Topic 1: Number Theory 1
1. calculation and properties of congruence
2. Euler's function
3. Fermat's little theorem
Topic 2: Number Theory 2
1. floor function
2. odd and even numbers
3. number of factors
4. conversion between different numerical systems
Topic 3: Functions and Polynomials
1. abstract functions
2. Symmetry
3. Vieta's theorem of high-degree polynomials
4. remainder theorem
5. factor theorem
Topic 4: Sequences and Series
1. recursive expressions
2. Fibonacci sequence
3. sum of sequences
4. geometrical series
Topic 5: Skills of Algebra
1. binomial theorem
2. factorization and equation
3. basic inequalities
Topic 6: 2-D Geometry and 3-D Geometry
1. sine rule and cosine rule
2. similar triangles
3. Heron's formula
4. properties of circle
5. 3-D geometry
Topic 7: Analytic Geometry
1. equation of straight lines
2. distance between a point and a line
3. equation of circle
Topic 8: Permutation and Combination
1. principle of inclusion and exclusion
2. principle of addition
3. principle of multiplication
4. models of permutation and combination
Topic 9: Probability and Statistics
1. conditional probability
2. complex probability problems
3. basic statistical concepts
Topic 10: Logic and Reasoning
1. word problems
2. comprehension of complex problems
3. conversion of problems
Topic 11: Logarithm
1. rules of logarithm
2. logarithm and exponent
3. equation of logarithm
Topic 12: Complex Numbers and Trigonometry
1. trigonometrical identities
2. maximum and minimum of trig functions
3. polar form and exponential form of complex numbers
4. De Moivre's theorem
