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- Extension Maths
- What’s new in extension maths?
- Main content of extension maths?
- Common challenges for students in extension maths?
- Main outcomes for extension maths?
- Most important concepts to ensure your child understands in extension maths?
- If you chose to get a tutor, study habits and content to focus on in extension maths?
- Main challenges involved in tutoring a extension maths student?
- Some good ideas on how to help your child in extension maths?
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This HSC maths course is inclusive of the year 12 maths syllabus and meant for those who have demonstrated thorough understanding of, and competence in, maths curriculums of earlier years. While an even more extensive HSC maths course is available, this one will suffice for those who wish to major in maths or in physical and engineering sciences at the tertiary level.
What’s new in extension maths?
Even more calculus including advanced methods of integration with and without primitive functions, inverse functions and trigonometric functions. More applications of calculus are also introduced as well as mathematical induction and application. Such applications include functions of velocity and acceleration, projectile motion and simple harmonic motion. Other new topics include advanced methods of solving polynomial equations through iteration of numerical estimation, the binomial theorem and advanced topics in probability.
Main content of extension maths
Advanced calculus is the core content of extension maths. Apart from expanded methods of differentiation, inverse functions and inverse trigonometric functions, calculus is mostly presented as specific applications. Such applications include: primitive functions, squares of functions of sine and cosines, equations of specific types, velocity and acceleration as a function of x(distance), projectile and simple harmonic motion. Other topics in extension maths include mathematical induction and its applications, principles of the binomial theorem including Pascal’s triangle, advanced topics in probability including permutation and combination; and using iterative methods for estimating roots of polynomial equations.
Common challenges for students in extension Maths
Students at this point must have demonstrated above average aptitude in maths. However, advanced topics in calculus will still present challenges especially with their applications in simple harmonic motion and projectile motion.
Main outcomes for extension maths
At the end of extension maths, students are expected to able to rigorously apply the principles of calculus. For those following this track, they must be able to use applications of calculus in pure or applied science disciplines at tertiary level. Knowledge of, and ability to apply the principles of the binomial theorem and mathematical induction will be required as well as solving polynomial equations by iterations.
Most important concepts to ensure your child understands in extension maths
The most important concepts to learn in extension maths are the applications of calculus. Not only will this help in higher studies later but those are actually the core of extension maths.
If hiring a tutor, what study habits and content to focus on in extension maths?
Maths tutors should help your child focus on learning the applications of calculus and indeed all aspects of maths education since the beginning of high school. Since this course is mostly about applying fundamental maths concepts, prepare to meet final assessment questions that require delving into different parts of maths to answer. A holistic approach to maths is needed but especially concentration in calculus.
Main challenges involved in tutoring a extension maths student
Grasping all aspects of the applications of calculus will be a challenge to extension maths students this year especially when solving questions needing overlapping applications from different areas of the course.
Some good ideas on how to help your child in extension maths
Hiring a tutor with extensive knowledge of extension maths is the best idea to help your child through this year. Consider a tutor who majored in maths or has a degree in a pure or applied science discipline with advanced maths foundation.
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