Quantitative Aptitude is where a single remembered formula can save you a full minute — and in a 15-minute sectional window, minutes are marks. This page is a complete SSC CGL maths cheat sheet: every chapter’s highest-yield formulas and the shortcuts that actually save time, arranged so you can jump to any topic, test yourself, and revise fast. Bookmark it and run through one group a day.
Updated: August 2026 · Compiled from the SSC CGL Quant syllabus and PYQ trends (2016–2025). Formulas are standard; the shortcuts are genuine time-savers, not replacements for understanding the concept.
Contents — tap any chapter to jump
A. Arithmetic Basics
B. Commercial Maths
C. Time-Based
D. Algebra
E. Geometry & Mensuration
F. Trigonometry & DI
A. Arithmetic Basics
Number System ★ PYQ
| Concept | Formula / Rule |
|---|---|
| HCF × LCM | = Product of the two numbers |
| Sum of first n natural numbers | n(n+1)2 |
| Sum of first n odd numbers | n2 |
| Sum of first n even numbers | n(n+1) |
| Sum of squares (12…n2) | n(n+1)(2n+1)6 |
| Sum of cubes (13…n3) | [n(n+1)2]2 |
| Number of factors of N = apbqcr | (p+1)(q+1)(r+1) |
Divisibility quick-checks: by 3 → digit sum divisible by 3; by 4 → last two digits; by 8 → last three digits; by 9 → digit sum; by 11 → difference of alternate-digit sums divisible by 11.
Simplification & Indices
| Rule | Formula |
|---|---|
| Order of operations | BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction) |
| Product of powers | am × an = am+n |
| Quotient of powers | am ÷ an = am−n |
| Power of a power | (am)n = amn |
| Zero & negative index | a0 = 1 ; a−n = 1an |
| Surds | √(ab) = √a × √b |
Percentage ★ PYQ
| Concept | Formula |
|---|---|
| x% of y | x100 × y |
| Percentage change | ChangeOriginal × 100 |
| A is x% more than B → B is less by | x100+x × 100 % |
| A is x% less than B → B is more by | x100−x × 100 % |
| Two successive changes a% and b% | a + b + ab100 % |
Learn the fraction table: ½=50%, ⅓=33⅓%, ¼=25%, ⅕=20%, ⅙=16⅔%, ⅛=12.5%, 1/9=11&frac19;%. It turns most percentage problems into one-step mental maths.
Ratio & Proportion
| Concept | Formula |
|---|---|
| Proportion | a : b = c : d ⇒ ad = bc |
| Mean proportional between a and b | √(ab) |
| Duplicate / sub-duplicate ratio | a2 : b2 / √a : √b |
| Componendo-dividendo | ab = cd ⇒ a+ba−b = c+dc−d |
Average
| Concept | Formula |
|---|---|
| Average | Sum of termsNumber of terms |
| Average of first n natural numbers | n+12 |
| Average of consecutive numbers | First + Last2 |
| Average speed (equal distances at x, y) | 2xyx + y |
✎ Quick self-test — Group A
1. What is 35% of 240?
84.
2. LCM of two numbers is 48 and HCF is 4. If one number is 12, find the other.
HCF × LCM = product → 4×48 = 192; other = 192/12 = 16.
3. Average of the first 10 natural numbers?
(10+1)/2 = 5.5.
4. If two numbers are in ratio 3:5 and their sum is 64, the larger number is?
64/8 = 8 → 5×8 = 40.
B. Commercial Maths
Profit, Loss & Discount ★ PYQ
| Concept | Formula |
|---|---|
| Profit / Loss | SP − CP / CP − SP |
| Profit% | ProfitCP × 100 |
| Loss% | LossCP × 100 |
| SP from CP | CP × 100 ± Profit%/Loss%100 |
| SP from MP & discount | MP × 100 − D%100 |
| Same SP, one at +x%, other at −x% | Always a loss of x2100 % |
Simple & Compound Interest ★ PYQ
| Concept | Formula |
|---|---|
| Simple Interest | P · R · T100 |
| Compound Amount | P(1 + R100)n |
| Compound Interest | P[(1 + R100)n − 1] |
| CI − SI for 2 years | P(R100)2 |
| CI − SI for 3 years | P(R100)2 × (3 + R100) |
| Compounded half-yearly | Rate = R2, Time = 2n |
Mixture & Alligation
| Concept | Formula |
|---|---|
| Alligation rule | Cheaper qtyDearer qty = Dearer − MeanMean − Cheaper |
| Repeated replacement (n times) | Initial × (1 − removedtotal)n |
Partnership
| Concept | Formula |
|---|---|
| Profit-sharing ratio | = Ratio of (Capital × Time) for each partner |
✎ Quick self-test — Group B
1. Buy at ₹400, sell at ₹500. Profit%?
(100/400)×100 = 25%.
2. SI on ₹1000 at 10% for 2 years?
1000×10×2/100 = ₹200.
3. CI − SI on ₹5000 at 10% for 2 years?
P(R/100)2 = 5000×(0.1)2 = ₹50.
4. Two articles sold at the same price, one at +20%, one at −20%. Net result?
A loss of (20)2/100 = 4%.
C. Time-Based
Time, Speed & Distance ★ PYQ
| Concept | Formula |
|---|---|
| Basic relation | Speed = DistanceTime |
| Unit conversion | km/h → m/s : × 518 ; m/s → km/h : × 185 |
| Average speed (equal distances) | 2xyx + y |
| Relative speed | Same direction: |a−b| ; Opposite: a+b |
Trains & Boats
| Concept | Formula |
|---|---|
| Train crossing a pole | Time = Length of trainSpeed |
| Train crossing a platform | Time = Train + Platform lengthSpeed |
| Downstream / Upstream speed | (b + s) / (b − s), where b = boat, s = stream |
| Boat & stream speed | Boat = down + up2 ; Stream = down − up2 |
Time & Work ★ PYQ
| Concept | Formula |
|---|---|
| One day’s work | If A finishes in x days, 1 day’s work = 1x |
| A and B together | Time = xyx + y |
| Work equation | M1D1H1W1 = M2D2H2W2 |
| Pipes & cisterns | Filling = positive rate, Emptying = negative rate |
✎ Quick self-test — Group C
1. Convert 72 km/h to m/s.
72 × 5/18 = 20 m/s.
2. A does a job in 10 days, B in 15 days. Together they take?
xy/(x+y) = 150/25 = 6 days.
3. A 200 m train crosses a pole in 10 s. Its speed?
200/10 = 20 m/s (= 72 km/h).
4. Boat speed 10 km/h, stream 2 km/h. Downstream speed?
10 + 2 = 12 km/h.
D. Algebra
Algebraic Identities ★ PYQ
| Identity | Expansion |
|---|---|
| (a + b)2 | a2 + 2ab + b2 |
| (a − b)2 | a2 − 2ab + b2 |
| a2 − b2 | (a + b)(a − b) |
| (a + b)3 | a3 + b3 + 3ab(a + b) |
| a3 + b3 | (a + b)(a2 − ab + b2) |
| a3 − b3 | (a − b)(a2 + ab + b2) |
| (a+b+c)2 | a2+b2+c2 + 2(ab+bc+ca) |
| If a+b+c = 0 | a3+b3+c3 = 3abc |
Very common in SSC: a + 1a = k ⇒ a2 + 1a2 = k2 − 2, and a3 + 1a3 = k3 − 3k.
Algebra Basics
| Concept | Rule |
|---|---|
| Quadratic roots (sum & product) | For ax2+bx+c: sum = −ba, product = ca |
| Quadratic formula | x = −b ± √(b2−4ac)2a |
✎ Quick self-test — Group D
1. If a + b = 7 and ab = 12, find a2 + b2.
(a+b)2 − 2ab = 49 − 24 = 25.
2. If a + 1/a = 3, find a2 + 1/a2.
32 − 2 = 7.
3. If a + b + c = 0, then a3 + b3 + c3 = ?
3abc.
4. Expand (x + 5)(x − 5).
x2 − 25.
E. Geometry & Mensuration
Geometry ★ PYQ
| Concept | Rule |
|---|---|
| Angle sum of triangle | 180° ; exterior angle = sum of two opposite interiors |
| Pythagoras theorem | Hypotenuse2 = Base2 + Perpendicular2 |
| Interior angles of an n-sided polygon | (n − 2) × 180° |
| Each exterior angle (regular polygon) | 360°n |
| Centroid divides a median | In ratio 2 : 1 |
| Circle | Angle at centre = 2 × angle at circumference; angle in a semicircle = 90° |
Mensuration — 2D ★ PYQ
| Shape | Area | Other |
|---|---|---|
| Rectangle | l × b | Diagonal = √(l2+b2) |
| Square | a2 | Diagonal = a√2 |
| Triangle | ½ × base × height | Heron: √[s(s−a)(s−b)(s−c)] |
| Equilateral triangle | √34 a2 | Height = √32 a |
| Circle | πr2 | Circumference = 2πr |
| Rhombus | ½ × d1 × d2 | — |
| Trapezium | ½ × (sum of parallel sides) × height | — |
Mensuration — 3D ★ PYQ
| Solid | Volume | Surface Area |
|---|---|---|
| Cube | a3 | TSA = 6a2; diagonal = a√3 |
| Cuboid | l × b × h | TSA = 2(lb+bh+hl) |
| Cylinder | πr2h | CSA = 2πrh; TSA = 2πr(r+h) |
| Cone | 13πr2h | CSA = πrl; l = √(r2+h2) |
| Sphere | 43πr3 | 4πr2 |
| Hemisphere | 23πr3 | CSA = 2πr2; TSA = 3πr2 |
✎ Quick self-test — Group E
1. Area of a circle of radius 7 (take π = 22/7).
22/7 × 49 = 154.
2. Volume of a cube with side 4.
43 = 64.
3. Area of an equilateral triangle with side 4.
(√3/4)×16 = 4√3 ≈ 6.93.
4. Sum of interior angles of a hexagon.
(6−2)×180° = 720°.
F. Trigonometry & Data Interpretation
Trigonometry ★ PYQ
| Concept | Formula |
|---|---|
| Basic ratios | sinθ = PH, cosθ = BH, tanθ = PB |
| Reciprocals | cosec = 1sin, sec = 1cos, cot = 1tan |
| Identity 1 | sin2θ + cos2θ = 1 |
| Identity 2 | 1 + tan2θ = sec2θ |
| Identity 3 | 1 + cot2θ = cosec2θ |
Standard values (θ = 0°, 30°, 45°, 60°, 90°):
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 12 | 1√2 | √32 | 1 |
| cos | 1 | √32 | 1√2 | 12 | 0 |
| tan | 0 | 1√3 | 1 | √3 | ∞ |
Height & Distance
| Concept | Rule |
|---|---|
| Core relation | tan(angle of elevation) = HeightHorizontal distance |
| Angle of depression | Equals the angle of elevation from the lower point (alternate angles) |
Data Interpretation (tips, not formulas)
- Read the title, units and legend before the questions — half of DI errors come from misreading the axis.
- Most DI is just percentage, ratio and average applied to a table or chart — the earlier chapters are the toolkit.
- Approximate first. If options are far apart, a rounded estimate answers the question without full calculation.
✎ Quick self-test — Group F
1. Value of sin 30° + cos 60°.
½ + ½ = 1.
2. sin2θ + cos2θ = ?
1.
3. What is tan 45°?
1.
4. If tanθ = 1 (0°–90°), then θ = ?
45°.
How to actually revise this cheat sheet
- One group a day. Read the tables, then close them and do the self-test from memory.
- Write, don’t just read. Copying a formula once by hand fixes it better than reading it ten times.
- Attach one PYQ to each formula. A formula you’ve used in a real question sticks; one you’ve only stared at fades.
- Keep a “leaky formula” list. The three or four you keep forgetting deserve a sticky note, not another full re-read.
Formulas only pay off under the clock. Take a free SSC CGL sectional mock in the exact 2026 pattern — the Quant section shows which formulas you recall instantly and which ones slow you down, so your revision targets the right chapters.
Frequently asked questions
Q1. How many maths questions come in SSC CGL Tier-1?
The Quantitative Aptitude section has 25 questions for 50 marks in Tier-1. This is fixed and official.
Q2. Which maths chapters are most important for SSC CGL?
Percentage, profit & loss, interest, time-speed-distance, time & work, algebra, geometry, mensuration and trigonometry appear most frequently. They are marked with a ★ PYQ flag on this page.
Q3. Are formulas enough to clear SSC CGL maths?
No. Formulas give speed, but only regular practice turns them into marks. Use this sheet for revision, alongside solving previous-year questions.
Q4. What is the level of maths in SSC CGL?
Roughly Class-10 standard. The challenge is speed and accuracy under the sectional clock rather than difficulty of concepts.
Q5. Does maths appear in SSC CGL Tier-2?
Yes, and with more weight. Tier-2 Paper-1 has a large Quantitative Aptitude module, so mastering these formulas now pays off in both tiers.
Q6. How do I stop forgetting formulas?
Revise a little every day rather than all at once, write formulas by hand, and always link each one to a question you’ve solved. Spaced repetition beats cramming.
Q7. Is a calculator allowed in SSC CGL?
No. All calculation is mental or on rough sheets, which is exactly why shortcuts and the fraction-to-percentage table matter so much.
Related reading: SSC CGL Static GK — One-Liner Mega List · Reasoning Syllabus · English Syllabus · General Awareness Guide
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