➕ Simplification – SSC Cheat Sheet
🔢 What is Simplification?
Simplification involves reducing complex mathematical expressions to their simplest form using arithmetic operations, BODMAS rules, identities, and mental math.
⚙️ BODMAS Rule
Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction
📌 Always follow this order when solving expressions.
🔣 Types of Questions Asked
- Arithmetic expressions (with brackets, powers)
- Missing number problems
- Square roots, cube roots
- Fractions & decimals
- Percentages + ratios
- Operations with BODMAS
- Approximation-based MCQs
🔢 Key Tricks and Tips
✅ Shortcut Squares (1–30)
1²=1 5²=25 10²=100 15²=225 20²=400 25²=625 30²=900
✅ Shortcut Cubes (1–20)
1³=1 4³=64 5³=125 10³=1000 15³=3375 20³=8000
✅ Common Fractions to Percentages
| Fraction | Percent |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 3/4 | 75% |
| 1/5 | 20% |
| 1/6 | 16.67% |
| 1/8 | 12.5% |
| 1/10 | 10% |
🧠 Mental Math Tips
✅ Multiplying by 5
Multiply by 10, then divide by 2
👉 68 × 5 = (68 × 10) / 2 = 340
✅ Dividing by 5
Multiply by 2, then divide by 10
👉 245 ÷ 5 = (245 × 2) / 10 = 49
✅ Squaring numbers ending in 5
Let number = x5
👉 Formula: (x × (x+1)) followed by 25
👉 25² = 2×3 = 6 ⇒ 625
📘 SSC Previous Year Questions
🔹 SSC CGL 2022
Simplify: √(144) + 25% of 80 – 3²
Solution:
√144 = 12
25% of 80 = 20
3² = 9
👉 12 + 20 – 9 = 23 ✅
🔹 SSC CHSL 2021
Simplify: (15 × 4) – [3² + (12 ÷ 3)]
Solution:
= 60 – [9 + 4]
= 60 – 13 = 47 ✅
🔹 SSC MTS 2020
What is the cube root of 3375?
Solution:
3375 = 15³
👉 Answer: 15 ✅
🧮 Common Identities to Remember
(a + b)² = a² + 2ab + b²(a – b)² = a² – 2ab + b²a² – b² = (a – b)(a + b)
🔁 Daily Practice Examples
1. Simplify: 25 × 4 + 16 ÷ 4
👉 100 + 4 = 104
2. Find value: √(121) + 2³
👉 11 + 8 = 19
3. Simplify: 8 + [16 – 4 × 2]
👉 8 + (16 – 8) = 16
🚀 Final Tips
- Practice square/cube roots mentally.
- Always follow BODMAS strictly.
- Learn tables up to 20.
- Focus on speed + accuracy for SSC Tier-1.
🔁 Flash Card Revision
🧮 Follow BODMAS 🧠 Know squares/cubes 1–30 📊 Use percent-fraction quick map ➕ Use mental math hacks