Math PG
10 comprehensive papers for effective math learnings
Paper 1: Algebra Fundamentals
Basic algebraic concepts and equations
Group A: Linear Equations
- Solving linear equations
- Graphing linear functions
- Systems of equations
- Word problems
Group B: Polynomials
- Polynomial operations
- Factoring techniques
- Polynomial division
- Solving polynomial equations
Paper 2: Geometry Essentials
Shapes, angles, and measurements
Group A: Plane Geometry
- Triangles and their properties
- Circles and arcs
- Quadrilaterals
- Perimeter and area calculations
Group B: Solid Geometry
- 3D shapes and nets
- Volume calculations
- Surface area problems
- Geometric proofs
Paper 3: Trigonometry Basics
Triangles and trigonometric functions
Group A: Right Triangle Trig
- Sine, cosine, tangent
- Solving right triangles
- Applications in real-world problems
- Trigonometric ratios
Group B: Trigonometric Functions
- Graphing trig functions
- Trig identities
- Law of sines and cosines
- Inverse trig functions
Paper 4: Calculus Introduction
Limits, derivatives, and integrals
Group A: Differential Calculus
- Limits and continuity
- Derivative rules
- Applications of derivatives
- Related rates problems
Group B: Integral Calculus
- Antiderivatives
- Definite integrals
- Area under curves
- Integration techniques
Paper 5: Statistics & Probability
Data analysis and chance
Group A: Descriptive Statistics
- Mean, median, mode
- Standard deviation
- Data visualization
- Correlation analysis
Group B: Probability Theory
- Basic probability rules
- Conditional probability
- Probability distributions
- Expected value
Paper 6: Advanced Algebra
Complex numbers and matrices
Group A: Complex Numbers
- Operations with complex numbers
- Complex plane
- Polar form
- De Moivre’s theorem
Group B: Matrices & Determinants
- Matrix operations
- Determinants
- Solving systems with matrices
- Eigenvalues and eigenvectors
Paper 7: Number Theory
Properties of numbers and sequences
Group A: Divisibility & Primes
- Prime factorization
- GCD and LCM
- Modular arithmetic
- Divisibility rules
Group B: Sequences & Series
- Arithmetic sequences
- Geometric sequences
- Series summation
- Mathematical induction
Paper 8: Coordinate Geometry
Graphs and analytical geometry
Group A: Cartesian System
- Distance formula
- Midpoint formula
- Slope of a line
- Equations of lines
Group B: Conic Sections
- Circles and ellipses
- Parabolas
- Hyperbolas
- Rotation of axes
Paper 9: Mathematical Logic
Proofs and logical reasoning
Group A: Propositional Logic
- Logical connectives
- Truth tables
- Logical equivalences
- Deductive reasoning
Group B: Proof Techniques
- Direct proof
- Proof by contradiction
- Mathematical induction
- Set theory proofs
Paper 10: Applied Mathematics
Real-world applications
Group A: Financial Math
- Simple and compound interest
- Annuities
- Loan amortization
- Investment analysis
Group B: Optimization Problems
- Linear programming
- Constraint optimization
- Resource allocation
- Max-min problems