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Welcome to my Blog!

This blog contains mathematical resources based on the Sijil Tinggi Pelajaran Malaysia (STPM) old syllabus for the paper Further Mathematics T. These resources are very suitable for A-level Further Mathematics, or even University level mathematics. Feel free to browse through and grab whatever you need. ☺

1. Logic & Proof
    1.1 Logic (propositions, quantifiers)
    1.2 Proof (direct, indirect, induction)

2. Complex Numbers
    2.1 Polar Form (geometrical effects, exponential form)
    2.2 de Moivre’s Theorem
    2.3 Equations (roots of unity, loci, transformation)

3. Matrices
    3.1 Row & Column Operations (properties of determinants)
    3.2 System of Linear Equations (consistency, uniqueness, Gaussian elimination,
          Cramer’s rule)
    3.3 Eigenvalues & Eigenvectors (diagonalization, Cayley-Hamilton theorem)

4. Recurrence Relations
    4.1 Recurrence Relations (problem models)
    4.2 Homogeneous Linear Recurrence Relations (2nd order, constant coefficients)
    4.3 Non-homogeneous Linear Recurrence Relations (2nd order, constant coefficients)

5. Functions
    5.1 Inverse Trigonometric Functions (graphs, identities)
    5.2 Hyperbolic Functions (graphs, identities, Osborn’s rule)
    5.3 Inverse Hyperbolic Functions (graphs, identities, logarithmic form)

6. Differentiation & Integration
    6.1 Differentiability of a Function (continuity)
    6.2 Derivatives of a Function Defined Implicitly or Parametrically (2nd derivatives)
    6.3 Derivatives & Integrals of Trigonometric & Inverse Trigonometric Functions
    6.4 Derivatives & Integrals of Hyperbolic & Inverse Hyperbolic Functions
    6.5 Reduction Formulae
    6.6 Applications of Integration (length of arc, surface area of revolution)

7. Power Series
    7.1 Taylor Polynomial (remainder theorem)
    7.2 Taylor Series (Maclaurin series, limits)

8. Differential Equations
    8.1 1st Order Linear Differential Equations (integrating factor)
    8.2 2nd Order Linear Differential Equations (complementary function, particular integral,
           general & particular solution, problem models)

9. Number Theory
    9.1 Divisibility (prime & composite numbers, unique factorisation, gcd & lcm, Euclid’s
           algorithm)
    9.2 Modular Arithmetic (linear congruences, Chinese Remainder Theorem)

10. Graph Theory
      10.1 Graphs (simple, complete, bipartite)
      10.2 Paths & Cycles (walk, trail, circuit, cycle, Eulerian, Hamiltonian)
      10.3 Matrix Representation (adjacency & incidence, problem models)

11. Transformation Geometry
      11.1 Transformation (isometries, similarity transformation, stretch & shears)
      11.2 Matrix Representation (images, scale-factor, operations)

12. Coordinate Geometry
      12.1 3D Vectors (scalar & vector product, properties)
      12.2 Straight Lines (equation, skew, parallel, intersect)
      12.3 Planes (equation, intersection, distance, angle)

13. Sampling & Estimation
      13.1 Random Samples (population, parameter, statistic)
      13.2 Sampling Distributions (sample proportion & mean, central limit theorem)
      13.3 Point Estimates (unbiased estimates, t-distribution, standard error)
      13.4 Interval Estimates (confidence intervals, large & small samples, sample size)

14. Hypothesis Testing
      14.1 Hypotheses (null & alternative hypotheses, test statistic, significance level)
      14.2 Critical Regions
      14.3 Tests of Significance (population proportion & mean, Type I & Type II errors)

15. χ² Tests
      15.1 χ² Distribution
      15.2 Tests for Goodness of Fit
      15.3 Tests for Independence (contingency table)

16. Correlation & Regression
      16.1 Scatter Diagrams
      16.2 Pearson Correlation Coefficient
      16.3 Linear Regression Lines (method of least squares, correlation & regression
               coefficient, coefficient of determination)