AISSEE cheat sheet

HCF × LCM = product of the two numbers (for two positive integers); use it to find LCM when the HCF is known.

Profit% and Loss% are always calculated on cost price: Profit% = (SP − CP) ÷ CP × 100.

Two successive discounts of a% and b% give a single equivalent discount of a + b − ab/100 percent, not a + b.

Simple Interest = P × R × T ÷ 100; Amount = Principal + SI, and the SI added is the same every year.

Average = sum of all observations ÷ number of observations; adding the same value k to every observation raises the average by k.

1 km/h = 5/18 m/s; for a fixed distance, time is inversely proportional to speed, so doubling speed halves the time.

Circle: area = πr² and circumference = 2πr; triangle area = ½ × base × height; rectangle area = length × breadth.

Sum of the first n natural numbers = n(n+1)/2; sum of the first n odd numbers = n².

Divisibility tests: 3 → digit sum divisible by 3; 4 → last two digits; 8 → last three digits; 11 → alternating digit sum divisible by 11.

Letter positions: A = 1, B = 2 … Z = 26; the anchor word EJOTY gives E = 5, J = 10, O = 15, T = 20, Y = 25.

Opposite letter pairs always sum to 27: A↔Z, B↔Y, C↔X … M↔N; use this in coding and analogy questions.

Facing North, every right turn is a 90° clockwise rotation: North → East → South → West; left turns go anticlockwise.

Rank from left + rank from right − 1 = total number of persons in the row or queue.

Clock angle = |30H − 5.5M| degrees, where H is the hour and M the minutes; if the result exceeds 180°, subtract it from 360°.

A mirror image reverses left and right but keeps top and bottom; a water image reverses top and bottom but keeps left and right.

In number series, test consecutive differences first, then ratios, then squares/cubes, then two interleaved alternating series.

Syllogism: 'All A are B' also gives 'Some B are A'; 'Some A are B' can never be stretched to 'All A are B'.

Use 'a' before a consonant sound and 'an' before a vowel sound, judged by pronunciation: an hour, an M.A., a university, a one-rupee coin.

'The' is used with superlatives, unique objects, rivers, mountain ranges, newspapers and ordinal numbers (the Ganga, the Himalayas, the first).

Simple present covers habits and universal truths; present continuous covers actions happening now or arranged near-future events.

With each, every, either, neither, everyone and everybody, use a singular verb and singular pronoun: Each boy was present.

Prepositions of time: in + month/year/season, on + day/date, at + clock time (in July, on Monday, at 5 p.m.).

Passive voice = correct tense of 'be' + past participle; the active object becomes the subject and the agent follows 'by'.

Comparative uses -er/more and is followed by 'than'; superlative uses -est/most and takes 'of' or 'in', not 'than'.

Direct → indirect: when the reporting verb is past, move the reported verb one step back (present → past, past → past perfect, will → would) and adjust pronouns.

National symbols of India: Bengal tiger (animal), peacock (bird), lotus (flower), mango (fruit), banyan (tree).

The Constitution was adopted on 26 November 1949 and came into force on 26 January 1950, celebrated as Republic Day.

The Ganga is the longest river flowing within India, rising at the Gangotri glacier and draining into the Bay of Bengal; the Thar Desert lies mainly in Rajasthan.

Dandi March / Salt Satyagraha took place in 1930; Quit India Movement in 1942; Jallianwala Bagh massacre in 1919.

In the solar system, Mercury is nearest the Sun, Jupiter is the largest planet, and Mars is called the red planet.

Chess uses 16 pieces per player; cricket and hockey field 11 players per side; the Summer Olympic Games are held every four years.

Dr Rajendra Prasad was India's first President (1950–1962), Jawaharlal Nehru the first Prime Minister, and Indira Gandhi the first woman Prime Minister.

The skin is the largest organ of the human body; red blood cells carry oxygen using haemoglobin.