Every successful SSC CGL candidate has some version of a formula sheet — a few pages they can revise in half an hour. The point is not to learn formulas from it at the last minute; it is to keep what you already know fresh and fast. Use this sheet as a model, then build your own with the results you personally tend to forget.
How to use it
- Read one section and cover the right-hand side; recall each formula.
- Mark anything you hesitate on.
- Solve two questions on each marked item the same day.
- Revise the whole sheet twice a week in the final month.
Arithmetic
| Topic | Key results |
|---|
| Successive % change | a + b + ab/100 |
| A is r% more than B | B is r/(100 + r) × 100% less than A |
| Price ↑ r%, keep expenditure | Cut consumption by r/(100 + r) × 100% |
| Profit % | (SP − CP)/CP × 100 |
| Markup and discount | MP/CP = (100 + profit%)/(100 − discount%) |
| Successive discounts | a + b − ab/100 |
| False weight | Profit % = error/(true weight − error) × 100 |
| Same SP, x% profit and x% loss | Loss = x²/100 % |
| Partnership | Profit ∝ capital × time |
| Alligation | Cheaper : dearer = (d − m) : (m − c) |
| Repeated replacement | x(1 − y/x)^n |
| SI | PRT/100 |
| CI amount | P(1 + R/100)^T |
| CI − SI, 2 years | P(R/100)² |
| CI − SI, 3 years | P(R/100)²(3 + R/100) |
| Time and work | Total work = LCM of times; rate = work/time |
| M₁D₁H₁/W₁ | = M₂D₂H₂/W₂ |
| km/h to m/s | × 5/18 |
| Average speed, equal distances | 2xy/(x + y) |
| Boats | b = (down + up)/2; s = (down − up)/2 |
Number system
| Result | Formula |
|---|
| HCF × LCM | Product of two numbers |
| Number of factors of a^p b^q | (p + 1)(q + 1) |
| Trailing zeros in n! | n/5 + n/25 + … (whole parts) |
| Unit digit cycles | 2, 3, 7, 8 → cycle of 4; 4, 9 → cycle of 2 |
Algebra
| Identity | Result |
|---|
| a³ + b³ | (a + b)³ − 3ab(a + b) |
| a³ + b³ + c³ − 3abc | (a + b + c)(a² + b² + c² − ab − bc − ca) |
| If a + b + c = 0 | a³ + b³ + c³ = 3abc |
| x + 1/x = k | x² + 1/x² = k² − 2; x³ + 1/x³ = k³ − 3k |
| x − 1/x = k | x² + 1/x² = k² + 2; x³ − 1/x³ = k³ + 3k |
| Quadratic roots | α + β = −b/a; αβ = c/a |
Geometry
| Result | Formula |
|---|
| Centroid | Divides median 2 : 1 |
| Incentre | ∠BIC = 90° + A/2 |
| Circumcentre | ∠BOC = 2A |
| Orthocentre | ∠BHC = 180° − A |
| Angle bisector | BD : DC = AB : AC |
| Similar triangles | Area ratio = (side ratio)² |
| Chord | r² = (half chord)² + d² |
| Tangent length | √(d² − r²) |
| Direct common tangent | √[d² − (r₁ − r₂)²] |
| Transverse common tangent | √[d² − (r₁ + r₂)²] |
| Cyclic quadrilateral | Opposite angles sum to 180° |
| Polygon | Interior sum (n − 2)180°; exterior 360°/n; diagonals n(n − 3)/2 |
Mensuration
| Figure | Formula |
|---|
| Equilateral triangle | Area (√3/4)a² |
| Heron's formula | √[s(s − a)(s − b)(s − c)] |
| Sector | Area (θ/360)πr²; arc (θ/360)2πr |
| Area change (x% and y%) | x + y + xy/100 |
| Cylinder | V = πr²h; CSA = 2πrh |
| Cone | V = ⅓πr²h; CSA = πrl |
| Sphere | V = (4/3)πr³; SA = 4πr² |
| Hemisphere | TSA = 3πr² |
| Frustum | V = ⅓πh(R² + r² + Rr) |
Trigonometry
| Result | Value |
|---|
| sin 30°, cos 60° | 1/2 |
| sin 60°, cos 30° | √3/2 |
| tan 30°, tan 60° | 1/√3, √3 |
| Identities | sin² + cos² = 1; sec² − tan² = 1; cosec² − cot² = 1 |
| (sec θ + tan θ)(sec θ − tan θ) | 1 |
| Max of a sin θ + b cos θ | √(a² + b²) |
Statistics and probability
| Result | Formula |
|---|
| Empirical relation | Mode = 3 Median − 2 Mean |
| Adding k to all values | Mean + k; SD unchanged |
| Two dice | 36 outcomes |
| Cards | 52; 12 face cards; 4 aces |
Practice
Cover the right-hand column of each table and write out every formula from memory. Score yourself. Anything you missed goes to the top of your revision list for the next three days.
Get the next SSC CGL guide by email
New guides every week. No spam, unsubscribe any time.
