Master these proven techniques and solve JEE Math problems 3x FASTER!
Solve algebraic equations faster
Problem:
65² = ?
💡 Trick:
More Examples:
25² = 2×3, 25 = 625
85² = 8×9, 25 = 7225
105² = 10×11, 25 = 11025
Problem:
103 × 97 = ?
💡 Trick:
More Examples:
52 × 48 = (50+2)(50-2) = 2496
205 × 195 = (200+5)(200-5) = 39975
💡 Remember These:
12.5% = 1/8
16.67% = 1/6
20% = 1/5
25% = 1/4
33.33% = 1/3
50% = 1/2
66.67% = 2/3
75% = 3/4
Example:
25% of 240 = 1/4 × 240 = 60 (Instant!)
Problem:
1+2+3+...+100 = ?
💡 Formula:
Sum = n(n+1)/2
= 100(101)/2 = 5050
Quick Examples:
Sum(1 to 50) = 50×51/2 = 1275
Sum(1 to 20) = 20×21/2 = 210
Differentiation & Integration made easy
💡 Pattern Recognition:
d/dx(sin nx) = n cos nx
d/dx(cos nx) = -n sin nx
d/dx(eⁿˣ) = n eⁿˣ
d/dx(ln nx) = 1/x
Example:
d/dx(sin 5x) = 5 cos 5x ⚡
d/dx(e³ˣ) = 3e³ˣ ⚡
💡 Reverse Pattern:
∫ sin nx dx = -cos nx/n + C
∫ cos nx dx = sin nx/n + C
∫ eⁿˣ dx = eⁿˣ/n + C
Quick Solve:
∫ sin 3x dx = -cos 3x/3 + C ⚡
∫ e⁵ˣ dx = e⁵ˣ/5 + C ⚡
💡 Integration by Parts Priority:
L - Logarithmic (ln x, log x)
I - Inverse Trig (sin⁻¹x, tan⁻¹x)
A - Algebraic (x, x², x³)
T - Trigonometric (sin x, cos x)
E - Exponential (eˣ, aˣ)
Choose first function from top of this list
Example:
∫ x·eˣ dx
x is Algebraic (A), eˣ is Exponential (E)
Choose x as first function (A comes before E)
Master trig identities instantly
💡 Remember "ASTC" Rule:
Quadrant I
All +ve
Quadrant II
Sin +ve
Quadrant III
Tan +ve
Quadrant IV
Cos +ve
Quick Examples:
sin 150° = sin(180°-30°) = sin 30° = 1/2
cos 210° = cos(180°+30°) = -cos 30°
💡 sin θ values using fingers:
For 0°, 30°, 45°, 60°, 90°:
sin value = √n/2 where n = finger number (0-4)
sin 0° = √0/2 = 0
sin 30° = √1/2 = 1/2
sin 45° = √2/2 = 1/√2
sin 60° = √3/2
sin 90° = √4/2 = 1
For cos: reverse the pattern!
💡 Quick Formulas:
2sinA·cosB = sin(A+B) + sin(A-B)
2cosA·cosB = cos(A+B) + cos(A-B)
2sinA·sinB = cos(A-B) - cos(A+B)
Solve geometry problems faster
💡 Mental Math:
Midpoint = (Average of x, Average of y)
Example: (2,3) and (8,7)
x: (2+8)/2 = 5
y: (3+7)/2 = 5
Midpoint = (5,5) ⚡
💡 Think Pythagoras:
Distance = Hypotenuse of right triangle
d = √[(Δx)² + (Δy)²]
Δx = difference in x, Δy = difference in y
Then find √(sum of squares)
Practice these tricks daily for 1 week and see the difference!