Foundational Mathematics

  1. Basic operations with Numbers & Variables
    • Addition, subtraction, division and multiplication, insertion and removal of brackets.
    • Playing with Fractions and Exponents
  2. Simple equations
  3. Simultaneous equations
  4. Word problems
  5. Binomial special products
  6. Factoring
  7. Quadratic equations
  8. Simultaneous Quadratic Equations
  9. Problems leading to Quadratic Equations

 

Higher Mathematics I

Algebra

  1. Complex Numbers
  2. Functions and Graphs
  3. Linear functions and equations
  4. Quadratic functions and equations
  5. Inequalities
  6. Arithmetic and Geometric progressions
  7. Logarithms
  8. Mathematical Induction
  9. The Binomial Theorem
  10. Permutations and Combinations
  11. Probability
  12. Determinants of Orders 2 and 3
  13. Systems of Linear Equations
  14. Matrices
  15. Partial Fractions

Trignonometry

  1. Historical Context
  2. Angles and Arc Length
  3. Reduction to Functions of Positive Acute Angles
  4. Variation and Graphs of Trigonometric Functions
  5. Solutions of Right Triangles
  6. Practical Applications
  7. Basic Relationships and Identities
  8. Reduction to Functions of Positive Acute Angles
  9. Trigonometric Functions of Two Angles
  10. Sum, difference and Product formulas
  11. Inverse Trigonometric Functions
  12. Trigonometric Equations

Higher Mathematics II

Coordinate Geometry

  1. The Straight Line
  2. The Circle
  3. The Parabola
  4. The Ellipse
  5. The Hyperbola
  6. Transformation of Coordinates
  7. Points in Space, Planes
  8. Polynomial Equations

Calculus I

  1. Functions
  2. Limits and Continuity
  3. Derivatives
  4. Implicit Differentiation
  5. Tangents and Normal Lines
  6. Mean Value Theorem
  7. Maxima and Minima
  8. Curve Sketching
  9. Differentiation of Trigonometric Functions
  10. Related Rates
  11. Differentials

Calculus 2

  1. The Anti-derivative
  2. The Definite Integral
  3. Applications of Integrals I -- Area and Arc Length
  4. Applications of Integrals II -- Volumes
  5. Techniques of Integration
  6. Applications of Calculus
  7. Series and Convergence
  8. Taylor and MacLaurin Series
  9. Partial Derivatives
  10. Vector Analysis