Algebra Questions for SSC CHSL

Core Algebraic Identities

These are the backbone of SSC CHSL Algebra. The exam constantly gives you expressions like (a+b)^2 or a^3+b^3 and asks you to find a value. Memorise all identities cold — do not derive them during the exam. Think of identities as shortcuts: instead of expanding everything, you plug in and get the answer in one step.

• (a+b)^2 = a^2 + 2ab + b^2
• (a-b)^2 = a^2 - 2ab + b^2
• (a+b)^2 + (a-b)^2 = 2(a^2 + b^2)
• (a+b)^2 - (a-b)^2 = 4ab
• a^2 - b^2 = (a+b)(a-b)
• a^3 + b^3 = (a+b)(a^2 - ab + b^2) and a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Value Finding — The x + 1/x Type

SSC CHSL loves questions where you are given x + 1/x = k and asked to find x^2 + 1/x^2, or x^3 + 1/x^3. These questions look hard but follow a fixed chain. Once you know the chain, you can solve in 20 seconds. Think of it like a staircase — each step uses the previous result.

• If x + 1/x = k, then x^2 + 1/x^2 = k^2 - 2
• If x + 1/x = k, then x^3 + 1/x^3 = k^3 - 3k
• If x - 1/x = k, then x^2 + 1/x^2 = k^2 + 2
• If x - 1/x = k, then x^3 - 1/x^3 = k^3 + 3k
• Always check sign — plus or minus 1/x changes the formula slightly

Linear Equations in One and Two Variables

SSC CHSL tests simple linear equations — either one variable or a pair of simultaneous equations. For two variables, the elimination or substitution method works. In exams, the fastest route is usually elimination — line up the two equations and cancel one variable directly. Do not spend time cross-multiplying unless the numbers force you.

• For ax + by = c and dx + ey = f, multiply to make coefficients of one variable equal then add or subtract
• Check for consistent (one solution), inconsistent (no solution), or dependent (infinite solutions) systems
• For a/b = d/e but c/f is different — no solution. For a/b = d/e = c/f — infinite solutions
• Word problems: assign variables clearly, form equations, then solve — do not guess

Factorisation and Simplification

Many SSC CHSL questions give a complex algebraic fraction or expression and ask you to simplify. The trick is always to spot a known identity in the numerator or denominator. Common patterns include difference of squares and sum or difference of cubes. Once you factor, things cancel out beautifully.

• Always try to factor the numerator and denominator before doing any arithmetic
• Spot a^2 - b^2 = (a+b)(a-b) whenever you see a difference of two squared terms
• For a^3 + b^3 type in numerator with (a+b) in denominator — they cancel leaving a^2 - ab + b^2
• If x = 2 or some small number satisfies an expression, substitution is faster than full factorisation

Substitution Trick for Quick Value Finding

When the question says 'if x + y + z = 0, find x^3 + y^3 + z^3', do not panic and expand. There is a direct identity. Similarly, many SSC expressions collapse to zero or a simple constant when you substitute smart values like x = 1 or x = 0. This trick alone saves 1-2 minutes per paper.

• If x + y + z = 0 then x^3 + y^3 + z^3 = 3xyz — memorise this unconditionally
• If the expression is symmetric in a, b, c — try a = b = c = 1 to get a feel for the answer
• Substituting x = 0 or x = 1 in complex expressions can quickly eliminate wrong options
• This trick works best in MCQ format — use it to verify your answer in 5 seconds

• Confusing (a+b)^3 = a^3 + b^3 + 3ab(a+b) with (a+b)^2 — students mix up the cube and square expansions under time pressure
• For x - 1/x type, using the formula for x + 1/x instead — the sign on the +2 vs -2 inside changes everything
• In simultaneous equations, making arithmetic errors when multiplying to equalise coefficients — double check the multiplied row
• Forgetting that x^3 + y^3 + z^3 = 3xyz only holds when x + y + z = 0 — applying it blindly when the sum is not zero
• Not simplifying before computing — students expand large expressions instead of factoring first, wasting 2-3 minutes

• Staircase for x+1/x: Square step = square minus 2, Cube step = cube minus 3 times original. Easy rule: the number in 'minus' matches the power.
• ZERO SUM THREE CUBES: If they add to Zero, the cubes give Three times product. Remember 0-3-3.
• For (a+b) vs (a-b) identities: Plus gives minus 2ab inside the squares, Minus gives plus 2ab. They are opposites — just flip the sign of 2ab.
• a^2 - b^2 mnemonic: SUM times DIFFERENCE. Always split a squared minus b squared into (a+b)(a-b) — never leave it as is.

• SSC CHSL typically has 3 to 5 algebra questions out of 25 Maths questions. Most are identity-based or x+1/x type — pure formula recall, not derivation.
• Questions are usually medium difficulty — they do not test advanced polynomial theory. If a question looks very hard, look for a substitution shortcut or identity match first.
• At least one question per paper involves x+y+z=0 and x^3+y^3+z^3 — this is nearly guaranteed based on past papers. Memorise that identity for free marks.
• In MCQ format, use substitution of x=1 or x=0 to verify answers in 5 seconds. This works especially for simplification questions with variable expressions.
• Target time: 40 to 50 seconds per algebra question. If you spend more than 60 seconds, mark and move — return if time permits. Identity questions must be instant.