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