SAMPAD Grade 7 Entrance Exam cheat sheet

BODMAS order: Brackets first, then Orders (powers/roots), then Division and Multiplication left to right, then Addition and Subtraction left to right.

For two positive integers: LCM × HCF = product of the two numbers, so HCF = (product) ÷ LCM.

Area formulas: rectangle = length × breadth; triangle = ½ × base × height; circle = πr²; circumference = 2πr.

Percentage: x% of N = (x ÷ 100) × N; percentage change = (change ÷ original value) × 100%.

Average = sum of all values ÷ number of values; total = average × number of values.

Simple interest = (Principal × Rate × Time) ÷ 100, with rate in percent per year and time in years.

Sum of interior angles of an n-sided polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360° ÷ n.

Profit% = (profit ÷ cost price) × 100 and loss% = (loss ÷ cost price) × 100; selling price = cost price × (100 ± percent) ÷ 100.

Subject-verb agreement: a singular subject takes the -s verb form in simple present (he runs); a plural subject takes the base form (they run).

Articles: use 'a' before a consonant sound and 'an' before a vowel sound, so 'an hour' but 'a university'.

Present perfect = has/have + past participle; use 'since' with a starting point in time and 'for' with a length of time.

Active to passive: object becomes subject, add the correct tense of 'be', use the past participle, then 'by' + agent.

Comparatives compare two items (-er / more); superlatives compare three or more (-est / most); never use both forms together.

its = possession; it's = it is or it has. their = possession; there = place; they're = they are.

Direct to indirect speech: shift pronouns to match the reporter, backshift the tense one step, and change time/place words (now → then, today → that day).

Prepositions of time: 'in' for months, years and seasons, 'on' for days and dates, 'at' for exact clock times.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, using sunlight and chlorophyll; it stores energy and releases oxygen.

Solids have fixed shape and volume; liquids have fixed volume but take the container's shape; gases fill any container.

Newton's laws: first - no change in motion without a net force; second - F = ma; third - every action has an equal and opposite reaction.

SI units: force in newtons (N), work and energy in joules (J), power in watts (W), pressure in pascals (Pa), current in amperes (A).

Arteries carry blood away from the heart under high pressure; veins carry blood back to the heart and contain valves.

Food chain order: producer → primary consumer → secondary consumer → decomposer; only about 10% of energy passes to the next level.

Water cycle order: evaporation → condensation → precipitation → collection or runoff.

Plant functions: roots absorb water and minerals, stems transport, leaves make food, flowers carry out reproduction.

বাংলা বর্ণমালায় স্বরবর্ণ ১১টি ও ব্যঞ্জনবর্ণ ৩৯টি; মোট বর্ণ ৫০টি।

কারক ৬ প্রকার: কর্তৃকারক, কর্মকারক, করণকারক, সম্প্রদানকারক, অপাদানকারক ও অধিকরণকারক।

সমাস ৬ প্রকার: দ্বন্দ্ব, কর্মধারয়, তৎপুরুষ, বহুব্রীহি, অব্যয়ীভাব ও দ্বিগু।

সন্ধি ৩ প্রকার: স্বরসন্ধি, ব্যঞ্জনসন্ধি ও বিসর্গসন্ধি।

কাল ৩ প্রকার: অতীত কাল, বর্তমান কাল ও ভবিষ্যৎ কাল।

বচন ২ প্রকার: একবচন ও বহুবচন; লিঙ্গ ৪ প্রকার: পুংলিঙ্গ, স্ত্রীলিঙ্গ, উভয়লিঙ্গ ও ক্লীবলিঙ্গ।

গঠন অনুসারে বাক্য ৩ প্রকার: সরল বাক্য, জটিল বাক্য ও যৌগিক বাক্য।

বাক্যের দুটি অংশ: উদ্দেশ্য (যার সম্পর্কে বলা হয়) ও বিধেয় (উদ্দেশ্য সম্পর্কে যা বলা হয়)।

Bangladesh dates: Independence Day 26 March 1971; Victory Day 16 December; Language Martyrs' Day 21 February.

Bangladesh national symbols: animal - Royal Bengal Tiger; flower - water lily (shapla); fruit - jackfruit; bird - oriental magpie-robin (doyel).

World facts: 7 continents and 5 oceans; Jupiter is the largest planet and Mercury the smallest; the Sun is a star, not a planet.

Number series rule: test the difference between consecutive terms first (constant difference = arithmetic), then test a constant multiplier (geometric).

Odd-one-out rule: name the shared property of most items (living, shape, number type) and select the item that lacks it.

Analogy rule: state the exact link in the first pair (part : whole, young : adult, tool : user) and apply the identical link to the second pair.

Coding-decoding rule: number letters A = 1 to Z = 26, find the shift between plain and coded letters, then apply the same shift to decode.

Direction sense: sketch the path with north up; for two perpendicular moves the shortest distance back is found with Pythagoras' theorem.