NTRCA School Level cheat sheet

Bengali grammar terms: বর্ণ (letter/sound unit), স্বরবর্ণ (vowel, 11 in number), ব্যঞ্জনবর্ণ (consonant, 39), and কার চিহ্ন marks vowel sounds attached to consonants.

Sandhi (সন্ধি) is the joining of two sounds; স্বরসন্ধি joins vowels (বিদ্যা + আলয় = বিদ্যালয়), ব্যঞ্জনসন্ধি joins consonant with vowel or consonant, বিসর্গসন্ধি involves বিসর্গ.

সমাস (compound) types: দ্বন্দ্ব (both words retain meaning), কর্মধারয় (apposition), তৎপুরুষ (later word dominant), বহুব্রীহি (meaning refers to a third thing), দ্বিগু (number-based), অব্যয়ীভাব (indeclinable prefix).

English tense rule: present perfect = have/has + past participle, used for past action with present relevance; simple past takes a definite past time marker (yesterday, last year).

Active to passive: object becomes subject, verb becomes be + past participle, agent follows 'by'; only transitive verbs can be made passive.

Math: area of triangle = ½ × base × height; area of circle = πr²; circumference = 2πr; Pythagoras theorem a² + b² = c² for right triangles.

Average = sum of quantities ÷ number of quantities; percentage change = (change ÷ original) × 100; simple interest I = P × r × t ÷ 100.

Science: photosynthesis occurs in chloroplasts using CO₂ + water + light to give glucose + O₂; respiration releases energy from glucose in mitochondria.

Bangladesh studies: national flower water lily (শাপলা), national fruit jackfruit (কাঁঠাল), national animal Royal Bengal tiger, national bird doel (দোয়েল).

Bengali literature periods: আদিকাল (ancient), মধ্যযুগ (medieval, with শ্রীকৃষ্ণকীর্তন and মঙ্গলকাব্য), and আধুনিক যুগ (modern, beginning with Michael Madhusudan Dutt's influence).

Figures of speech: উপমা (simile, uses মতো/সদৃশ), রূপক (metaphor, direct identification), অনুপ্রাস (alliteration, repeated consonant), শ্লেষ (pun/wordplay), অতিশয়োক্তি (hyperbole).

English voice and narration: reported speech shifts present to past and changes pronouns (I → he/she) and time words (now → then, today → that day).

Conditional sentences: first conditional (if + present, will + verb) for real future; second conditional (if + past, would + verb) for unreal present.

Algebra: (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; a² − b² = (a + b)(a − b); solving linear equations by elimination or substitution.

Geometry: sum of interior angles of a polygon = (n − 2) × 180°; each interior angle of a regular polygon = (n − 2) × 180° ÷ n.

Physics: speed = distance ÷ time; Newton's second law F = ma; work W = F × d; power P = W ÷ t; density = mass ÷ volume.

Chemistry: atomic number = number of protons; mass number = protons + neutrons; isotopes have same protons but different neutrons; pH below 7 is acidic, above 7 basic.

Biology: blood groups A, B, AB, O; O negative is the universal donor, AB positive the universal recipient; mitosis produces two identical diploid cells.

Calculus: d/dx(xⁿ) = nxⁿ⁻¹; ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1; derivative of sin x is cos x; derivative of eˣ is eˣ; derivative of ln x is 1/x.

Limits: lim(x→0) sin x / x = 1; a function is continuous at a point if the left limit, right limit, and function value all agree.

Physics: equations of motion v = u + at, s = ut + ½at², v² = u² + 2as; kinetic energy = ½mv²; potential energy = mgh; momentum p = mv is conserved in collisions.

Chemistry: Le Chatelier's principle - a system at equilibrium shifts to oppose any change in concentration, pressure, or temperature; catalysts speed equilibrium without shifting it.

Organic chemistry: alkanes (CₙH₂ₙ₊₂) are saturated; alkenes (CₙH₂ₙ) contain a C=C double bond; alkynes (CₙH₂ₙ₋₂) contain a C≡C triple bond; alcohols contain −OH.

Biology: DNA replication is semi-conservative; transcription makes mRNA from DNA; translation at ribosomes assembles amino acids using codons (triplets).

Logic and set theory: A ∪ B combines elements; A ∩ B gives common elements; De Morgan's laws: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′.

Economics: law of demand - other things equal, quantity demanded falls as price rises; price elasticity of demand = percentage change in quantity ÷ percentage change in price.

Statistics: mean = Σx ÷ n; median is the middle value of ordered data; mode is the most frequent value; standard deviation measures spread around the mean.