Quantitative Aptitude
Algebra
Algebra
Algebra covers equations, identities, and inequalities. Exam questions test linear and quadratic equations, standard algebraic identities, polynomial remainder theorem, and inequality rules.
Key Idea
Convert word problems into equations, then solve. For quadratics, use the discriminant (b²−4ac) to determine the nature of roots without fully solving.
Core Formulas
Linear Equation (Two Variables) — Substitution / Elimination
ax + b = 0 → x = −b/a | For two variables: solve one equation for x, substitute into the other
One variable: direct substitution. Two variables: use elimination when coefficients can be matched, substitution otherwise.
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a | Sum of roots = −b/a | Product of roots = c/a
Find roots of ax²+bx+c=0. Use sum/product shortcuts to answer questions about roots without fully solving.
Key Algebraic Identities
(a+b)² = a²+2ab+b² | (a−b)² = a²−2ab+b² | (a+b)(a−b) = a²−b² | a³+b³ = (a+b)(a²−ab+b²)
Simplify expressions or find missing values when two of the three terms are known; recognise the pattern first.
Remainder Theorem
Remainder when f(x) is divided by (x−a) = f(a) | If f(a)=0, (x−a) is a factor
Find remainder without performing polynomial long division; also used to check whether a given binomial is a factor.
Inequalities — Sign Flip Rule
Multiplying or dividing both sides by a negative number flips the inequality sign | |x| < a ⟺ −a < x < a
Solving inequalities involving negative coefficients or absolute values; always check whether you are multiplying by a negative.
Relevant Exams
Algebra is a high-weight topic in SSC and banking exams — expect 3–5 questions per paper. Quadratic roots, identity shortcuts, and age/number word problems are the most frequently tested sub-types.