Algebra — SSC CHSL Study Notes

Overview

Algebra is a core scoring area in SSC CHSL Tier 1, typically contributing 3–5 direct questions. The exam focuses on three pillars: solving linear and quadratic equations, applying polynomial identities, and factorising expressions. Mastery here is non-negotiable because algebra underpins several other topics like time-speed-distance word problems and profit-loss equations.

SSC CHSL algebra questions are application-based rather than theoretical. You won't be asked to "prove" an identity, but you must recognise which identity applies and use it instantly. Speed matters — most algebra questions should take 45–60 seconds. The syllabus emphasises practical problem-solving: given an equation or expression, transform it using identities or factorisation, then compute the answer. Topics like linear equations in one or two variables, quadratic formula, discriminant-based questions, and standard polynomial identities (a² – b², a³ + b³) appear regularly.

Students often lose marks by misapplying identities or making sign errors during factorisation. The goal of these notes is to give you a mental toolkit — formulas you can recall instantly, the logic behind factorisation, and the common question types you'll face.

Key Concepts

• **Linear equation in one variable**: An equation of the form ax + b = 0 where a ≠ 0. Solution is x = –b/a. Always isolate the variable on one side by performing inverse operations.

• **Linear equation in two variables**: Form ax + by = c. SSC CHSL typically gives simultaneous equations (a pair) which you solve by substitution, elimination, or cross-multiplication to find unique values of x and y.

• **Quadratic equation**: Standard form ax² + bx + c = 0 where a ≠ 0. Solutions come from factorisation, completing the square, or the quadratic formula x = (–b ± √(b² – 4ac)) / 2a.

• **Discriminant (D)**: For ax² + bx + c = 0, D = b² – 4ac. If D > 0, two distinct real roots; D = 0, two equal real roots; D < 0, no real roots (complex roots, rarely tested in CHSL).

• **Polynomial identities**: Pre-memorised algebraic formulas that let you expand or factorise expressions in one step. SSC CHSL heavily tests the ability to recognise which identity fits a given expression.

• **Factorisation**: Expressing a polynomial as a product of simpler polynomials. Methods include taking out common factors, grouping, using identities, and splitting the middle term for quadratics.

• **Roots and coefficients**: For ax² + bx + c = 0 with roots α and β, sum of roots α + β = –b/a and product αβ = c/a. Use these for questions asking about root properties without solving the equation.