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SSC CGL Algebraic Formula Practice Test 2026 — Free Chapter Wise Questions

Squares and cubes of two terms, difference of squares, scaled and shifted brackets, three-variable identities and the a + b + c = 0 shortcut, completing the square and factorisation — 25 questions per test, with full solutions and shortcut tricks in English or हिंदी.

2 Difficulty Levels 25 Questions per Test 30 min optional timer English & हिंदी

Algebraic Formula Tests — Pick a Level and Start

Tap a level to see every test in it. Start at Level 1 the day you finish learning the identities, then move to Level 2 with the timer running to push accuracy under pressure.

Level 1 Basic Checking… View tests

One identity applied cleanly — find a2 + b2 from a sum and a product, factorise a difference of squares, use the cube rule, and read off a pairwise sum from a squared total. Attempt these without the clock while the identities are still fresh.

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Level 2 Tier I Standard Checking… View tests

Real SSC CGL Tier I difficulty — two ideas chained in one question: a coefficient that must be divided back out, an identity read backwards to recover a factor, a hidden zero total, a condition that quietly forces a = b = c, and a least-value question that needs the square completed first. This is the score that tells you the chapter is exam-ready.

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Algebraic formulas are one of the steadiest scorers in the SSC CGL Quantitative Aptitude paper. A shift almost always carries a question that belongs to the chapter outright — a sum and a product that must become a cube, three numbers that quietly add to zero, or a decimal fraction that collapses the moment the right identity is spotted — and the same identities decide how fast you get through simplification and the advanced maths block.

These practice tests put twenty-five identity questions in front of you in one sitting, which is what turns the formulas from something you can recite into something you apply without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.

How Many Algebraic Formula Questions Are Asked in SSC CGL?

The chapter usually gets one to two direct questions, and its identities are reused inside simplification, algebraic results and the quadratic equation questions across the advanced maths block.

ChapterTier I (out of 25)Tier II Paper I (out of 30)
Algebraic Formula1–22–3
Algebraic Result (x + 1/x)1–22–3
Algebraic Expressions11–2
Quadratic Equations11–2
Simplification1–22–3

Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.

What You Will Practice in the Algebraic Formula Chapter

Core topics

  • The two basic squares, and the four bridges between sum, difference, product and squares
  • Adding and subtracting the squared brackets — when the product disappears and when only it survives
  • Coefficients on the terms, and converting PQ back to the plain product
  • Difference of squares — large numbers, decimals, and the chain that collapses
  • Brackets in place of letters, and the sign flip when a bracket is subtracted
  • Cube expansion, the correction term, and the factorised form with its sign rule
  • Scaled cubes: 8x3, 27y3, 64a3, 125p3
  • Three-variable identities: squared total, pairwise sum, half-sum of squared differences
  • The condition that forces a = b = c, and how examiners disguise it
  • The cubic identity, the a + b + c = 0 shortcut, and reading it backwards
  • Completing the square, least value, and grouping four terms into a square
  • Factorisation and rational expressions — what may and may not be cancelled

Every one of these is explained from zero, with a worked example and the common trap, in the Algebraic Formula study notes (also in हिंदी).

Solved Examples — SSC CGL Algebraic Formula

Q1. If a + b = 8 and ab = 15, find a2 + b2.
Use a2 + b2 = (a + b)2 − 2ab = 64 − 30. Answer: 34
Q2. Find [(213)2 − (187)2] ÷ 26.
Factorise instead of squaring: (400)(26) ÷ 26. The divisor was placed there to cancel one factor. Answer: 400
Q3. If 3m + 2n = 7 and 27m3 + 8n3 = 91, find mn.
With P = 3m, Q = 2n: 91 = 343 − 21PQ, so PQ = 12. But PQ = 6mn, so divide the coefficients back out. Answer: mn = 2
Q4. Find [(1.2)3 + (2.3)3 − (3.5)3] ÷ [1.2 × 2.3 × 3.5].
1.2 + 2.3 − 3.5 = 0, so the numerator is 3 × 1.2 × 2.3 × (−3.5). The sign of the third cube is what makes it negative. Answer: −3
Q5. If a3 + b3 + c3 − 3abc = 108 and a2 + b2 + c2 − ab − bc − ca = 12, find a + b + c.
The identity makes the first a product of the total and the second, so 108 = (a+b+c) × 12. Divide, do not subtract. Answer: 9

How the Algebraic Formula Chapter Tests Work

  • 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
  • Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the rules.
  • Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
  • Solutions, shortcut tricks and concept notes open after you submit, question by question.
  • English and हिंदी, chosen at the start of every test.
  • Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.

How to Prepare Algebraic Formula for SSC CGL

  1. Learn the two basic squares until you can write either without pausing. Every other identity in the chapter is these two rearranged.
  2. Fix the cube sign rule early. A sum of cubes has a minus inside the long bracket; a difference has all pluses. It is the opposite of what most candidates expect.
  3. Check for a zero total before anything else. If three numbers or brackets add to zero, the cube sum is simply 3abc — the fastest win in the chapter.
  4. Treat a coefficient as part of the term. Work with P = 2x and Q = 3y, then remember PQ = 6xy when you convert back.
  5. Never compute a large square or cube until you have checked whether it cancels. Almost every numeric question here is built to cancel.
  6. Do Level 1 untimed, the same day you finish the identities. The aim is correct recall, not speed.
  7. Move to Level 2 with the 30-minute clock on. An identity that takes more than twenty seconds means you are still deriving it instead of applying it.
  8. Study it with its sibling chapters. Do algebraic result right after, since the cube rule carries straight over, and read the chapter notes beside the tests.
  9. Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.

SSC CGL बीजीय सूत्र (Algebraic Formula) चैप्टर टेस्ट — हिंदी में

बीजीय सूत्र SSC CGL गणित का एक स्थिर अंक देने वाला अध्याय है। लगभग हर शिफ्ट में इसका 1–2 प्रश्न सीधे आता है — जैसे योग और गुणनफल से घन निकालना, तीन संख्याओं का योग शून्य पहचानकर a3+b3+c3 = 3abc लगाना, या दशमलव वाली भिन्न जो सही सर्वसमिका पहचानते ही सिमट जाती है — और यही सर्वसमिकाएँ सरलीकरण तथा उन्नत गणित के प्रश्नों में भी काम आती हैं।

TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 30 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।

याद रखने योग्य नियम: a2 + b2 = (a+b)2 − 2ab; a3 + b3 = (a+b)3 − 3ab(a+b) — योग में सुधार घटता है, अंतर में जुड़ता है; और घनों के योग के लंबे कोष्ठक में ऋण चिह्न होता है जबकि अंतर में सभी चिह्न धन। पूरे नोट्स यहाँ हिंदी में पढ़ें।

SSC CGL Algebraic Formula — Frequently Asked Questions

What are the most important algebraic identities for SSC CGL?
The two squares (a ± b)2, the difference of squares a2 − b2 = (a+b)(a−b), the two cube forms, the squared total (a+b+c)2, and the cubic identity a3+b3+c3 − 3abc. About ten lines cover almost every question asked.
How do I find a3 + b3 from a + b and ab?
Use a3 + b3 = (a+b)3 − 3ab(a+b). Cube the sum, then subtract three times the product times the sum. For a difference of cubes the correction is added instead of subtracted.
What happens when a + b + c = 0?
The cubic identity collapses and a3 + b3 + c3 = 3abc. Whenever three numbers or three brackets add to zero, this turns a long calculation into one multiplication, so check for it first.
What does a2 + b2 + c2 = ab + bc + ca mean?
It means a = b = c. The condition is the same as saying the three squared differences add to zero, and a square is never negative, so each difference must be zero. Examiners often disguise it by doubling every term.
How many algebraic formula questions are asked in SSC CGL?
One to two in a typical Tier I shift, and two to three in Tier II Paper I. The identities also feed simplification, algebraic results and quadratic equation questions, so the chapter is worth more than its direct count.
How many questions are in each algebraic formula practice test?
Twenty-five questions per test, with an optional 30-minute timer and the real exam marking scheme of +2 for a correct answer, −0.5 for a wrong one and 0 for an unattempted question.
Are the algebraic formula tests available in Hindi and are they free?
Yes to both. Questions, options, detailed solutions and shortcut tricks are available in हिंदी, and you pick English or Hindi before the test starts. Every test is free — you only need a free TrickySSC account, and the sign-in box opens on the page itself when you start a test.

More Free SSC CGL Practice

SSC CGL Maths Chapter Wise TestAll chapters, Level 1–3 All SSC CGL ChaptersEvery subject in one place SSC CGL Previous Year PapersShift-wise papers with solutions SSC CGL Mock Test 2026Full-length, real sectional timing