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HSC Mathematics Extension 2 Tutoring
HSC Mathematics Extension 2 course at Wisdom Education will assist students to gain critical thinking skills to solve complex problems in your exams.
The Mathematics 4 Unit course is defined in the same terms as the 3 Unit Course in other subjects. Thus it offers a suitable preparation for study of the subject at tertiary level, as well as a deeper and more extensive treatment of certain topics than is offered in other Mathematics courses.
This syllabus is designed for students with a special interest in mathematics who have shown that they possess special aptitude for the subject. It represents a distinctly high level in school mathematics involving the development of considerable manipulative skill and a high degree of understanding of the fundamental ideas of algebra and calculus. These topics are treated in some depth. Thus the course provides a sufficient basis for a wide range of useful applications of mathematics as well as an adequate foundation for the further study of the subject.
The objectives of this syllabus are addressed through eight topics:

Graphs

Basic Curves

Drawing graphs by addition and subtraction of ordinates

Drawing graphs by reflecting functions in coordinate axes

Sketching functions by multiplication of ordinates

Sketching functions by division of ordinates

Drawing graphs of various forms

General approach to curve sketching

Using graphs


Complex Numbers

Arithmetic of complex numbers and solving quadratic equations

Geometric representation of a complex number as a point

Geometrical representations of a complex number as a vector

Powers and roots of complex numbers

Curves and Regions


Conics

The Ellipse

The Hyperbola

The Rectangular Hyperbola

General descriptive properties of conics


Integration

Decompostion practice

Derivation of formula for integration by parts

Further integration techniques

Integration by partial fractions

Integration by parts

Integration by substitution

Integration by trigonometric substitution

Partial fractions

Partial fractions and their integration

Reduction formula

Summary of Mathematics course integral calculus

The integrator (integrates any function + other applications)


Volumes

Disk method for volume

Cylindrical Shell Method for volume

Computing the volume of water in a tipped glass

Volume by shells


Mechanics

Calculating Orbital Motion

Forces for Mathematics Extension 2

Projectile and orbital motion

Resisted Motion and Circular Motion


Polynomials

Integer roots of polynomials with integer coefficients

Multiple Roots

Fundamental Theorem of Algebra

Factoring Polynomials

Roots and Coefficients of a Polynomial Equation

Partial Fractions


Harder 3 Unit topics.

Geometry of the Circle

Induction

Inequalities

TERM 4 / 2015  HSC

HSC examinations