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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


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