Algebra and Functions

Indices

• Introduction
• Multiplication rule 1
• Multiplication rule 2
• Division
• Negative indices
• Fractions to negative indices
• Fractional type
• Simplifying (negative powers)
• Expressing terms in the form axⁿ

Exponential functions

• Exponential functions (Videos still to do - not e^x, but 2^x etc)

Logarithms

• What do we mean by a log?
• Rules of logs
• Simplifying
• Solving equations and inequalities

Sequences and series

• Recurrence relationships
• Sigma notation
• Arithmetic sequences and series
  • Exam Questions
• Geometric series
  • Proof of Sum of first n terms, Sn
  • Sum to infinity
• Binomial expansion
  • nCr method of expanding
  • Pascal's triangle method
  • Binomial formula method

Trigonometry

• Sin, cos and tan of special angles, 30^o, 60^o and 45^o and multiples of these
• Trigonometric graphs
• Transformations
  • Translations
  • Reflections
  • Stretches
  • Combining
• Area of a triangle given two sides and an included angle
• Sine rule
• Cosine rule
• Radians
• Arc length and sector area
• Area of a segment
• The quadrant rule
  • Using the quadrant rule to solve sinθ = ±0.5, cosθ = ±0.5, tanθ = ±√(3)
  • Using the quadrant rule for multiple angles to solve 2sin2x=√(3)
• Solving trigonometric equations that factorise
• Two basic trigonometric identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
• Proving trignometric identities
• Solving trigonometric equations using identities

Differentiation

• The gradient function dy/dx
• axⁿ type
• Tangents and normals
• The second derivative
• Stationary points, Maximum and Minimum
• Applications
• Increasing and decreasing functions

Integration

• axⁿ type
• Finding the constant of integration
• Definite integration
• Infinite integrals
• Area under a curve
• Numerical integration - trapezium rule
  • Type of estimate