BHSEC (Class XII) cheat sheet

Active to passive: move the object to subject position, use a form of 'be' plus the past participle, and keep the tense of the original verb.

Reported speech: shift present to past, past to past perfect, and change pronouns and time markers (now→then, today→that day, tomorrow→the next day).

Conditionals: Type 1 if + present, will + base; Type 2 if + past, would + base; Type 3 if + past perfect, would have + past participle.

Relative clauses: 'who' for people, 'which' for things, 'whose' for possession, 'where' for place; non-defining clauses take commas.

Subject-verb agreement: indefinite pronouns (everyone, each, nobody) take singular verbs; 'either...or' agrees with the nearer subject.

Figures of speech: simile uses like/as, metaphor states identity, personification gives human traits to non-human things, hyperbole is deliberate exaggeration.

Precis writing: retain the central idea and key supporting points, cut examples and repetition, and keep the original point of view.

Dzongkha is written in the Uchen script; letters hang from a continuous top line and consonant clusters stack vertically.

The alphabet has 30 base letters; each consonant carries an inherent vowel 'a' unless a vowel sign (gi-gu, zhabs-kyu, etc.) modifies it.

Syllables are separated by a tsheg (a small dot-like mark), while a shad marks the end of a phrase or sentence.

Noun gender and number are often marked by suffixes; plural is commonly indicated by ཚོ (tsho) after the noun.

Verb tense is carried by suffixes: a present/habitual marker differs from the past marker and from the future marker.

Honorific vocabulary replaces ordinary nouns and verbs when the subject is a respected person, such as a lama or a senior official.

Dzongkha is the national language of Bhutan and the medium of instruction for the Dzongkha paper at Class XII.

Derivative rules: d/dx(x^n)=nx^(n-1); product rule (uv)'=u'v+uv'; quotient rule (u/v)'=(u'v-uv')/v^2.

Integration by parts: ∫u dv = uv − ∫v du, choosing u by the LIATE order (log, inverse trig, algebraic, trig, exponential).

Limits: lim(x→0) sin x / x = 1 and lim(x→0)(1−cos x)/x^2 = 1/2; L'Hôpital applies only to 0/0 or ∞/∞ forms.

Definite integral property: ∫ from a to b f(x)dx = F(b) − F(a) by the Fundamental Theorem of Calculus.

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

Matrices: (AB)^T = B^T A^T; a square matrix is invertible only when its determinant is non-zero, and A^-1 = adj(A)/|A|.

Conic sections: circle x^2+y^2=r^2; parabola y^2=4ax with focus (a,0); ellipse x^2/a^2+y^2/b^2=1 with e=√(1−b^2/a^2).

Vectors: a·b = |a||b|cosθ; a×b is perpendicular to both, and |a×b| equals the area of the parallelogram they span.

Equations of motion: v=u+at, s=ut+½at^2, v^2=u^2+2as apply only for constant acceleration.

Newton's second law: F=ma; impulse equals change in momentum, FΔt = Δp.

Work-energy theorem: net work done equals change in kinetic energy, W = ½mv^2 − ½mu^2.

Coulomb's law: F = kq₁q₂/r^2 with k ≈ 9×10^9 N·m²/C²; electric field E = F/q and potential V = W/q.

Ohm's law V=IR; resistors in series add, in parallel 1/R = 1/R₁ + 1/R₂; power P = VI = I^2R = V^2/R.

Lens/mirror formula: 1/f = 1/v − 1/u for lenses and 1/f = 1/v + 1/u for mirrors; magnification m = v/u.

Photoelectric effect: maximum kinetic energy = hf − φ, where φ is the work function; emission stops below the threshold frequency f₀ = φ/h.

Radioactive decay: N = N₀e^(−λt); half-life T½ = 0.693/λ.

Mole concept: 1 mole = 6.022×10^23 particles; moles = mass/molar mass; at STP one mole of ideal gas occupies 22.4 L.

Ideal gas equation PV = nRT with R = 8.314 J/(mol·K); at constant T, P₁V₁ = P₂V₂ (Boyle's law).

Le Chatelier's principle: raising pressure shifts equilibrium toward fewer gas moles; raising temperature favors the endothermic direction.

pH = −log[H⁺]; for a strong acid pH = −log C; a buffer resists pH change and is described by the Henderson–Hasselbalch equation.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain; the oxidizing agent is itself reduced.

Hybridization: steric number 2 = sp (linear), 3 = sp² (trigonal planar), 4 = sp³ (tetrahedral).

Organic reaction types: substitution (alkanes, benzene), addition (alkenes, alkynes), elimination (alcohols to alkenes with conc. H₂SO₄).

Rate law expresses rate = k[A]^m[B]^n; the order is determined experimentally, not from the balanced equation.

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

Cellular respiration: glycolysis in cytoplasm yields 2 ATP and 2 pyruvate; the Krebs cycle and electron transport chain occur in mitochondria.

Mendel's laws: segregation of alleles and independent assortment; a monohybrid cross of heterozygotes gives a 3:1 phenotype ratio.

DNA structure: double helix with antiparallel strands, adenine pairs with thymine (2 H-bonds) and guanine with cytosine (3 H-bonds).

Central dogma: DNA → RNA (transcription) → protein (translation); codons are triplet bases, and AUG is the start codon.

Blood circulation: the left ventricle pumps oxygenated blood to the body via the aorta; the right ventricle sends deoxygenated blood to the lungs.

Nephron function: filtration in the glomerulus, selective reabsorption of glucose and water in the tubules, secretion, and urine formation.

Ecosystem energy flow is unidirectional; roughly 10% of energy passes to the next trophic level, so food chains rarely exceed four or five links.

Law of demand: quantity demanded falls as price rises, other things equal; the demand curve slopes downward.

Price elasticity of demand = (% change in quantity)/(% change in price); demand is elastic when the value exceeds 1.

GDP = C + I + G + (X − M); real GDP is measured at constant prices to remove inflation effects.

Money multiplier = 1/reserve ratio; central banks raise the repo rate to contract credit and lower it to expand credit.

Inflation is a sustained rise in the general price level, measured by CPI or WPI; demand-pull and cost-push are its two main sources.

Opportunity cost is the value of the next best alternative forgone when a choice is made.

Balance of payments records all transactions with the rest of the world; a current account deficit must be financed by capital inflows.

Perfect competition: many buyers and sellers, homogeneous product, free entry and exit, and price taken from the market.

Accounting equation: Assets = Liabilities + Capital; every transaction keeps the equation balanced.

Double entry: every transaction has equal debits and credits; total debits must equal total credits in the trial balance.

Depreciation by straight-line method = (Cost − Scrap value)/Useful life; written-down value method applies a fixed rate to the book value.

Bank reconciliation statement starts from the cash book or pass book balance and adjusts for cheques issued but not presented, deposits not credited, and bank charges.

Trading account gives gross profit = Net sales − Cost of goods sold; the profit and loss account gives net profit after operating expenses.

Balance sheet shows assets and liabilities at a date; it is a statement of position, not an account of profit.

Goodwill arises on admission or retirement of a partner and is shared in the sacrificing or gaining ratio.

Capital and revenue distinction: capital expenditure creates an asset, while revenue expenditure is charged to the profit and loss account.

Forms of organization: sole proprietorship (unlimited liability), partnership (shared liability), company (separate legal entity, limited liability).

Management functions: planning, organizing, staffing, directing, and controlling form the process cycle.

Principles of management (Fayol): unity of command, unity of direction, division of work, scalar chain, and equity.

Maslow's hierarchy of needs runs physiological, safety, social, esteem, self-actualization; lower needs must be met first.

Marketing mix: the four Ps are product, price, place, and promotion.

Delegation transfers authority and responsibility but the delegator remains accountable for results.

Recruitment sources are internal (promotion, transfer) and external (advertisement, campus placement, employment exchange).

Number systems: binary base 2, octal base 8, decimal base 10, hexadecimal base 16; each hex digit maps to exactly four binary bits.

Two's complement negation: invert all bits and add 1; this allows subtraction to be performed as addition.

Boolean algebra: De Morgan's laws state (A+B)' = A'·B' and (A·B)' = A'+B'.

Data structures: a stack follows LIFO (push/pop) and a queue follows FIFO (enqueue/dequeue).

SQL commands: SELECT retrieves rows, WHERE filters, GROUP BY aggregates, and ORDER BY sorts; DDL covers CREATE and DROP.

Python: len() gives sequence length, range(a,b) excludes b, and a function is defined with def and returns with return.

Networking: an IP address identifies a host; TCP is connection-oriented and reliable, UDP is connectionless and faster.

Algorithm complexity: binary search runs in O(log n) on sorted data, while linear search runs in O(n).