SAMPAD Grade 10 Entrance Exam cheat sheet

Quadratic formula: x = [-b ± √(b² - 4ac)] / (2a); discriminant D = b² - 4ac; D>0 two real roots, D=0 equal roots, D<0 no real roots.

Arithmetic progression: nth term aₙ = a + (n-1)d; sum Sₙ = n/2 [2a + (n-1)d].

Geometric progression: nth term aₙ = a r^(n-1); sum Sₙ = a(1 - rⁿ)/(1 - r) for r ≠ 1; infinite sum S∞ = a/(1 - r) if |r|<1.

Area formulas: triangle = ½ × base × height; circle = πr²; trapezium = ½(a+b)h; parallelogram = base × height.

Pythagorean theorem: in a right triangle, a² + b² = c², where c is the hypotenuse.

Trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; sin²θ + cos²θ = 1.

Probability of an event = (number of favourable outcomes) / (total number of equally likely outcomes).

Simple interest = P × R × T / 100; compound amount = P(1 + R/100)^T.

Newton's second law: F = ma; SI unit of force is newton (N).

Ohm's law: V = IR; power P = VI = I²R = V²/R.

Speed of light in vacuum ≈ 3 × 10⁸ m/s; speed of sound in air ≈ 343 m/s at 20°C.

Atomic number = number of protons; mass number = protons + neutrons; isotopes have same protons, different neutrons.

pH scale: pH < 7 acidic, pH = 7 neutral, pH > 7 basic; pH = -log[H⁺].

Photosynthesis equation: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ (in presence of chlorophyll and sunlight).

Human blood groups: A, B, AB, O; O negative is universal donor, AB positive is universal recipient.

Cell organelles: mitochondria = ATP production; ribosomes = protein synthesis; chloroplast = photosynthesis (plants only).

Subject-verb agreement: singular subject takes singular verb; plural subject takes plural verb; ignore prepositional phrases between subject and verb.

Active to passive: object becomes subject, verb becomes be + past participle, subject becomes by-agent (often omitted).

Direct to indirect speech: change pronouns (first person to subject, second to object, third unchanged); shift tense back one step if reporting verb is past.

Articles: 'a' before consonant sounds, 'an' before vowel sounds, 'the' for specific or unique nouns.

Common prepositions: in (enclosed space), on (surface), at (point); since (point in time), for (duration).

Reading comprehension: identify main idea, supporting details, tone, and inference; eliminate options that are too broad or not stated.

Synonyms/antonyms: use context clues; words often have multiple meanings, so match the meaning in the sentence.

Punctuation: comma for lists and clauses, semicolon between independent clauses, apostrophe for possession or contraction.

Bangladesh gained independence in 1971; Victory Day is 16 December; Independence Day is 26 March.

The Sundarbans, a UNESCO World Heritage Site, is the largest mangrove forest in the world and lies in Bangladesh and India.

The United Nations was founded in 1945; headquarters in New York; current Secretary-General is António Guterres (as of 2024).

SAARC headquarters: Kathmandu, Nepal; ASEAN headquarters: Jakarta, Indonesia.

Bangladesh's national animal is the Bengal tiger, national bird is the oriental magpie-robin, national flower is the water lily.

The Padma Bridge, opened in 2022, is Bangladesh's longest bridge and connects Munshiganj to Shariatpur.

Nobel Prizes: Physics, Chemistry, Medicine, Literature, Peace, and Economic Sciences; awarded annually (except Economics, added 1969).

Current affairs: verify recent events (elections, summits, sports) from reliable sources because facts change frequently.

Number series: check differences, ratios, squares, cubes, or alternating patterns before assuming a simple rule.

Blood relations: draw a family tree; use + for male, - for female; vertical lines for generations, horizontal for siblings/spouses.

Direction sense: N, S, E, W; after each turn, update facing direction; use Pythagoras for shortest distance.

Syllogism: use Venn diagrams; 'All A are B' means A is inside B; 'Some A are B' means overlap; 'No A is B' means disjoint.

Coding-decoding: map letters to numbers (A=1, B=2, …); check shifts (+1, -1, +2) or reversals.

Seating arrangement: fix one person as reference, then place others relative to that position; consider left/right facing.

Analogy: identify relationship type (part-whole, cause-effect, synonym, worker-tool) and apply to the pair.

Odd one out: look for category, property, or pattern that differs from the rest.

বাংলা বর্ণমালায় স্বরবর্ণ ১১টি, ব্যঞ্জনবর্ণ ৩৯টি, মোট ৫০টি বর্ণ।

সন্ধি: স্বরসন্ধি, ব্যঞ্জনসন্ধি, বিসর্গসন্ধি-দুই বর্ণ মিলে এক হওয়ার নিয়ম।

সমাসের প্রকার: দ্বন্দ্ব, কর্মধারয়, তৎপুরুষ, বহুব্রীহি, দ্বিগু, অব্যয়ীভাব-৬ প্রকার।

কারক ও বিভক্তি: কর্তৃ, কর্ম, করণ, সম্প্রদান, অপাদান, অধিকরণ-৬ প্রকার।

বাংলা সাহিত্যের আদি নিদর্শন 'চর্যাপদ', রচয়িতা সিদ্ধাচার্যগণ, আবিষ্কৃত ১৯০৭ সালে হরপ্রসাদ শাস্ত্রী কর্তৃক।

মাইকেল মধুসূদন দত্তের 'মেঘনাদবধ কাব্য' বাংলা সাহিত্যের প্রথম সার্থক মহাকাব্য।

রবীন্দ্রনাথ ঠাকুর ১৯১৩ সালে 'গীতাঞ্জলি' কাব্যের জন্য নোবেল পুরস্কার পান।

কাজী নজরুল ইসলাম 'বিদ্রোহী' কবিতার রচয়িতা; বাংলাদেশের জাতীয় কবি।