SSC CGL Formula Sheet
Ten formulas, what each one is for, and a worked example.
SSC CGL maths goes beyond arithmetic. Tier 1 and Tier 2 both give a large share of questions to algebra, geometry, trigonometry and mensuration, alongside percentages, profit and loss, and interest.
These ten formulas are the highest-value ones across both tiers, with a worked Heron's formula example.
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The 10 Formulas
1
Formula
Square identities
Expression
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²
Use it for
Algebra simplification.
2
Formula
Cube identities
Expression
a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²)
Use it for
Algebra and value-finding questions.
3
Formula
a³ + b³ + c³ − 3abc
Expression
(a + b + c)(a² + b² + c² − ab − bc − ca)
Use it for
If a + b + c = 0, then a³ + b³ + c³ = 3abc.
4
Formula
Pythagorean identities
Expression
sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1
Use it for
Trigonometry simplification.
5
Formula
Heron's formula
Expression
Area = √[s(s − a)(s − b)(s − c)], s = (a + b + c) ÷ 2
Use it for
Area of a triangle from its three sides.
6
Formula
Pythagoras theorem
Expression
Hypotenuse² = Base² + Height²
Use it for
Right triangles, heights and distances.
7
Formula
Sphere
Expression
Volume = (4/3)πr³; Surface area = 4πr²
Use it for
Mensuration (3D).
8
Formula
Profit %
Expression
(SP − CP) ÷ CP × 100
Use it for
Profit or loss on cost price.
9
Formula
Compound interest
Expression
A = P × (1 + R/100)ᵀ; CI = A − P
Use it for
Interest compounded once a year.
10
Formula
Speed, distance, time
Expression
Distance = Speed × Time; km/h × 5/18 = m/s
Use it for
Trains, journeys and unit conversions.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Square identities | (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b² | Algebra simplification. |
| 2 | Cube identities | a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²) | Algebra and value-finding questions. |
| 3 | a³ + b³ + c³ − 3abc | (a + b + c)(a² + b² + c² − ab − bc − ca) | If a + b + c = 0, then a³ + b³ + c³ = 3abc. |
| 4 | Pythagorean identities | sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1 | Trigonometry simplification. |
| 5 | Heron's formula | Area = √[s(s − a)(s − b)(s − c)], s = (a + b + c) ÷ 2 | Area of a triangle from its three sides. |
| 6 | Pythagoras theorem | Hypotenuse² = Base² + Height² | Right triangles, heights and distances. |
| 7 | Sphere | Volume = (4/3)πr³; Surface area = 4πr² | Mensuration (3D). |
| 8 | Profit % | (SP − CP) ÷ CP × 100 | Profit or loss on cost price. |
| 9 | Compound interest | A = P × (1 + R/100)ᵀ; CI = A − P | Interest compounded once a year. |
| 10 | Speed, distance, time | Distance = Speed × Time; km/h × 5/18 = m/s | Trains, journeys and unit conversions. |
Worked Example: Heron's Formula
Find the area of a triangle with sides 13 cm, 14 cm and 15 cm.
- 1
Semi-perimeter
s = (13 + 14 + 15) ÷ 2 = 21.
- 2
Apply the formula
√[21 × 8 × 7 × 6] = √7,056.
- 3
Area
84 cm².
Questions from this exact syllabus. No signup.
Use Values to Test Algebra Options
For algebra and trigonometry identities, substitute easy values (a = 1, b = 0, or θ = 45°) into the options. The one that matches the question at those values is usually the answer.
FAQs
Which maths topics carry the most weight in SSC CGL?expand_more
Advanced maths (algebra, geometry, trigonometry, mensuration) and arithmetic both carry heavy weight. Data interpretation appears too.
Is Tier 2 maths harder than Tier 1?expand_more
Yes. Tier 2 Mathematical Abilities goes deeper into the same topics.
Should I memorise trig tables?expand_more
Memorise the values for 0°, 30°, 45°, 60° and 90°. They come up in nearly every paper.
Next steps
Take a full SSC CGL mock testThe whole Tier 1 syllabus in one timed, scored paper.