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The Year 12 Mathematics Extension 2 course is designed for students seeking to deepen their understanding of advanced mathematical concepts, focusing on areas such as complex numbers, vectors, mechanics, proofs, integration, and differential equations. The course emphasizes problem-solving, mathematical reasoning, and the real-world application of advanced mathematical principles, preparing students for both the HSC exam and further study in mathematics and related fields.
Book LessonReports are sent via email, by the end of term.
Reports are included in the price below. Also note the reports sent are more comprehensive.
89%, +12% Term 3
82%, +7% Term 3
The student has shown steady improvement across the terms, in Math Extension 2. Homework completion is consistent with a few late submissions. Overall, excellent progress!
In Term 1, students begin with complex numbers, exploring their geometric representation on the complex plane and their algebraic properties. They learn operations such as addition, multiplication, and the application of complex numbers in solving quadratic equations. The study then progresses to vectors, where students develop an understanding of vector operations such as addition, scalar and vector products, and the geometric interpretation of vectors. Vectors are applied to both two- and three-dimensional problems, particularly in physics-related contexts like force and motion. The mechanics section introduces students to advanced topics in motion, focusing on kinematics, forces, and projectile motion, integrating both vector and calculus techniques. This term serves as a foundation for the application of mathematical principles to real-world scenarios.
In Term 2, students focus on developing their understanding of mathematical proofs, an essential skill for higher-level mathematics. Students learn various techniques for constructing formal mathematical arguments, including proof by induction, direct proof, and proof by contradiction. They apply these techniques to prove results related to sequences, series, inequalities, and other areas of advanced mathematics. The study of proofs helps students develop logical reasoning and critical thinking, which are foundational skills in both mathematics and other scientific disciplines. The term also focuses on the importance of rigor and precision in mathematical arguments.
Term 3 introduces students to the advanced techniques of integration and the application of calculus to solve real-world problems. Students study both indefinite and definite integration, learning techniques such as substitution, integration by parts, and partial fractions. The course also covers the application of integration to problems involving areas under curves and optimization. Students are introduced to differential equations, particularly first-order and second-order equations, and learn how to solve them in various contexts, such as population dynamics, exponential growth, and mechanical systems. The use of differential equations in modeling real-world phenomena is emphasized throughout this term.
In Term 4, students focus on consolidating their knowledge through mathematical modeling and preparing for the final HSC exams. Students learn to formulate and solve mathematical models for real-world scenarios using the techniques they have studied throughout the year, such as calculus, vectors, and differential equations. This term also includes a thorough review of all topics covered in the course, with an emphasis on problem-solving, exam techniques, and addressing any gaps in knowledge. Mock exams and revision sessions help students refine their skills and strategies for the final assessment, ensuring they are fully prepared for their HSC exam.