BASIC NUMERACY

This section tests the mathematical skills of candidates at the Class X level. However, candidates may also expect questions of a little bit higher standard than Class X level like Permutations and Combination, Probability etc in connection with problem solving.

Types of Numbers:

1. Natural Numbers: These are the set of positive integers starting from 1. (e.g., 1, 2, 3, 4, …)
2. Whole Numbers: Natural numbers including zero. (e.g., 0, 1, 2, 3, …)
3. Integers: This set includes all positive, negative numbers, and zero. (e.g., …, -3, -2, -1, 0, 1, 2, 3, …)
4. Rational Numbers: Numbers that can be expressed as a fraction of two integers, where the denominator is not zero. (e.g., 1/2, 7/3)
5. Irrational Numbers: Numbers that cannot be expressed as a simple fraction. Their decimal representation is non-recurring and non-terminating. (e.g., √2, π)
6. Real Numbers: This set encompasses both rational and irrational numbers.
7. Complex Numbers: Numbers that have both a real and an imaginary part. (e.g., 3 + 2i)

Relations Between Numbers:

1. Equality: Two numbers are said to be equal if they represent the same value. (e.g., 2 + 3 = 5)
2. Inequality: Numbers can be greater than, less than, greater than or equal to, or less than or equal to other numbers. (e.g., 5 > 3, 2 ≤ 4)
3. Divisibility: One number is divisible by another if, upon division, the remainder is zero. (e.g., 8 is divisible by 2)
4. Factors: If ‘a’ is divisible by ‘b’, then ‘b’ is a factor of ‘a’. (e.g., 1, 2, 4 are factors of 8)
5. Multiples: The result of multiplying a number by an integer. (e.g., 10, 20, 30 are multiples of 10)

Properties of Numbers:

1. 1. Commutative Property: The order of numbers does not affect the result (applies to addition and multiplication). a + b = b + a a × b = b × a
2. 2. Associative Property: Grouping of numbers does not affect the result (applies to addition and multiplication). (a + b) + c = a + (b + c) (a × b) × c = a × (b × c)
3. 3. Distributive Property: Multiplying a number by a group of numbers added together is the same as doing each multiplication separately. a × (b + c) = (a × b) + (a × c)
4. 4. Distributive Property: Multiplying a number by a group of numbers added together is the same as doing each multiplication separately. a × (b + c) = (a × b) + (a × c)

Orders of magnitudeOrders of magnitude

de a broad way to understand and compare the relative sizes or extents of quantities. It’s a concept that helps us grasp the scale of numbers, especially when they range from very large to very small, by representing numbers as powers of ten.

Orders of magnitude

Orders of magnitude provide a broad way to understand and compare the relative sizes or extents of quantities. It’s a concept that helps us grasp the scale of numbers, especially when they range from very large to very small, by representing numbers as powers of ten.

Understanding Orders of Magnitude:

When we say that two quantities differ by an order of magnitude, we essentially mean that one is roughly ten times larger than the other. For instance, 100 is one order of magnitude larger than 10, and 1,000 is two orders of magnitude larger than 10.