SSC CGL Quant · Study & Practice

Algebra & Identities

AreaAlgebra DifficultyModerate–Hard SSC weightage4–6 questions (heavy in Tier 2)

SSC algebra rewards pattern recognition over grinding. A handful of identities — the square and cube expansions, and the symmetric results for x + 1/x — solve the bulk of Tier-2 questions in one step. The recurring move: you are given x + 1/x and asked for x^2 + 1/x^2 or x^3 + 1/x^3, which follow instantly from the identities. Add clean handling of linear and quadratic equations and you cover the whole block.

Topics

1 Algebraic Identities 4 worked · 5 practice · 8-Q test Start → 2 x + 1/x Problems 4 worked · 5 practice · 8-Q test Start → 3 Linear Equations 4 worked · 5 practice · 8-Q test Start → 4 Quadratic Equations 4 worked · 5 practice · 8-Q test Start →

⚡ SSC shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

a^2 + b^2 = (a+b)^2 - 2ab; a^3 + b^3 = (a+b)^3 - 3ab(a+b).
x + 1/x = k -> x^2 + 1/x^2 = k^2 - 2, x^3 + 1/x^3 = k^3 - 3k.
a + b + c = 0 -> a^3 + b^3 + c^3 = 3abc.
Quadratic: sum of roots = -b/a, product = c/a.
Two-digit number = 10t + u; reversed = 10u + t.

⚠️ Common mistakes & traps

SSC is designed so that careless errors here cost you marks. Internalise each trap before the exam.

Forgetting the -2 (or +2) when going from (x+1/x)^2 to x^2+1/x^2.
Sign errors in sum/product of roots (sum is -b/a).
Expanding (a+b)^3 without the 3ab(a+b) middle term.
Treating a negative discriminant as if real roots exist.

📈 SSC exam insight & PYQ analysis

SSC Tier 2 leans heavily on x + 1/x identities and symmetric a,b,c results, plus quick factorisable quadratics and roots relations.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

x + 1/x = 4 -> x^2 + 1/x^2?Tap to reveal

a^3+b^3+c^3 when a+b+c=0?Tap to reveal

3abc

Sum of roots of ax^2+bx+c?Tap to reveal

-b/a

105^2 - 95^2?Tap to reveal

2000

(a+b)^3 = ?Tap to reveal

a^3 + b^3 + 3ab(a+b)

📌 Quick revision

Memorise the square/cube identities and the x + 1/x results; spot what is given and pick the matching identity. Solve linear systems by elimination, quadratics by factor/formula, and use sum = -b/a, product = c/a for roots.

Chapter test

📝 Algebra & Identities — Chapter Test

25 fresh questions · timed · full solutions

Start chapter test →

📊 My SSC analytics

Track scores, accuracy by topic and progress over time.

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🏆 Vidaara SSC success checklist

You have truly mastered Algebra & Identities when you can tick every box below.

Recall every formula in this chapter without looking them up
Solve each topic’s practice set with at least 80% accuracy
Use the chapter shortcuts to cut your solving time in half
Spot and avoid every common trap listed above
Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpoint	Target
Concept theory & formulas understood	100%
Topic practice sets attempted (4 topics)	4/4
Best topic-test score	— → 80%+
Chapter test score	— → 80%+
Flashcards drilled to instant recall	5 cards

Formula Reference Sheet

This chapter

Identities

Square of sum	(a + b)^2 = a^2 + 2ab + b^2
Difference of squares	a^2 - b^2 = (a + b)(a - b)
Cube of sum	(a + b)^3 = a^3 + b^3 + 3ab(a + b)
Sum/diff of cubes	a^3 +/- b^3 = (a +/- b)(a^2 -/+ ab + b^2)
Three-term	a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)

x + 1/x family

Square	x^2 + 1/x^2 = (x + 1/x)^2 - 2
Cube	x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)
Quadratic roots	x = (-b +/- root(b^2 - 4ac)) / 2a

SSC reference