SSC CGL 2026 Maths: 100 Golden Formulas & Short Tricks Cheatsheet
The ultimate Quantitative Aptitude formula compilation for SSC CGL Tier 1 & Tier 2. Features Geometry theorems, Algebra shortcuts, Trigonometry tables, 3D Mensuration matrix, and rapid revision cards.
SSC CGL 2026 MATHS GOLDEN FORMULAS
100 High-Yield Formulae • Short Tricks • Geometry Theorems • 3D Mensuration
- Geometry & Circle Theorems (Triangle centers, inradius, tangent-secants – High weightage)
- Algebra Expansions (x + 1/x = k power series, symmetric cubic identities)
- Trigonometric Identities (Complementary angle ratios, maximum & minimum value matrix)
- Mensuration 2D & 3D (Frustum of cone, hollow cylinder, pyramid, sphere volume)
- Arithmetic Speed Shortcuts (Relative speed, successive discount, CI/SI difference for 2 & 3 years)
*Note: There is a strict negative marking of 0.50 marks for every wrong answer in Tier 1 and 1.00 mark in Tier 2. Accurate practice is highly necessary.
SSC CGL Maths Formula PDF, Download for Free
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1. Geometry Golden Theorems & Circle Properties
Geometry contributes 3 to 5 questions in Tier 1 and up to 8 questions in Tier 2. Key theorems focused on triangle centers and circle tangents:
Incenter & Angle Bisector Theorem
High WeightageIn triangle ABC, if I is the incenter (intersection of interior angle bisectors):
- Angle BIC = 90° + ½(Angle A)
- Angle AIC = 90° + ½(Angle B)
- Angle AIB = 90° + ½(Angle C)
- Inradius r = Area of Triangle / Semi-perimeter (s)
Circumcenter & Orthocenter Relations
Repeated PYQIf O is the circumcenter of triangle ABC:
- Angle BOC = 2 × Angle A
- Circumradius for Right-angled triangle R = Hypotenuse / 2
- Circumradius for Equilateral triangle R = a / √3, Inradius r = a / 2√3 (Ratio R : r = 2 : 1)
Tangent-Secant Theorem (Circle Intersections)
Must-KnowWhen secant PAB and tangent PT intersect outside a circle at point P:
- PT² = PA × PB
- Direct Common Tangent Length DCT = √(d² - (r₁ - r₂)²), where d is distance between centers
- Transverse Common Tangent Length TCT = √(d² - (r₁ + r₂)²)"
2. Algebra Identities & Shortcut Expansions
x + 1/x = k Shortcut Matrix
Top Exam TrickIf x + 1/x = k, use these direct power expansions:
- x² + 1/x² = k² - 2
- x³ + 1/x³ = k³ - 3k
- x⁴ + 1/x⁴ = (k² - 2)² - 2
- x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) - (x + 1/x)
Symmetric Cubic Identity (a³ + b³ + c³ - 3abc)
Mandatory Tier 2If a + b + c = 0, then a³ + b³ + c³ = 3abc. In general:
- a³ + b³ + c³ - 3abc = (a+b+c)(a² + b² + c² - ab - bc - ca)
- a³ + b³ + c³ - 3abc = ½(a+b+c)[(a-b)² + (b-c)² + (c-a)²]
3. Trigonometry Standard Values & Height-Distance Rules
Pythagorean Triplets & Max/Min Values
Speed SaverMemorize these common right-angle triplets to skip calculating √(a²+b²):
- Triplets: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (20, 21, 29)
- Max/Min for a sin θ + b cos θ: Maximum = √(a² + b²), Minimum = -√(a² + b²)
4. Mensuration 2D & 3D Surface Area / Volume Matrix
| 3D Solid Shape | Curved / Lateral Surface Area | Total Surface Area (TSA) | Volume (V) |
|---|---|---|---|
| Cylinder | 2πrh | 2πr(h + r) | πr²h |
| Cone | πrl (l = √(r²+h²)) | πr(l + r) | ⅓πr²h |
| Sphere | 4πr² | 4πr² | ⁴⁄₃πr³ |
| Hemisphere | 2πr² | 3πr² | ⅔πr³ |
| Frustum of Cone | πl(R + r) | πl(R + r) + πR² + πr² | ⅓πh(R² + r² + Rr) |
5. Arithmetic Speed Tricks (Percentage, CI/SI & Speed-Time)
Compound Interest (CI) vs Simple Interest (SI) Difference
Guaranteed QuestionFor Principal P and Rate R%:
- 2-Year Difference (CI₂ - SI₂): D₂ = P(R / 100)²
- 3-Year Difference (CI₃ - SI₃): D₃ = P(R / 100)² × [(300 + R) / 100]
Sample SSC CGL PYQ Practice Questions with Solutions
Attempt these high-yield questions to test your quantitative speed and accuracy:
Description: Applying the Incenter Angle Theorem: Angle BIC = 90° + ½(Angle A) = 90° + ½(70°) = 90° + 35° = 125°.
Description: Using the direct shortcut formula x³ + 1/x³ = k³ - 3k = 5³ - 3(5) = 125 - 15 = 110.
Description: Using 2-year difference formula D₂ = P(R / 100)² = 10,000 × (10 / 100)² = 10,000 × (1 / 100) = ₹100.
6. Rapid Revision Flashcards (Click to Flip)
Test your memory before exam day! Click any card below to reveal the answer:
What is the inradius of an equilateral triangle with side a?
Click to flipr = a / 2√3 (Circumradius R = a / √3)
If x + 1/x = 5, what is x³ + 1/x³?
Click to flipk³ - 3k = 5³ - 3(5) = 125 - 15 = 110
What is the 2-Year CI minus SI difference formula?
Click to flipD₂ = P(R / 100)²
7. Frequently Asked Questions (FAQ)
How many math questions are asked in SSC CGL Tier 1?
SSC CGL Tier 1 contains 25 Quantitative Aptitude questions carrying 2 marks each (Total 50 marks) with 0.5 negative marking per wrong answer.
Can I download this math formula sheet as a PDF?
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