Questions
5–8 questions per paper
Difficulty
Easy
Importance
High yield for SSC and Banking exams
Overview
Simplification and Approximation form the foundation of quantitative aptitude in Indian competitive exams. Mastering this topic is essential for clearing the cut-off, as it tests your calculation speed, accuracy, and adherence to the order of operations under strict time constraints.
BODMAS Rule and Order of Operations
BODMAS defines the standard sequence for solving complex arithmetic expressions. Ignoring this rule leads to incorrect results, as the operator precedence is strictly mandated in all competitive exams.
- B: Brackets ( ) [ ] { }
- O: Of (Multiplication)
- D: Division
- M: Multiplication
- A: Addition
- S: Subtraction
Approximation Techniques
Approximation is used when exact values are not required, allowing you to round off complex decimals to the nearest whole number. This tactic is crucial for saving time during long calculations in PO and CGL level exams.
- Round decimals to the nearest integer for speed
- Approximate percentages like 33.33% to 1/3
- Approximate 49.9% of X as 0.5 * X
- Ignore insignificant decimal digits in multi-step problems
Surds, Indices, and Powers
Operations involving exponents and radicals appear frequently to test your understanding of power laws. Memorizing these identity-based rules allows for rapid reduction of complex numbers.
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
- (a^m)^n = a^(m*n)
- a^0 = 1 (where a is not 0)
- n-th root of a = a^(1/n)
- Negative exponent rule: a^-n = 1/a^n
Formula Sheet
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
a^2 - b^2 = (a-b)(a+b)
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Exam Tip
Focus on memorizing squares up to 30, cubes up to 20, and fraction-to-percentage conversions to perform calculations mentally without relying on paper.
Common Mistakes
- Failing to follow BODMAS sequence and performing operations left-to-right strictly.
- Over-approximating values too early in the steps, which leads to a significant cumulative error.
- Neglecting the signs (positive vs negative) during the expansion of bracketed terms.
More Revision Notes
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