Cadet College Admission cheat sheet

Area formulas: triangle = ½ × base × height; rectangle = length × width; 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.

Simple interest I = P × R × T / 100; compound amount A = P(1 + R/100)^T; profit% = (profit / cost price) × 100.

Average (mean) = sum of all values ÷ number of values; to find a missing value, multiply the average by the count and subtract the known sum.

LCM × HCF of two positive integers = product of the integers; use prime factorization to find both efficiently.

Speed = distance ÷ time; 1 km/h = 5/18 m/s; to convert m/s to km/h multiply by 18/5.

Sum of interior angles of an n-sided polygon = (n − 2) × 180°; each interior angle of a regular n-gon = (n − 2) × 180° / n.

Rules of divisibility: by 3 if digit sum divisible by 3; by 4 if last two digits form a multiple of 4; by 9 if digit sum divisible by 9; by 11 if alternating digit sum difference is 0 or a multiple of 11.

Ratio and proportion: if a : b = c : d then ad = bc; to divide a quantity Q in ratio m : n, the parts are Qm/(m+n) and Qn/(m+n).

Present perfect tense uses has/have + past participle and connects a past action to the present; simple past is used with a definite past time (yesterday, last year).

Passive voice structure: object + be (conjugated) + past participle + by + subject; only transitive verbs can be made passive.

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

Prepositions of time: in (months, years, seasons), on (days, dates), at (clock times, night, noon).

Subject-verb agreement: singular subject takes singular verb; collective nouns (team, family) usually take a singular verb when acting as one unit.

Direct to indirect speech: change present to past, 'now' to 'then', 'today' to 'that day', 'tomorrow' to 'the next day', and adjust pronouns to the reporter.

Commonly confused pairs: affect (verb) vs effect (noun); its (possessive) vs it's (it is); their (possessive) vs there (place) vs they're (they are).

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

Bangladesh gained independence on 26 March 1971 and observes Victory Day on 16 December 1971, when Pakistani forces surrendered in Dhaka.

The national anthem 'Amar Shonar Bangla' was written by Rabindranath Tagore; the national poet is Kazi Nazrul Islam; the national flower is the water lily (shapla).

The Sundarbans, the world's largest mangrove forest, lies in the southwest and is famous for the Royal Bengal Tiger; it is a UNESCO World Heritage Site.

The Padma, Meghna, Jamuna, Brahmaputra, and Karnaphuli are major rivers; the Padma is a main distributary of the Ganges.

Dhaka is the capital and largest city; Chattogram (Chittagong) is the main port city; the Port of Mongla serves the southwest.

Bangladesh shares borders with India (west, north, east) and Myanmar (southeast), and has the Bay of Bengal to the south.

The national animal is the Royal Bengal Tiger, the national bird is the oriental magpie-robin (doyel), and the national fruit is jackfruit.

The 1970 general election gave the Awami League a majority; the Liberation War was fought in 1971 under the leadership of Bangabandhu Sheikh Mujibur Rahman.

Newton's laws: (1) an object stays at rest or in uniform motion unless acted on by a net force; (2) F = ma; (3) every action has an equal and opposite reaction.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts containing chlorophyll.

The pH scale runs 0–14: pH < 7 acidic, pH = 7 neutral, pH > 7 basic; litmus turns red in acid and blue in base.

Speed of light in vacuum ≈ 3 × 10⁸ m/s; sound travels faster in solids than in liquids and faster in liquids than in gases.

Human body: the heart has four chambers; lungs exchange oxygen and carbon dioxide; kidneys filter blood and produce urine; the liver produces bile.

Chemical symbols: H hydrogen, O oxygen, C carbon, N nitrogen, Na sodium, K potassium, Fe iron, Ca calcium, Cl chlorine.

Density = mass ÷ volume; water has density ≈ 1 g/cm³, so objects less dense than water float.

Electric current is measured in amperes (A), voltage in volts (V), resistance in ohms (Ω); Ohm's law states V = IR.

বাংলা বর্ণমালায় মোট ৫০টি বর্ণ: ১১টি স্বরবর্ণ এবং ৩৯টি ব্যঞ্জনবর্ণ।

স্বরবর্ণ: অ, আ, ই, ঈ, উ, ঊ, ঋ, এ, ঐ, ও, ঔ; ব্যঞ্জনবর্ণের প্রথম বর্ণ ক ও শেষ বর্ণ হ।

বাংলা ভাষায় তিনটি কাল: অতীত, বর্তমান, ভবিষ্যৎ; প্রত্যেক কালের আবার সাধারণ, ঘটমান, পুরাঘটিত প্রভৃতি রূপ আছে।

বাক্যের তিনটি প্রধান অংশ: কর্তা, কর্ম ও ক্রিয়া; উদাহরণ-রহিম ভাত খায় (কর্তা রহিম, কর্ম ভাত, ক্রিয়া খায়)।

সন্ধি হলো দুই বর্ণের মিলন; স্বরসন্ধির উদাহরণ: বিদ্যা + আলয় = বিদ্যালয়; ব্যঞ্জনসন্ধির উদাহরণ: উৎ + হার = উত্থার।

সমাস হলো একাধিক পদের এক পদে পরিণত হওয়া; প্রধান প্রকার: দ্বন্দ্ব, কর্মধারয়, তৎপুরুষ, বহুব্রীহি, অব্যয়ীভাব ও দ্বিগু।

কারক ও বিভক্তি: কর্তৃকারকে শূন্য বিভক্তি, কর্মকারকে দ্বিতীয়া (কে/রে), করণকারকে তৃতীয়া (দ্বারা/দিয়ে)।

বাংলা ভাষার প্রধান উপভাষাগুলোর মধ্যে রয়েছে ঢাকাইয়া, চট্টগ্রামি, সিলেটি, বরিশালি ও রংপুরি।

Islam has five pillars: Shahadah (declaration of faith), Salah (prayer), Zakat (charity), Sawm (fasting in Ramadan), and Hajj (pilgrimage to Makkah).

The Qur'an has 114 surahs; the first surah is Al-Fatihah and the longest is Al-Baqarah.

Muslims pray five times daily: Fajr, Zuhr, Asr, Maghrib, and Isha; each prayer has a fixed time window.

Zakat is obligatory on wealth above the nisab threshold, generally 2.5% of qualifying savings and wealth held for one lunar year.

Sawm requires abstaining from food, drink, and other invalidating acts from dawn (Fajr) to sunset (Maghrib) during Ramadan.

Hajj is performed in the month of Dhul-Hijjah; its essential rites include ihram, tawaf, sa'i, and standing at Arafah.

The four rightly guided caliphs (Khulafa-e-Rashidun) were Abu Bakr, Umar, Uthman, and Ali.

Moral education emphasizes honesty, truthfulness, respect for parents and teachers, charity, and avoiding backbiting and lying.

A paragraph has one controlling idea expressed in a topic sentence, followed by supporting sentences and a concluding sentence.

A formal letter includes sender's address, date, receiver's address, salutation, subject line, body, closing, and signature.

An essay typically has three parts: introduction (state the thesis), body paragraphs (one main point each), and conclusion (restate and summarize).

Cohesive devices such as 'however', 'therefore', 'moreover', and 'in addition' link sentences and clarify logical relationships.

Punctuation rules: use a full stop at the end of a statement, a question mark after a question, and commas to separate items in a list.

Subject-verb agreement and consistent tense are essential; avoid shifting from past to present within one narrative.

A good composition stays on topic, uses specific details rather than vague words, and avoids repetition of the same sentence structure.

Direct quotation requires quotation marks; indirect quotation reports the words without quotation marks and adjusts pronouns and tense.