NTRCA School-2 cheat sheet

বাংলা বর্ণমালায় স্বরবর্ণ ১১টি, ব্যঞ্জনবর্ণ ৩৯টি, মোট ৫০টি বর্ণ; এগুলোর মধ্যে ৩২টি ব্যঞ্জনবর্ণ ও ৮টি স্বরবর্ণ যুক্তবর্ণে অংশ নেয়।

স্বরবর্ণের সংক্ষিপ্ত রূপকে কার ও ব্যঞ্জনবর্ণের সংক্ষিপ্ত রূপকে ফলা বলে; যেমন-ক্ + া = কা (কার), ক্ + র = ক্র (ফলা)।

বাংলা ভাষার উপভাষাগুলোকে প্রধানত পাঁচ ভাগে ভাগ করা হয়: রাঢ়ি, বঙ্গালী (পূর্ব ও পশ্চিম), কামরূপী, বরেন্দ্রী ও ঝাড়খণ্ডী।

বাংলা সাহিত্যের আদি নিদর্শন চর্যাপদ (আনুমানিক ৯৫০–১২০০ খ্রিষ্টাব্দ), যা ১৯০৭ সালে হরপ্রসাদ শাস্ত্রী নেপালের রাজদরবারে আবিষ্কার করেন; এটি বৌদ্ধ সহজিয়া সিদ্ধাচার্যদের পদসংকলন।

মধ্যযুগের প্রধান কাব্যধারা: শ্রীকৃষ্ণকীর্তন (বড়ু চণ্ডীদাস), মঙ্গলকাব্য (মনসামঙ্গল, চণ্ডীমঙ্গল, অন্নদামঙ্গল), ও বৈষ্ণব পদাবলি (বিদ্যাপতি, চণ্ডীদাস, জ্ঞানদাস, গোবিন্দদাস)।

আধুনিক বাংলা সাহিত্যের সূচনা মাইকেল মধুসূদন দত্তের 'মেঘনাদবধ কাব্য' (১৮৬১) ও 'তিলোত্তমাসম্ভব কাব্য' (১৮৬০) দিয়ে; তিনি বাংলা সনেটের প্রবর্তক।

রবীন্দ্রনাথ ঠাকুর ১৯১৩ সালে 'গীতাঞ্জলি' কাব্যের ইংরেজি অনুবাদ 'Song Offerings'-এর জন্য সাহিত্যে নোবেল পুরস্কার পান; তিনিই প্রথম এশীয় নোবেল বিজয়ী।

বাংলা ব্যাকরণে বাক্যের প্রধান তিনটি অংশ: কর্তা, কর্ম ও ক্রিয়া; কর্ম অনুপস্থিত থাকলে অকর্মক ক্রিয়া, আর কর্ম থাকলে সকর্মক ক্রিয়া হয়।

The eight parts of speech are noun, pronoun, verb, adjective, adverb, preposition, conjunction, and interjection; every English word functions as one of these in context.

Present perfect tense structure: subject + have/has + past participle; it links a past action to the present and cannot be used with a definite past time expression such as 'yesterday'.

Passive voice transformation: move the object to subject position, use the correct form of 'be' plus past participle, and add 'by' before the original subject (e.g., 'She wrote the letter' → 'The letter was written by her').

Reported speech backshift rule: when the reporting verb is in the past, present simple becomes past simple, present continuous becomes past continuous, and present perfect becomes past perfect.

Conditional sentences: zero conditional (present + present) for general truths; first (present + will) for real future; second (past + would) for unreal present; third (past perfect + would have) for unreal past.

Subject-verb agreement: singular subjects take singular verbs; compound subjects joined by 'and' take plural verbs; 'either...or' and 'neither...nor' agree with the nearer subject.

Common preposition collocations: 'depend on', 'consist of', 'composed of', 'afraid of', 'good at', 'married to', 'listen to', 'wait for', 'interested in'.

Articles: 'a' before consonant sounds, 'an' before vowel sounds, 'the' for specific or previously mentioned nouns and unique items; no article before uncountable nouns used generally.

Area formulas: rectangle = length × width; triangle = ½ × base × height; circle = πr²; trapezium = ½ × (sum of parallel sides) × height.

Pythagorean theorem: in a right triangle, a² + b² = c², where c is the hypotenuse; common triples include (3,4,5), (5,12,13), (8,15,17), and (7,24,25).

Quadratic formula: for ax² + bx + c = 0 (a ≠ 0), x = [−b ± √(b² − 4ac)] / (2a); the discriminant b² − 4ac determines the nature of roots (positive: two real, zero: one real, negative: complex).

Sum of the first n natural numbers = n(n+1)/2; sum of squares = n(n+1)(2n+1)/6; sum of cubes = [n(n+1)/2]².

Simple interest I = Prt/100; compound interest A = P(1 + r/100)^t, where P is principal, r is annual rate percent, and t is time in years.

Profit and loss: profit percent = (profit / cost price) × 100; loss percent = (loss / cost price) × 100; selling price = cost price × (100 + profit%)/100.

Average (mean) = sum of observations / number of observations; if a quantity increases by x% then decreases by x%, the net change is a decrease of x²/100 percent.

LCM and HCF relationship: LCM(a, b) × HCF(a, b) = a × b for any two positive integers; HCF is always a divisor of LCM.

Bangladesh gained independence on 26 March 1971; Victory Day is celebrated on 16 December, marking the surrender of Pakistani forces in 1971.

The Constitution of Bangladesh was adopted on 4 November 1972 and came into effect on 16 December 1972; it originally had 153 articles and has been amended multiple times.

The national anthem 'Amar Sonar Bangla' was written by Rabindranath Tagore; the national flag is green with a red circle, and the national animal is the Royal Bengal Tiger.

Bangladesh has eight administrative divisions: Dhaka, Chattogram, Rajshahi, Khulna, Barishal, Sylhet, Rangpur, and Mymensingh (created in 2015).

The Sundarbans, the world's largest mangrove forest, is a UNESCO World Heritage Site (declared 1997) and lies across Khulna, Satkhira, and Bagerhat districts.

The Padma Bridge, Bangladesh's longest bridge, was inaugurated on 25 June 2022; it spans the Padma River and connects Munshiganj with Shariatpur.

Bangladesh is a member of SAARC (founded 1985 in Dhaka), BIMSTEC, the United Nations (joined 1974), the Commonwealth, and the OIC.

The national poet of Bangladesh is Kazi Nazrul Islam; the national flower is the water lily (shapla), and the national fruit is jackfruit.

The three domains of educational objectives in Bloom's taxonomy (original 1956) are cognitive (knowledge, comprehension, application, analysis, synthesis, evaluation), affective (receiving, responding, valuing, organizing, characterizing), and psychomotor (perception, set, guided response, mechanism, complex overt response, adaptation, origination).

The revised Bloom's taxonomy (Anderson & Krathwohl, 2001) replaces synthesis with 'create' and orders the cognitive levels as remember, understand, apply, analyze, evaluate, create.

Bangladesh's education system has three main streams: general education, madrasah education, and technical-vocational education; primary education is compulsory and free under the Primary Education (Compulsory) Act, 1990.

The National Education Policy of Bangladesh was adopted in 2010; it recommends a unified education system and extends free compulsory primary education from five to eight years.

The Bangladesh National Curriculum Framework 2021 introduced competency-based education; the National Curriculum and Textbook Board (NCTB) develops and distributes textbooks free of charge up to secondary level.

Education commissions that shaped Bangladesh's system include the Qudrat-e-Khuda Commission (1972–74), the Mofizuddin Ahmed Commission (1987–88), and the Shamsul Haque Commission (1997).

The four pillars of education according to UNESCO's Delors Report (1996) are learning to know, learning to do, learning to be, and learning to live together.

Universal Primary Education (UPE) and Education for All (EFA) are international commitments; Bangladesh achieved gender parity in primary and secondary enrollment and received the UNESCO Confucius Prize for Literacy in 2012.

Piaget's stages of cognitive development: sensorimotor (0–2 years), preoperational (2–7), concrete operational (7–11), and formal operational (11+); teaching should match the learner's stage.

Vygotsky's Zone of Proximal Development (ZPD) is the gap between what a learner can do alone and what they can do with guidance; scaffolding is support within this zone.

Kohlberg's stages of moral development: pre-conventional (punishment/obedience and instrumental exchange), conventional (good boy/girl and law and order), post-conventional (social contract and universal ethical principles).

Erikson's psychosocial stages relevant to schooling include industry vs. inferiority (6–12 years) and identity vs. role confusion (adolescence).

Teaching methods: lecture (teacher-centered, efficient for large groups), discussion (promotes critical thinking), project method (Kilpatrick), problem-solving (Dewey), and demonstration (shows procedures).

Formative assessment occurs during instruction to provide feedback and adjust teaching; summative assessment occurs at the end to evaluate learning against standards.

Maslow's hierarchy of needs (physiological, safety, belonging, esteem, self-actualization) implies that unmet lower-level needs impede learning; teachers should address safety and belonging first.

Classroom management principles: establish clear rules and routines, use positive reinforcement, maintain proximity control, and apply the principle of least intervention to minor disruptions.