Speed Math Tricksfor Class 11
JEE/competitive exam speed tricks for Class 11 — permutations, binomial theorem, and calculus shortcuts that give you the time advantage.
Speed TricksYou'll Master
Each trick includes step-by-step instructions and real examples. Practice these daily and watch your speed multiply.
nCr Pascal's Triangle
Use Pascal's triangle pattern for quick combination values
Steps
- 1Row 0: 1
- 2Row 4: 1,4,6,4,1
- 3Row 5: 1,5,10,10,5,1
- 45C2 = 10 (read from row 5, position 2)
Example
5C2 = 10, 6C3 = 20
Binomial Expansion Pattern
Expand (a+b)ⁿ using coefficient patterns
Steps
- 1(x+1)⁴ = x⁴ + 4x³ + 6x² + 4x + 1
- 2Coefficients from Pascal's row 4
- 3General term: nCr × aⁿ⁻ʳ × bʳ
- 4Identify specific terms by position
Example
(x+1)⁴ = x⁴+4x³+6x²+4x+1
Limits Speed Evaluation
Recognize standard limits and apply L'Hôpital's shortcut
Steps
- 1lim(x→0) sin(x)/x = 1
- 2lim(x→0) (eˣ-1)/x = 1
- 3lim(x→0) ln(1+x)/x = 1
- 4For 0/0 form: differentiate top & bottom
Example
lim(x→0) sin(3x)/x = 3
Exam Tips for Class 11
Memorize first 8 rows of Pascal's triangle
Practice limits by pattern recognition, not L'Hôpital every time
Use calculator verification during practice (not exams)
Build a formula sheet and revise before every test
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