SSC MTS · Bite-size lessons

Algebra

About 7 min · Numerical and Mathematical Ability · English

Time worked out from the lesson's 555 words at 150 words a minute, plus a minute for each question.

Algebra in SSC MTS Session-I focuses on solving linear equations (one or two variables), basic quadratic equations, and applying algebraic identities to simplify expressions. Unlike advanced algebra, MTS tests your ability to manipulate variables, factorize simple expressions, and substitute values correctly. Mastery here requires recognizing patterns quickly (which identity applies?), avoiding calculation errors (especially sign mistakes), and solving equations methodically. Questions often interweave with arithmetic—for example, translating a word problem into an equation or verifying an identity numerically.

Key ideas

• Linear equation in one variable: An equation of the form ax + b = c, where a ≠ 0. Solve by isolating x through inverse operations (add/subtract constants, then divide by coefficient).
• Linear equation in two variables: Equations like 2x + 3y = 12. Questions may give two such equations (simultaneous equations) and ask for x and y. Solve by substitution (express one variable in terms of the other) or elimination (add/subtract equations to cancel one variable).
• Quadratic equation: An equation of the form ax² + bx + c = 0, where a ≠ 0. For MTS, factorization is the primary method—split the middle term or recognize perfect squares. The discriminant (b² − 4ac) and quadratic formula are worth knowing for non-factorable cases.
• Algebraic identities: Pre-memorized expansion formulas that simplify expressions without multiplying term-by-term. The exam tests both direct substitution (given a + b = 5 and ab = 6, find a² + b²) and reverse recognition (factor x² − y² immediately as (x + y)(x − y)).
• Substitution and simplification: Replace variables with given numerical values and compute the result. Watch for negative signs and fractions—errors here cost marks despite correct method.

Watch out for

• Sign errors during transposition: Students write 5x − 3 = 12, then 5x = 12 − 3 instead of 12 + 3. Fix: When moving a term across =, always reverse its sign (− becomes +, + becomes −).
• Confusing (a − b)² with a² − b²: Writing (a − b)² = a² − b² misses the middle term −2ab. Fix: Memorize the full identity (a − b)² = a² − 2ab + b², and note a² − b² is a separate identity (difference of squares).
• Incorrect middle-term splitting: Attempting to factor x² + 7x + 10 by choosing numbers that don't multiply to 10 or don't add to 7 (e.g., 3 and 4). Fix: Always verify both conditions—product equals constant term, sum equals coefficient of x.

Quick reference

• Linear equation one variable: Isolate x by inverse operations; always transpose with sign change.
• Simultaneous equations: Use elimination (add/subtract equations) or substitution (solve one, plug into other).
• (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b²—know both cold.
• a² − b² = (a + b)(a − b)—instant factorization for difference of squares.
• Factorize quadratics: Find pair of numbers (product = c, sum = b in x² + bx + c).

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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