Year 12 Mathematics Syllabus1. Functions:- Definition and notation of functions
- Domain and range
- Function transformations
- Composite functions
- Inverse functions
2. Families of Functions:- Linear functions
- Quadratic functions
- Exponential functions
- Logarithmic functions
- Trigonometric functions
3. Quadratic Functions:- Graphing quadratic functions
- Solving quadratic equations
- Completing the square
- Quadratic inequalities
4. Polynomials:- Polynomial long division
- Polynomial factorization
- Synthetic division
- Polynomial equations and inequalities
5. Exponential and Logarithmic Functions:- Properties of exponential functions
- Graphing exponential functions
- Solving exponential equations
- Properties of logarithmic functions
- Graphing logarithmic functions
- Solving logarithmic equations
6. Exponents:- Laws of exponents
- Negative and fractional exponents
- Scientific notation
7. Simultaneous Equations:- Solving systems of linear equations
- Graphical method
- Substitution method
- Elimination method
8. Linear Programming:- Linear inequalities
- Graphical method
- Feasible region
- Objective function
9. Matrices:- Matrix operations
- Determinants
- Inverse of a matrix
- Solving systems of linear equations using matrices
10. Trigonometry:- Trigonometric ratios
- Trigonometric identities
- Solving trigonometric equations
11. Trigonometric Functions:- Sine, cosine, and tangent functions
- Graphs of trigonometric functions
- Period and amplitude
- Phase shift and vertical shift
12. Trigonometric Identities:- Pythagorean identities
- Double angle identities
- Half angle identities
- Sum and difference identities
13. Conic Sections:- Circles
- Parabolas
- Ellipses
- Hyperbolas
14. Complex Numbers:- Complex number notation
- Operations with complex numbers
- Complex conjugates
- Polar form of complex numbers
15. Complex Plane:- Plotting complex numbers on the complex plane
- Modulus and argument of a complex number
16. Polar Form:- Converting between rectangular and polar form
- Multiplication and division of complex numbers in polar form
- De Moivre's theorem
17. Two Dimensional Vectors:- Vector notation
- Vector operations
- Dot product
- Cross product
18. Three Dimensional Vectors:- Vector in three dimensions
- Vector operations in three dimensions
- Scalar triple product
- Vector triple product
19. Sequence and Series:- Arithmetic sequences and series
- Geometric sequences and series
- Summation notation
- Infinite series
20. Probability & Distributions:- Probability rules and concepts
- Discrete probability distributions
- Continuous probability distributions
- Expected value and variance
21. Statistics:- Statistical measures (mean, median, mode)
- Measures of dispersion (range, standard deviation)
- Correlation and regression analysis
- Sampling methods and bias
22. Derivatives:- Definition of derivative
- Derivative rules (power rule, product rule, chain rule)
- Applications of derivatives (rate of change, optimization)
This comprehensive Year 12 Mathematics syllabus covers a wide range of topics and skills necessary for success in the subject. It is designed to develop students' understanding and proficiency in various mathematical concepts and their applications.
This course is helpful for the following exams: Year 12