Basic Maths – Study Notes for NIFT Entrance
(General Awareness & Aptitude – General Maths)
Goal: Get comfortable with everyday maths problems.
Tip: Think of maths as a way to solve simple real‑life puzzles.
1. Numbers & Operations
| What | Everyday Analogy | Tiny Example |
|---|---|---|
| Whole Numbers | Counting apples in a basket | You have 7 apples. Add 3 more → 10 apples. |
| Decimals | Money – 3.50 rupees | 1.20 + 2.30 = 3.50 |
| Fractions | Cutting a pizza | ½ of a pizza + ¼ of a pizza = ¾ of a pizza |
2. Percentages
- What is a percent?
Think of 100 slices of a cake. One slice = 1 %.
| Problem | How to solve | Tiny Example |
|---|---|---|
| “What is 20 % of 50?” | 20 % = 20 out of 100 → (20 × 50) ÷ 100 | 20 % of 50 = 10 |
| “If a book costs ₹200 and is 15 % off, what’s the sale price?” | Find 15 % of ₹200 → 30. Subtract from 200. | 200 – 30 = ₹170 |
3. Ratios & Proportions
- Ratio = “A is to B” (like “2:3”).
- Proportion = Two ratios are equal.
| Problem | How to solve | Tiny Example |
|---|---|---|
| “Cars travel at 4 km in 3 min, how far in 9 min?” | Keep the ratio 4 km : 3 min. Multiply both sides by 3 → 12 km. | 4 km/3 min × 3 = 12 km |
| “If 2 pens cost ₹30, how much will 5 pens cost?” | Ratio 2:5 = 30:?. Cross‑multiply. | 5 × 30 ÷ 2 = ₹75 |
4. Simple Algebra (Very Basic)
- Unknown = a missing number.
- Use “X” or “?”.
| Problem | How to solve | Tiny Example |
|---|---|---|
| “5 + X = 12” | Subtract 5 from 12 → X = 7 | 5 + 7 = 12 |
| “2X = 8” | Divide both sides by 2 → X = 4 | 2 × 4 = 8 |
5. Basic Geometry
| Concept | Everyday Analogy | Tiny Example |
|---|---|---|
| Area of a Rectangle | Floor area in a room | Length × Width = 4 m × 3 m = 12 m² |
| Area of a Triangle | Half of a rectangle | ½ × 5 m × 4 m = 10 m² |
| Circle Area | Paint a round table | π × r² (π ≈ 3.14). r = 2 m → 12.56 m² |
6. Time & Speed
- Speed = Distance ÷ Time.
- Distance = Speed × Time.
- Time = Distance ÷ Speed.
| Problem | How to solve | Tiny Example |
|---|---|---|
| “A train travels 120 km in 2 h. What is its speed?” | 120 ÷ 2 = 60 km/h | 120 km / 2 h = 60 km/h |
| “How long will it take to travel 90 km at 30 km/h?” | 90 ÷ 30 = 3 h | 90 km / 30 km/h = 3 h |
7. Conversion Basics
| Unit | 1 Unit = How many? | Example |
|---|---|---|
| 1 km = 1000 m | 1 m = 0.001 km | 5 km = 5000 m |
| 1 kg = 1000 g | 1 g = 0.001 kg | 250 g = 0.25 kg |
| 1 L = 1000 mL | 1 mL = 0.001 L | 3 L = 3000 mL |
8. Order of Operations (PEMDAS)
- Parentheses
- Exponents (powers) – rarely needed for NIFT
- Multiplication & Division (left to right)
- Addition & Subtraction (left to right)
| Problem | How to solve | Tiny Example |
|---|---|---|
| “2 + 3 × 4” | Multiply first: 3 × 4 = 12, then add 2 → 14 | 2 + 12 = 14 |
| “(5 + 3) ÷ 2” | Do inside parentheses first: 5 + 3 = 8, then divide → 4 | 8 ÷ 2 = 4 |
9. Quick Problem‑Solving Tips
- Read carefully – find the numbers you need.
- Write down the numbers and the operation you need.
- Check units – if the answer should be in km, make sure you used km.
- Round only at the end, unless asked for a decimal.
- Re‑check by plugging the answer back into the problem.
10. Mini Practice Set
| # | Question | Quick Answer |
|---|---|---|
| 1 | 15 % of 80? | 12 |
| 2 | 5 km travel time @ 25 km/h? | 0.2 h (12 min) |
| 3 | 3 |