Basic Mathematics syllabus

Basic Mathematics

• 1 Set Theory and Real Number System (6 LHs)

  • Sets: notation, types, relations, Venn diagrams and operations
  • Set algebra and three-set problems
  • Natural, integer, rational, irrational and real numbers
  • Real-number properties, inequalities, intervals and modulus
• 2 Complex Numbers (4 LHs)

  • Complex-number definition and powers of i
  • Complex arithmetic, conjugate and modulus
  • Argand diagram and polar representation
  • Square roots and De-Moivre's theorem (through cube roots)
• 3 Functions, Limits and Continuity (6 LHs)

  • Function types, graphs, values, domain and range
  • Applications of functions in business and economics
  • Limits at a point and infinity; limit properties
  • Continuity and discontinuity tests
• 4 Differentiation and Its Application (8 LHs)

  • Rates of change, derivatives and tangent slope
  • First-principle differentiation and power/product/quotient/chain rules
  • Implicit and parametric differentiation
  • Increasing/decreasing functions, stationary points and inflection
  • Higher-order derivatives through third order
  • Economic maxima and minima
• 5 Integration and Its Application (6 LHs)

  • Standard forms, substitution and integration by parts
  • Algebraic, logarithmic and exponential integrals
  • Definite integrals and area under a curve
  • Consumer and producer surplus
• 6 Differential Equations (5 LHs)

  • Order, degree, general and particular solutions
  • First-order equations: separation, homogeneous and linear methods
• 7 Vectors (5 LHs)

  • Plane/space vectors, magnitude, types and scalar multiplication
  • Vector addition and parallelogram law
  • Collinear, coplanar and linear dependence
  • Scalar and vector products; orthogonality
  • Numerical exercises
• 8 Matrices and Determinants (6 LHs)

  • Matrix types, equality, algebra and transpose
  • Determinants, minors, cofactors and inverse
  • Linear systems: Cramer's rule, inverse-matrix and Gaussian elimination
• 9 Least square method (2 LHs)

  • Least-squares line of best fit (two variables)
  • Trend measurement and time-series analysis