Number Concepts and Operations
This topic builds the foundation for all numerical reasoning in the test: place value, order of operations, factors/multiples, powers/roots, patterns, sets, logic, and unit conversions.
- Order of operations (BODMAS): Always solve in this sequence — Brackets → Orders (powers/roots) → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Example: 12 + 6 ÷ 3 x (2+1)^2 → brackets first: (2+1)=3 → powers: 3^2=9 → division/multiplication left to right: 6÷3=2, then 2x9=18 → addition: 12+18 = 30.
- Place value: Each digit's value depends on its position (units, tens, hundreds...). This matters when comparing or rounding numbers.
- Factors and multiples:
- A factor of a number divides it exactly (no remainder). E.g., factors of 12 = 1,2,3,4,6,12.
- A multiple is the result of multiplying a number by an integer. E.g., multiples of 4 = 4,8,12,16...
- HCF (Highest Common Factor) = largest number dividing two or more numbers exactly.
- LCM (Lowest Common Multiple) = smallest number that is a multiple of two or more numbers.
- Trick: HCF x LCM = product of the two numbers (useful for quick checks).
- Powers and roots: a^n means a multiplied by itself n times (e.g., 2^3 = 8). A root reverses this (e.g., √8 is not whole, but √9 = 3).
- Number patterns: Sequences following a rule (arithmetic: add/subtract a fixed number; geometric: multiply/divide by a fixed number). Identify the rule to find the next term.
- Sets:
- A set is a well-defined collection of distinct elements, e.g., A = {1,2,3}.
- A set with n elements has 2^n subsets (including the empty set {} and the full set itself). E.g., a 3-element set has 2^3 = 8 subsets.
- Logic: Basic reasoning questions test statements, if-then relationships, and valid conclusions — read carefully and don't assume extra information.
- Scientific notation: Large or small numbers are written as a x 10^n, where 1 ≤ a < 10. E.g., 45,000 = 4.5 x 10^4.
- Unit conversions (memorize these):
- 1 km = 1000 m
- 1 h = 60 min (1 min = 60 s)
- 1 MB = 1024 KB
Test tip: Most number questions are solved fastest by strictly following BODMAS and double-checking sign/order errors — these are the most common mistakes under time pressure.