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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. χ ^{2} Tests**

15.1 χ

^{2}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)