Bank Exam Speed Maths Master Series – Page 17
Algebra Basics Tricks & Fast Calculation Methods
Learn Algebra shortcut tricks, aptitude formulas, and fast calculation methods for Bank Exams, SSC, Railways, Insurance, and Competitive Exams.
Importance of Algebra in Competitive Exams
Algebra is one of the most important foundation topics in:
- Bank Exams
- SSC
- Railway Exams
- Insurance Exams
- Quantitative Aptitude
This topic is highly useful in:
- Simplification
- Equation solving
- Quadratic equations
- Data Interpretation
- Advanced arithmetic
🎯 What is Algebra?
Algebra uses:
- Variables
- Numbers
- Symbols
- Mathematical operations
Example:
x + 5 = 10
Basic Algebraic Expressions
| Expression | Meaning |
|---|---|
| x + y | Addition |
| x − y | Subtraction |
| xy | Multiplication |
| x/y | Division |
| x² | Square |
| x³ | Cube |
Important Algebra Formula
Trick 1: Square Expansion Shortcut
Example:
(5 + 3)²
Using formula:
25 + 30 + 9
✅ Answer = 64
Difference of Squares Formula
Trick 2: Fast Multiplication Using Formula
Example:
99 × 101
Using:
2100² − 1²
10000 − 1
✅ Answer = 9999
Cube Formula
Trick 3: Cube Expansion Shortcut
Example:
(2 + 1)³
8 + 12 + 6 + 1
✅ Answer = 27
Quadratic Equation Formula
Trick 4: Factorization Method
Example:
x² − 5x + 6
Find two numbers:
- Product = 6
- Sum = 5
Numbers: 2 and 3
So:
(x−2)(x−3)
✅ Factors Found
Trick 5: Identity Shortcut
| Formula | Shortcut |
|---|---|
| (a+b)² | a² + 2ab + b² |
| (a−b)² | a² − 2ab + b² |
| a²−b² | (a+b)(a−b) |
| (a+b)³ | Cube expansion |
Trick 6: Linear Equation Shortcut
Example:
2x + 6 = 20
2x = 14
x = 7
✅ Answer = 7
Important Observation Trick
Memorizing algebraic identities saves huge calculation time in:
- Simplification
- Approximation
- Equation solving
Important Algebra Shortcuts
| Topic | Shortcut |
|---|---|
| Square Formula | (a+b)² |
| Difference Formula | a²−b² |
| Cube Formula | (a+b)³ |
| Quadratic Formula | Standard formula |
| Factorization | Product & Sum method |
Practice Questions
- Find (4 + 2)²
- Solve: x² − 7x + 12
- Find 98 × 102 using identity
- Solve: 3x + 9 = 24
- Find value of (3 + 1)³
✅ Answers
- 36
- (x−3)(x−4)
- 9996
- x = 5
- 64
Practice algebraic identities, factorization methods, equation solving, and square & cube formulas daily to improve simplification speed and mental calculation ability.
Bank Exam Speed Maths Master Series
Bank Exam Speed Maths Master Series – Page 16
Simplification & Approximation Tricks & Fast Calculation Methods
Learn Simplification & Approximation shortcut tricks, aptitude formulas, and fast calculation methods for Bank Exams, SSC, Railways, Insurance, and Competitive Exams.
Importance of Simplification in Competitive Exams
Simplification is one of the most scoring sections in:
- Bank Exams
- SSC
- Railway Exams
- Insurance Exams
- Quantitative Aptitude
This topic improves:
- Calculation speed
- Accuracy
- Mental maths ability
- Time management
🎯 Basic BODMAS Rule
Follow order:
- Bracket
- Of
- Division
- Multiplication
- Addition
- Subtraction
Simplification Formula Rule
Trick 1: Square Shortcut
Important Squares:
| Number | Square |
|---|---|
| 15 | 225 |
| 25 | 625 |
| 35 | 1225 |
| 45 | 2025 |
Trick 2: Multiplication by 5
Shortcut:
Multiply by 10 and divide by 2
Example:
48 × 5
48 × 10 = 480
480 ÷ 2 = 240
✅ Answer = 240
Trick 3: Percentage Approximation
Important Fraction Conversions:
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/8 | 12.5% |
Trick 4: Approximation Method
Round numbers for faster calculations.
Example:
498 × 21
≈ 500 × 20
= 10000
✅ Approximate Answer = 10000
Trick 5: Cube Shortcut
Important Cubes:
| Number | Cube |
|---|---|
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
Trick 6: Digital Sum Shortcut
Add digits repeatedly until single digit comes.
Example:
9875
9 + 8 + 7 + 5 = 29
2 + 9 = 11
1 + 1 = 2
✅ Digital Sum = 2
Important Observation Trick
Approximation saves time in competitive exams.
Use:
- Nearest values
- Known squares
- Known cubes
- Fraction-percentage conversions
Important Simplification Shortcuts
| Topic | Shortcut |
|---|---|
| BODMAS | Order rule |
| Multiply by 5 | ×10 ÷2 |
| Approximation | Round values |
| Percentages | Fraction conversion |
| Digital Sum | Repeated addition |
Practice Questions
- Find 48 × 5
- Approximate 503 × 19
- Find square of 25
- Convert 1/8 into percentage
- Find digital sum of 4567
✅ Answers
- 240
- 10000 approximately
- 625
- 12.5%
- 4
Practice approximation methods, squares, cubes, fraction-percentage conversions, and digital sum shortcuts daily to improve calculation speed and accuracy.
Bank Exam Speed Maths Master Series
Bank Exam Speed Maths Master Series – Page 17
Algebra Basics Tricks & Fast Calculation Methods
Learn Algebra shortcut tricks, aptitude formulas, and fast calculation methods for Bank Exams, SSC, Railways, Insurance, and Competitive Exams.
Importance of Algebra in Competitive Exams
Algebra is one of the most important foundation topics in:
- Bank Exams
- SSC
- Railway Exams
- Insurance Exams
- Quantitative Aptitude
This topic is highly useful in:
- Simplification
- Equation solving
- Quadratic equations
- Data Interpretation
- Advanced arithmetic
🎯 What is Algebra?
Algebra uses:
- Variables
- Numbers
- Symbols
- Mathematical operations
Example:
x + 5 = 10
Basic Algebraic Expressions
| Expression | Meaning |
|---|---|
| x + y | Addition |
| x − y | Subtraction |
| xy | Multiplication |
| x/y | Division |
| x² | Square |
| x³ | Cube |
Important Algebra Formula
Trick 1: Square Expansion Shortcut
Example:
(5 + 3)²
Using formula:
25 + 30 + 9
✅ Answer = 64
Difference of Squares Formula
Trick 2: Fast Multiplication Using Formula
Example:
99 × 101
Using:
2100² − 1²
10000 − 1
✅ Answer = 9999
Cube Formula
Trick 3: Cube Expansion Shortcut
Example:
(2 + 1)³
8 + 12 + 6 + 1
✅ Answer = 27
Quadratic Equation Formula
Trick 4: Factorization Method
Example:
x² − 5x + 6
Find two numbers:
- Product = 6
- Sum = 5
Numbers: 2 and 3
So:
(x−2)(x−3)
✅ Factors Found
Trick 5: Identity Shortcut
| Formula | Shortcut |
|---|---|
| (a+b)² | a² + 2ab + b² |
| (a−b)² | a² − 2ab + b² |
| a²−b² | (a+b)(a−b) |
| (a+b)³ | Cube expansion |
Trick 6: Linear Equation Shortcut
Example:
2x + 6 = 20
2x = 14
x = 7
✅ Answer = 7
Important Observation Trick
Memorizing algebraic identities saves huge calculation time in:
- Simplification
- Approximation
- Equation solving
📖 Important Algebra Shortcuts
| Topic | Shortcut |
|---|---|
| Square Formula | (a+b)² |
| Difference Formula | a²−b² |
| Cube Formula | (a+b)³ |
| Quadratic Formula | Standard formula |
| Factorization | Product & Sum method |
Practice Questions
- Find (4 + 2)²
- Solve: x² − 7x + 12
- Find 98 × 102 using identity
- Solve: 3x + 9 = 24
- Find value of (3 + 1)³
✅ Answers
- 36
- (x−3)(x−4)
- 9996
- x = 5
- 64
Practice algebraic identities, factorization methods, equation solving, and square & cube formulas daily to improve simplification speed and mental calculation ability.
Bank Exam Speed Maths Master Series
No comments:
Post a Comment