In this guide
This is a sheet to read, not a chapter to study. Use it before each mock test and every day in the final week. Cover the right-hand side of each line and try to say it from memory. Anything you cannot recall needs five practice questions today, from the full guide on that topic.
The SSC GD maths section is 20 questions (as reported for recent cycles; check the latest notification). The topics below cover what the Class 10 level syllabus usually asks.
Numbers
- Divisible by 3 or 9: check the sum of the digits.
- Divisible by 4: last two digits. By 8: last three digits. By 11: difference of alternate digit sums is 0 or a multiple of 11.
- 1 is neither prime nor composite. 2 is the only even prime.
- Sum of 1 to n = n(n + 1) ÷ 2.
- LCM × HCF = product of the two numbers.
- LCM of fractions = LCM of numerators ÷ HCF of denominators.
BODMAS
Brackets → Of → Division and Multiplication (left to right) → Addition and Subtraction (left to right).
Squares and roots
- Know squares to 30 and cubes to 15.
- A perfect square never ends in 2, 3, 7 or 8.
- (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². a² − b² = (a + b)(a − b).
Fractions and percentages
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/2 | 50% | 1/6 | 16⅔% |
| 1/3 | 33⅓% | 1/8 | 12.5% |
| 1/4 | 25% | 1/10 | 10% |
| 1/5 | 20% | 1/12 | 8⅓% |
- Percentage change = change ÷ original × 100.
- Two changes a% and b% in a row: net = a + b + (a × b ÷ 100). Use minus for a fall.
- If A is r% more than B, then B is r ÷ (100 + r) × 100 % less than A.
Ratio and average
- Share in the ratio a : b: a/(a + b) and b/(a + b) of the total.
- Total = average × number.
- New member's value = new total − old total.
Profit, loss and discount
- Profit % = profit ÷ CP × 100.
- SP = CP × (100 + profit %) ÷ 100.
- Discount % = discount ÷ MP × 100.
- Two discounts a% and b% = a + b − (a × b ÷ 100).
- "Buy x, get y free" discount = y ÷ (x + y) × 100.
Interest
- SI = P × R × T ÷ 100.
- Compound amount = P × (1 + R/100)ᵀ, where T is the number of years.
- CI − SI for 2 years = P × (R/100)².
Time and work
- Total work = LCM of the days. Add each person's work per day.
- Emptying pipe or leak: subtract.
- M1 × D1 × H1 = M2 × D2 × H2.
Time and distance
- Distance = speed × time.
- km/h × 5/18 = m/s. m/s × 18/5 = km/h.
- Train passing a pole: its own length. Passing a platform: train + platform.
- Opposite directions: add speeds. Same direction: subtract.
- Average speed for the same distance at x and y = 2xy ÷ (x + y).
Mensuration
- Square: area a², perimeter 4a. Rectangle: area l × b, perimeter 2(l + b).
- Triangle: area ½ × base × height. Right triangle: hypotenuse² = base² + height².
- Circle: area πr², circumference 2πr (π = 22/7).
- Cube: volume a³, surface 6a². Cuboid: l × b × h. Cylinder: πr²h.
- 1 m³ = 1,000 litres. 1 litre = 1,000 cm³.
Ages and mixtures
- Age difference never changes. "Ago" means subtract, "after" means add, for everyone.
- Mixing to a target price: cheaper : dearer = (dearer − mean) : (mean − cheaper).
- Partnership: profit in the ratio of investment × months.
Worked reminders
1. Successive change. A price rises 20% and then falls 10%. Net = 20 − 10 − (20 × 10 ÷ 100) = 10 − 2 = 8% rise. Check: 100 → 120 → 108.
2. Two discounts. Discounts of 20% and 10% equal 20 + 10 − 2 = 28% in one step. Check: 100 → 80 → 72.
3. CI minus SI. On ₹10,000 at 5% for 2 years: 10,000 × (5/100)² = 10,000 × 1/400 = ₹25.
4. Selling price for a profit. CP ₹450, profit 20%: SP = 450 × 120 ÷ 100 = ₹540.
5. LCM × HCF. Two numbers have a product of 360 and an HCF of 6. LCM = 360 ÷ 6 = 60.
Self-test (15 minutes)
- 20% of 350
- Divide ₹1,000 in the ratio 2 : 3.
- Average of 8, 12, 16 and 20
- Profit % when CP = ₹400 and SP = ₹460
- SI on ₹2,000 at 5% for 3 years
- A and B finish a job in 6 and 12 days. How long together?
- 72 km/h in m/s
- Area of a circle with a radius of 7 cm
- CI on ₹5,000 at 10% for 2 years
- A price rises 25% and then falls 20%. Net change?
Answers:
- 350 ÷ 5 = 70.
- 2/5 × 1,000 and 3/5 × 1,000: ₹400 and ₹600.
- 56 ÷ 4 = 14.
- 60 ÷ 400 × 100 = 15%.
- 2,000 × 5 × 3 ÷ 100 = ₹300.
- Total 12 units; A 2, B 1 a day; 12 ÷ 3 = 4 days.
- 72 × 5/18 = 20 m/s.
- 22/7 × 7 × 7 = 154 cm².
- Amount = 5,000 × 1.1 × 1.1 = 6,050. CI = ₹1,050.
- 25 − 20 − 5 = 0, no change. Check: 100 → 125 → 100.
How to use this sheet in the last week
| Day | Do this |
|---|---|
| 1–2 | Read the sheet; mark every line you could not recall |
| 3–4 | Practise the marked topics, ten questions each |
| 5 | Take a full mock; check every maths error against this sheet |
| 6 | Redo the self-test without looking at the answers |
| 7 | Light reading of the sheet only, then rest |
For the errors that keep coming back, read common maths mistakes. For speed, see calculation tricks.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
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