SSC & UPSC math formula guide
A distraction-free revision sheet of every geometry formula, algebra equation, mensuration rule, trigonometric identity and arithmetic shortcut that repeats in SSC CGL, CHSL, GD, UPSC CSAT, Banking and Railway papers. No sign-up, no clutter — skim it before a mock test, then jump straight into a lecture.
Algebra equations
| Square of a sum | (a + b)² = a² + 2ab + b² |
|---|---|
| Square of a difference | (a − b)² = a² − 2ab + b² |
| Difference of squares | a² − b² = (a + b)(a − b) |
| Cube of a sum | (a + b)³ = a³ + 3ab(a + b) + b³ |
| Sum of cubes | a³ + b³ = (a + b)(a² − ab + b²) |
| Three-term identity | a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) |
| Quadratic roots | x = [−b ± √(b² − 4ac)] / 2a |
Geometry formulas
| Area of triangle | ½ × base × height |
|---|---|
| Heron's formula | √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2 |
| Pythagoras theorem | hypotenuse² = base² + perpendicular² |
| Circle area / circumference | πr² | 2πr |
| Sector area | (θ/360) × πr² |
| Parallelogram area | base × height |
| Trapezium area | ½ × (sum of parallel sides) × height |
| Sum of interior angles | (n − 2) × 180° |
Mensuration (3D)
| Cube volume / surface | a³ | 6a² |
|---|---|
| Cuboid volume / surface | lbh | 2(lb + bh + hl) |
| Cylinder volume / CSA | πr²h | 2πrh |
| Cone volume / CSA | ⅓πr²h | πrl |
| Sphere volume / surface | ⁴⁄₃πr³ | 4πr² |
| Hemisphere volume / TSA | ⅔πr³ | 3πr² |
Trigonometry
| Fundamental identity | sin²θ + cos²θ = 1 |
|---|---|
| Secant identity | 1 + tan²θ = sec²θ |
| Cosecant identity | 1 + cot²θ = cosec²θ |
| Double angle | sin 2θ = 2 sinθ cosθ |
| Height & distance | tanθ = height / base distance |
Arithmetic shortcuts
| Percentage change | [(new − old) / old] × 100 |
|---|---|
| Successive change | a + b + (ab/100) |
| Profit / loss % | (profit or loss / cost price) × 100 |
| Simple interest | P × R × T / 100 |
| Compound interest | P[(1 + R/100)^T − 1] |
| Speed–distance–time | speed = distance / time |
| Average speed (equal distance) | 2xy / (x + y) |
| Work done together | xy / (x + y) days |
Math formulas — frequently asked questions
- Which math formulas are most important for SSC CGL?
- Mensuration, geometry, trigonometry identities, percentage and profit-loss shortcuts cover the majority of the SSC CGL quantitative aptitude section.
- Are these formulas useful for UPSC CSAT?
- Yes. CSAT arithmetic leans on percentages, ratios, time-speed-distance and basic geometry — all listed on this sheet.
- How should I revise these formulas?
- Revise one group a day, then immediately solve 10 questions on that group. Pair the sheet with the free lectures on PadhakuMonk for concept clarity.