Basic Maths & Physics Concepts for NEET Preparation

Introduction

• Discussed struggling with NEET preparation.
• Emphasis on not feeling too stressed about study loads.
• Presenter: Dr. Ayush, who cleared NEET in 1 hour 40 minutes.

Basic Maths Essentials

Math is Crucial in Medical Studies

• Statistics: Mean, Median, Mode, etc.
• Logarithms, LCM, etc.
• Maths remains relevant in medical education.

Logarithms (Log)

• Definition: Log of a base b: b^x = a => log_b(a) = x.
• Examples: Log of common values:
  • log_2(4) = 2; 2^2 = 4.
  • log_2(16) = 4; 2^4 = 16.
• Power Rules:
  • log(ab) = log(a) + log(b).
  • log(a/b) = log(a) - log(b).
  • log(a^b) = b*log(a).
• Common & Natural Logarithms:
  • Common: log base 10; if base not mentioned, assume 10.
  • Natural: ln; base e.
• Conversion between log scales:
  • ln(x) = 2.303 * log(x).

Basic Math Operations

• Basic Powers of 2:
  • 2^0 = 1; 2^1 = 2; 2^2 = 4 etc.
• LCM Calculation:
  • Example: LCM(60, 40) using prime factorization.
• Fraction Operations:
  • Adding/Subtracting fractions, finding common denominators.

Trigonometry Basics

• Sine, Cosine, Tangent definitions.
  • sin θ = opposite/hypotenuse
  • cos θ = adjacent/hypotenuse
  • tan θ = opposite/adjacent
• 0, 30, 45, 60, 90-degree values.
• Trigonometric Identities:
  • sin^2θ + cos^2θ = 1
  • 1 + tan^2θ = sec^2θ
  • 1 + cot^2θ = csc^2θ
• Double Angle Formulas:
  • sin(2θ) = 2sinθcosθ
  • cos(2θ) = cos^2θ - sin^2θ
  • tan(2θ) = 2tanθ / (1 - tan^2θ)
• Special Angles and Quadrants:
  • Values of sine, cosine at 90°, 180°, etc.
• Basic Trigonometric Graphs:
  • Sine and Cosine waveforms.

Derivatives (Differentiation)

• Basic Rules:
  • Constant rule: d/dx [c] = 0
  • Power rule: d/dx [x^n] = nx^(n-1).
  • Sum rule: d/dx [u + v] = du/dx + dv/dx.
• Chain Rule:
  • d/dx [f(g(x))] = f'(g(x)) * g'(x).
• Product Rule:
  • d/dx [uv] = u'v + uv'
• Special Derivatives:
  • d/dx [sin x] = cos x
  • d/dx [cos x] = -sin x
  • d/dx [e^x] = e^x*

Integrals (Integration)

• Basic Indefinite Integrals:
  • ∫ x^n dx = (x^(n+1))/(n+1) + C
  • ∫ e^x dx = e^x + C
  • ∫ sin x dx = -cos x + C
  • ∫ cos x dx = sin x + C
  • ∫ 1/x dx = ln|x| + C
• Definite Integrals: Evaluated between limits a to b.
  • Example: ∫[a to b] x dx = [x^2/2] from a to b
  • Area under curve interpretation.
  • Symmetry properties: Integration of symmetric functions over symmetric intervals.

Graphs

• Linear Equations (y = mx + c):
  • Slope m: If m > 0, positive slope; if m < 0, negative slope.
  • Intercept c: y-intercept: point where graph crosses y-axis.
• Parabolas (y = ax^2 + bx + c):
  • Positive a forms upward parabola (smiling). Negative a forms downward parabola (sad face).
• Circles (x^2 + y^2 = r^2):
  • Center at origin, radius r.
• Hyperbolas and Ellipses: Defined algebraically, visually elongated circles (ellipses), or shape with two branches (hyperbolas).

Conclusion

• Emphasis on comprehensive understanding of NEET syllabus topics.
• Encouraged regular consistent study.
• Mentioned next session will cover Vectors.