Elementary Algebra — RRB NTPC Study Notes
Overview
Elementary Algebra forms the backbone of quantitative reasoning in RRB NTPC Mathematics. Roughly 3–5 questions appear directly from this topic, and algebraic manipulation skills apply across Number System, Time-Work, Profit-Loss and other areas. Mastery means you can solve linear equations in seconds, handle simultaneous equations systematically, expand and factorise polynomials accurately, and apply standard identities without hesitation.
RRB NTPC tests algebra at a foundational level—no calculus, no complex polynomials. The focus is speed and accuracy with linear equations (one variable), pairs of simultaneous equations (two variables), recognising and applying the four basic polynomial identities, and factorising simple quadratic and cubic expressions. Questions often disguise algebra in word problems: "A number increased by 7 equals thrice the number decreased by 5—find the number." Your job is to translate English into equations and solve cleanly.
Expect a mix of direct computation ("Solve 3x − 5 = 2x + 7") and application problems. Time management is critical: you should spend 30–45 seconds per algebraic question. Practice until the identities and factorisation patterns become reflex.
Key Concepts
- **Linear equation in one variable**: An equation of the form ax + b = c, where a ≠ 0. Solution: isolate x by inverse operations—subtract, add, divide, multiply in reverse order of BODMAS.
- **Simultaneous linear equations**: Two equations in two unknowns (x and y). Three solution methods: substitution (solve one for x, plug into the other), elimination (add/subtract equations to cancel one variable), and cross-multiplication (determinant-based shortcut). All three yield the same answer; pick the fastest for the given problem.
- **Polynomial identity**: An equation true for all values of the variable. The four must-know identities let you expand or factorise instantly without multiplying term-by-term.
- **Factorisation**: Expressing a polynomial as a product of simpler polynomials. Techniques include taking out the common factor, grouping terms, and applying identities in reverse. Factorisation simplifies division, solves equations (set each factor = 0), and speeds up substitution.
- **Transposition**: Moving a term from one side of an equation to the other by changing its sign (addition ↔ subtraction, multiplication ↔ division). The golden rule: whatever you do to one side, do to the other to maintain equality.
- **Zero-product property**: If ab = 0, then a = 0 or b = 0. This is why factorising a quadratic lets you find roots immediately.