Algebra Questions for SSC MTS

Linear Equations in One Variable

These are equations with one unknown (usually x) and no exponents. SSC MTS loves simple real-world scenarios: age problems, work-sharing, money distribution. The key is isolating x by moving terms across the equals sign, flipping their operation. Always check your answer by substituting back.

• Form: ax + b = c. Solve by: x = (c - b) / a
• Watch signs when moving terms: +5 becomes -5 when crossing equals
• Word problems: define variable clearly, translate sentence to equation, solve, verify
• Common trap: forgetting to divide the entire right side by the coefficient of x
• Always substitute answer back into original equation to confirm

Linear Equations in Two Variables

Two unknowns (x and y), usually two equations. SSC MTS uses substitution or elimination method. Elimination is faster in exams: multiply one/both equations to make one variable's coefficient equal, then subtract. Substitution works when one variable has coefficient 1.

• Elimination method: make coefficients of one variable equal, subtract equations, solve for remaining variable
• Substitution: express one variable in terms of other from one equation, plug into second equation
• Graphically: two straight lines; unique solution = lines intersect at one point
• No solution if lines are parallel (same slope, different intercept)
• Infinite solutions if equations represent the same line

Quadratic Equations

Equations of form ax^2 + bx + c = 0. SSC MTS mostly tests factorization and quadratic formula. Factorization is faster if the quadratic factors nicely (which it usually does in this exam). Always rearrange to standard form first. Two solutions possible (real or complex, but MTS stays with real).

• Standard form: ax^2 + bx + c = 0
• Factorization: find two numbers that multiply to ac and add to b, split middle term, factor by grouping
• Quadratic formula works always but slower — use only if factorization fails
• Sum of roots = -b/a, Product of roots = c/a (useful for verification)
• If discriminant (b^2 - 4ac) is negative, no real roots; if zero, one repeated root; if positive, two distinct roots

Algebraic Identities

Standard expansions and factorizations that save time. SSC MTS tests these heavily in simplification and factorization questions. Memorize the core six. These are shortcuts — using them is faster than expanding manually.

• (a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2
• (a + b)(a - b) = a^2 - b^2 (difference of squares — very common)
• (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 and (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
• a^3 + b^3 = (a + b)(a^2 - ab + b^2) and a^3 - b^3 = (a - b)(a^2 + ab + b^2)
• Recognize patterns in questions: if you see x^2 - 9, immediately think (x - 3)(x + 3)

Simplification & Substitution

SSC MTS often gives algebraic expressions and asks you to simplify or evaluate them. Use identities to collapse terms quickly. Substitution questions give you values (like x = 2, y = 3) and ask you to find the value of a complex expression. Always substitute carefully and follow order of operations.

• Simplify by grouping like terms and applying identities
• For substitution: write out the expression, substitute values, compute step-by-step
• Watch order of operations: exponents before multiplication/division, then addition/subtraction
• If expression has fractions, find common denominator before simplifying
• Negative signs are easy to mess up — double-check when substituting negative values

• Sign error when moving terms: forgetting to flip sign when crossing equals sign. Example: 2x + 5 = 13 becomes 2x = 13 - 5, not 13 + 5.
• Forgetting to divide entire right side by coefficient of x. Example: 3x = 15 gives x = 5, but students sometimes write x = 15 - 3.
• In quadratic factorization, finding numbers that multiply to ac but forgetting they must also add to b. Always check both conditions.
• Misapplying identities: writing (a + b)^2 = a^2 + b^2 (wrong — missing the 2ab term).
• In two-variable equations, solving for one variable correctly but then substituting into wrong equation or making arithmetic error in final substitution.
• Ignoring the ± in quadratic formula and writing only one root when two exist.

• PEMDAS for order: Parentheses, Exponents, Multiply/Divide (left to right), Add/Subtract (left to right).
• Difference of Squares: 'A squared minus B squared is (A plus B) times (A minus B)' — rhyme it.
• Quadratic roots: 'Minus B plus-minus square root of B squared minus 4AC, all over 2A' — sing it to a tune.
• Identity check: (a+b)^2 always has a MIDDLE term (2ab). If you forget it, you're wrong.
• Elimination method: 'Make, Match, Subtract' — make coefficients equal, match signs, subtract to eliminate.

• SSC MTS Quant has 25 questions in 90 minutes. Algebra is 5-8 of these. Spend max 1-1.5 min per question. If factorization doesn't work in 30 seconds, switch to quadratic formula.
• Recent papers (2022-2024) show preference for word problems (age, distance, work) over pure algebraic manipulation. Read carefully, define variable clearly.
• Identities are tested as 'simplify' or 'find value' questions. These are quick wins if you memorize the six core identities. Expect 1-2 identity questions per paper.
• Two-variable equations appear as 'find x and y' or 'find x + y'. Elimination is faster than substitution in timed exams. Practice elimination until it's automatic.
• Quadratic questions rarely ask for complex roots. If discriminant is negative, the answer is usually 'no real solution' or the question is designed so it doesn't happen. Don't overthink.
• Always verify your answer by substituting back. This takes 10 seconds and catches 90% of careless errors. In SSC MTS, accuracy > speed.