■ Mathematics Short Guide (College/University
Level)
1. Algebra
→ Exponents Rules: a^m × a^n = a^(m+n), (a^m)^n = a^(mn), a^(-n) = 1/a^n
→ Quadratic Formula: x = [-b ± √(b²-4ac)] / 2a
→ Factorization Example: x² + 5x + 6 = (x+2)(x+3)
2. Geometry
→ Area of Circle = πr²
→ Volume of Sphere = (4/3)πr³
→ Pythagoras Theorem: a² + b² = c²
3. Trigonometry
→ sin²θ + cos²θ = 1
→ tanθ = sinθ / cosθ
→ Key Angles: sin(30°)=1/2, cos(60°)=1/2
4. Calculus
→ Derivative of x^n = n·x^(n-1)
→ d/dx (e^x) = e^x
→ ∫ x^n dx = (x^(n+1))/(n+1) + C (n ≠ -1)
5. Probability & Statistics
→ Mean = (Σx)/n
→ Variance = (Σ(x - mean)²)/n
→ Probability = (Favorable outcomes) / (Total outcomes)
Level)
1. Algebra
→ Exponents Rules: a^m × a^n = a^(m+n), (a^m)^n = a^(mn), a^(-n) = 1/a^n
→ Quadratic Formula: x = [-b ± √(b²-4ac)] / 2a
→ Factorization Example: x² + 5x + 6 = (x+2)(x+3)
2. Geometry
→ Area of Circle = πr²
→ Volume of Sphere = (4/3)πr³
→ Pythagoras Theorem: a² + b² = c²
3. Trigonometry
→ sin²θ + cos²θ = 1
→ tanθ = sinθ / cosθ
→ Key Angles: sin(30°)=1/2, cos(60°)=1/2
4. Calculus
→ Derivative of x^n = n·x^(n-1)
→ d/dx (e^x) = e^x
→ ∫ x^n dx = (x^(n+1))/(n+1) + C (n ≠ -1)
5. Probability & Statistics
→ Mean = (Σx)/n
→ Variance = (Σ(x - mean)²)/n
→ Probability = (Favorable outcomes) / (Total outcomes)
