AISSEE key terms

The smallest number that is a multiple of two or more given numbers. For example, the LCM of 4 and 6 is 12. Find it by listing multiples or by comparing prime factorisations.

The largest number that divides two or more given numbers exactly, leaving no remainder. Also called the greatest common divisor. It is used to simplify fractions and to split things into equal groups.

A number written as one whole number above another, such as 3/4, showing parts of a whole. The top number is the numerator and the bottom is the denominator, which is never zero.

A quantity written as a part of one hundred, using the % sign. To change a fraction into a percentage, multiply it by 100; 45% means 45 out of every 100.

A ratio compares two quantities of the same kind by division and is written as a:b. A proportion states that two ratios are equal, as in 2:3 = 4:6, so cross products match.

The sum of a group of values divided by how many values there are. Also called the arithmetic mean. It gives one figure that stands for the whole group, often used for marks and speeds.

Interest calculated only on the original sum lent or borrowed, never on interest already earned. The formula is SI = (P × R × T) ÷ 100, with P principal, R rate per year and T years.

Profit is the selling price minus the cost price when goods are sold for more than they cost. Loss is the cost price minus the selling price when goods are sold for less.

Distance equals speed multiplied by time. Speed is the distance covered in one unit of time, such as kilometres per hour, while time is distance divided by speed.

The measure of the surface a flat shape covers, given in square units such as square metres. A rectangle's area is length × breadth; a triangle's area is ½ × base × height.

The amount of space a solid object occupies, measured in cubic units such as cubic centimetres. For a cuboid it is length × breadth × height; for a cube it is side cubed.

A mathematical phrase that mixes numbers, variables and operation signs, such as 5x − 7. It has no equals sign, and the parts joined by plus or minus signs are called terms.

A question that gives a pair of items linked by a certain relationship and asks you to complete a second pair in the same way, for example 'Doctor : Hospital :: Teacher : ?'.

A question that lists several items where all but one share a common feature. You must find the item that does not fit, such as the only non-prime number in a group.

A row of numbers arranged by a hidden rule, such as adding 4 each time, squaring consecutive numbers, or alternating two patterns. You find the rule and then supply the missing term.

A puzzle in which letters, words or numbers are replaced by others according to a fixed rule, such as shifting every letter two places forward. You work out the rule and apply it to new words.

Reasoning questions that describe family links in words, such as 'A is the brother of B's mother', and then ask how two people are related. A small family tree makes them simple.

Problems about a person walking and turning through different directions. You sketch the path, mark north, south, east and west, then find the final facing direction or the shortest distance from the start.

A logic question with two or more statements accepted as true, followed by conclusions. You decide which conclusions must always follow, often by drawing circles to stand for each group.

A non-verbal question that shows a figure and asks which option is its reflection in a mirror. Left and right swap over while top and bottom stay the same, and letters may reverse.

A puzzle in which people or objects must be placed in a row or around a table using clues such as 'P sits third to the left of Q'. Drawing the arrangement as you read helps.

A reasoning question where symbols stand for arithmetic operations, for example '+' means divide and '×' means add. You replace each symbol as directed and then simplify using the BODMAS order.

A word that means the same as, or nearly the same as, another word, such as 'quick' and 'fast'. Synonym questions test how wide and precise your vocabulary is.

A word that means the opposite of another word, such as 'victory' for 'defeat'. Antonym questions ask you to choose the option most nearly opposite in meaning to the given word.

One of two or more words that sound alike but differ in spelling and meaning, such as 'peace' and 'piece'. Only the meaning of the sentence tells you which one is correct.

Word parts fixed to a root word to change its meaning or its grammatical role. A prefix comes at the beginning, as in un-kind; a suffix comes at the end, as in kind-ness.

A small word placed before a noun or pronoun to show its link in place, time or direction to something else, such as 'under', 'during', 'between' or 'towards'.

The rule that a verb must match its subject in number and person. A singular subject takes a singular verb, even when a phrase or clause sits between the subject and the verb.

Two ways of stating the same action. In the active voice the subject performs it ('Meera washed the car'); in the passive voice the object becomes the subject ('The car was washed by Meera').

A fixed group of words whose meaning cannot be guessed from the separate words, such as 'to bite the bullet', which means to face something difficult bravely instead of avoiding it.

A vocabulary item that asks for a single word to replace a whole phrase, as 'astronomer' replaces 'one who studies the stars'. Knowing common word roots helps you guess correctly.

The supreme law of the country, adopted on 26 November 1949 and brought into force on 26 January 1950. It sets out the organs of government and the rights and duties of citizens.

Rights guaranteed to citizens in Part III of the Indian Constitution, such as equality before the law, freedom of speech and protection from exploitation. Citizens can approach courts to enforce them.

The law-making body of the Union, consisting of the President, the Rajya Sabha and the Lok Sabha. Most laws must be passed by both Houses before the President gives assent.

The three military services of India, the Army, the Navy and the Air Force, with the President as Supreme Commander. Their duty is to defend the country against external and internal threats.

India's highest wartime gallantry decoration, awarded for the most conspicuous bravery or self-sacrifice in the presence of the enemy. It was instituted in 1950 and takes precedence over other awards.

A youth organisation for school and college students that trains them in drill, discipline, leadership and adventure, and encourages interest in a career in the armed forces.

The seasonal reversal of winds over South Asia that brings most of India's rainfall, chiefly from June to September when the south-west monsoon blows. Farming and water supply depend on it.

The long movement against British rule, from the revolt of 1857 through the founding of the Indian National Congress in 1885 to Gandhi's non-cooperation and Quit India movements, ending in independence in 1947.