; third conditional if + had + past participle, would have + past participle.

Relative clauses: use who for people, which for things, that for both in defining clauses; non-defining clauses take commas and usually not 'that'.

Comparatives and superlatives: short adjectives take -er/-est; long adjectives take more/most; irregular forms include good–better–best and bad–worse–worst.

Prepositions of time: at for clock times, on for days and dates, in for months, years, and longer periods; since + starting point, for + duration.

Reading strategies: skim for main idea, scan for specific details, and infer meaning from context; do not rely on word-by-word translation.