Questions
3 questions per paper
Difficulty
Medium
Importance
Medium yield; essential for clearing sectional cut-offs in SSC and Banking.
Overview
Algebra is a cornerstone of competitive quantitative aptitude, bridging basic arithmetic with logical problem-solving. Mastery of algebraic identities and manipulation is essential for reducing calculation time in SSC and Banking exams, where speed is the primary differentiator.
Linear and Quadratic Equations
Linear equations solve for a single variable, while quadratic equations involve second-degree polynomials. In exams, you must prioritize finding roots using the discriminant and sum/product relationships rather than manual factoring to save time.
- Quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a
- Sum of roots: -b/a
- Product of roots: c/a
- Discriminant D = b^2 - 4ac; if D > 0, real and distinct roots
- If D = 0, real and equal roots; if D < 0, complex roots
Algebraic Identities
These are the shortcuts that transform complex expressions into manageable ones. Memorizing these is not optional, as examiners frequently use expressions that cancel out perfectly if the correct identity is applied.
- (a + b)^2 = a^2 + b^2 + 2ab
- (a - b)^2 = a^2 + b^2 - 2ab
- 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)
- If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc
Surds and Indices
Surds deal with irrational roots, while indices govern the behavior of exponents. Understanding the laws of powers is critical for solving equations involving nested roots or variable bases.
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1
- a^(-n) = 1/a^n
- n-th root of a = a^(1/n)
Formula Sheet
(a + b)^2 = a^2 + b^2 + 2ab
(a - b)^2 = a^2 + b^2 - 2ab
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)
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)
x = (-b ± sqrt(b^2 - 4ac)) / 2a
a^(m) * a^(n) = a^(m+n)
(a^m)^n = a^(mn)
Exam Tip
Instead of solving complex equations, use 'Option Substitution' or 'Value Plugging' (letting x=1 or 2) to identify the correct answer in seconds.
Common Mistakes
- Misapplying sign conventions in the quadratic formula, particularly with negative coefficients.
- Forgetting the (a+b+c=0) condition when attempting to use the 3abc identity.
- Errors in exponent handling when the base is a fraction.
More Revision Notes
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