Casharka 1: Sum and Difference Identities for Cosine

• Sum and difference formulas for cosine
• Cofunction identities
• Alternating current
• Verifying identities
• Chapter Exercise

Casharka 2: Sum and Difference Identities for Sine and Tangent

• Sum and difference identities for sine
• Sum and difference identities for tangent
• Finding function values of A + B
• Verifying identities
• Chapter Exercise

Casharka 3: Double-angle identities

• Double angle identities
• Finding function values of 2θ
• Identities with larger multiples
• Product to sum identities
• Sum to product identities
• Chapter Exercise

Casharka 4: Half-Angle Identities

• Deriving the half angle identities
• Half angle identities
• Finding exact values
• Simplifying and verifying
• Chapter Exercise

Casharka 5: Trigonometric Equations I

• Solving by linear methods
• Solving by factoring
• Solving by quadratic methods
• Solving by using trigonometric identities
• Chapter Exercise

Casharka 6: Trigonometric Equations II

• Equations with half angles
• Equations with double angles
• Solving equations by double angle identities
• Solving equations using a multiple angle identity
• Applications of trigonometric equations

Casharka 1: Complex numbers

• What is a complex number?
• Equality of complex numbers

Casharka 2: Elementary operations of complex numbers

• Addition and subtraction
• Multiplication of two complex numbers
• Conjugates of a complex number
• Division of two complex numbers

Casharka 3: Square roots of complex numbers

• Square roots of complex numbers
• Complex roots of polynomial equations

Casharka 4: Argand Diagram

• Argand diagram
• Geometrical representation of z1 + z2 and z1 - z2

Casharka 5: Modulus and Argument of a Complex Number

• Modulus and argument
• Complex numbers in polar form

Casharka 6: Multiplication and Division of Two complex numbers In polar form

• Multiplication in polar form
• Division in polar form

Casharka 7: De Moivre's theorem

• De Moivre's theorem
• Roots of a complex number

Casharka 1: The basic counting principle

• The basic counting principle

Casharka 2: Permutations

• Permutations
• Factorial notation
• Permutation of r objects from n different objects
• Permutations with restrictions

Casharka 3: Combinations

• Combinations

Casharka 4: Probability of An event

• Probability of an event
• Sample space and elements
• Events

Casharka 5: Possibility Diagram

• Possibility diagram

Casharka 6: Probabilities of Mutually Exclusive Events

• Mutually exclusive events
• Non mutually exclusive events
• Using Venn diagrams
• Independent events
• Dependent events

Casharka 7: Tree Diagram

• Tree diagram

Casharka 8: Conditional probability

• Conditional probability
• Independent and mutually exclusive events
• Chapter Exercise

Casharka 1: Mean, Median, Mode of Grouped Data

• Measures of central tendency
• Mean of Grouped Data
• Median for grouped data
• Mode of a Grouped Data

Casharka 2: Cumulative Frequency Curve (or Ogive)

• Cumulative frequency curve
• 'Less than' series
• 'Greater than' series
• Median from cumulative frequency curve

Casharka 3: Measures of dispersion (spread)

• Range and interquartile range
• Standard deviation of ungrouped data
• Standard Deviation of Grouped Data

Casharka 4: Stem-and-leaf Plots

• Stem-and-leaf plots

Casharka 1: Limits

• Concept of limits
• Theorems on limits
• Chapter exercise

Casharka 2: One-sided limits

• One-sided limits

Casharka 3: Limits at infinity

• Limits at infinity

Casharka 4: Limits of Trigonometric functions

• Limits of trigonometric functions

Casharka 5: Continuity

• Continuity of a function at a point
• Discontinuity at a point
• Continuity of function on an interval

Casharka 1: Derivatives

• Gradient of a curve
• Derivatives
• Derivatives of kf(x) where k is a constant
• Some more rules for differentiation

Casharka 2: The Product and Quotient Rule

• The product rule
• The quotient rule
• The chain rule

Casharka 3: Second Derivative

• Second derivative

Casharka 4: Differentiation of Trigonometric Functions

• Differentiation of trigonometric functions
• Derivatives of sin f(x) and cos f(x) by the chain rule

Casharka 5: Increasing and Decreasing Functions

• Increasing and decreasing functions
• The relationship between the sign of d^2y/dx^2 and concavity

Casharka 6: Stationary Point, Maximum Point and Minimum Point

• Stationary points
• Maximum or Minimum Points (Local Extremum Points)
• First derivative test
• Second Derivative test or Maximum and Minimum Points
• Point of inflexion

Casharka 7: Rates of Change

• Rates of change
• Velocity and acceleration
• Chapter Exercise

Casharka 1: Indefinite Integrals

• Indefinite Integration as the Reverse Process of Differentiation
• Notation
• Basic Properties of Indefinite Integral
• Equation of a curve from its gradient
• Integration of (ax + b)^n
• Integration of 1/x

Casharka 2: Integration of Trigonometric Functions

• Integrals of sin, cos and sec^2
• Using trigonometric identities

Casharka 3: Definite integrals

• Definite integrals
• Area Under A Curve
• Area Between Two Curves
• Regions below the x axis
• Chapter Exercise