EARLY START MATHEMATICS COURSE
Our exclusive Early Start course provides talented and highly motivated Year 10 Mathematics students (2010) with a rare opportunity to begin both the Preliminary Advanced and Extension –1 courses one full year ahead of their peers.
The advantages of participating in this course are :
- you will spread your study of the Advanced and/or Extension –1 Mathematics courses over three years rather than just two, relieving much of the stress experienced by students in the senior years
- you will have much more time to cover each topic, which leads to greater understanding and a much greater likelihood that you will be able to solve the more difficult questions in the HSC exams
- you will already understand fully every Year 11 and 12 topic before it is introduced at school, giving you a tremendous advantage over other students in your year
- you will explore a greater number of applications of the senior work, thus minimising the number of unfamiliar questions that appear on school assessment tasks
- you can achieve a higher assessment ranking throughout the senior years and gain a much better final HSC result and ATAR
- you will reinforce your understanding of the Year 10 coursework and gain better results on your Year 10 assessment tasks.
The Early Start course consists of :
- a 2.5 hour lesson per week for 44 weeks, beginning in January 2010
- a weekly revision assignment to reinforce your understanding of new content and to keep you in touch with previous topics (approx. 2 hours per week)
- a 2 hour exam at the end of each term set in the HSC format to monitor your understanding and to provide informed feedback on your progress
Continued enrolment in the course is subject to the following conditions :
- attendance at either the weekday or the weekend lesson each week during school terms, other than in exceptional circumstances such as illness or unavoidable school commitments
- completion of all weekly assignments by the due date
- a satisfactory result in the end-of-term exam
It is anticipated that there will be a high demand for places in the Early Start course. Therefore, students intending to take part in the course in 2010 will need to register by Friday December 18 2009. Enrolments for 2010 are limited and cannot be guaranteed after this date.
The regular Year 10 topics provide much of the prerequisite knowledge for the new work. As such, the topics in this course will be introduced in an order that best fits in with those that students have already covered at school.
The topics to be covered in 2010 and the number of lessons for each topic are :
Advanced Course (30 lessons)
Algebra (3)
- harder factorisation, including sum and difference of cubes
- simultaneous equations with 3 unknowns
- expansions of cubes of sums and differences
- harder algebraic fractions, including fractions within fractions
Indices and Logarithms (2)
- harder applications of index laws
- definition of a logarithm
- logarithm laws
Functions, Graphs and Inequalities (5.5)
- function notation
- domain and range
- curve sketching
- transformations of known graphs
- odd and even functions
- absolute value equations, inequations and graphs
- using graphs to solve inequations
- using limits to sketch curves with asymptotes
- regions
Geometry (3)
- polygons
- properties of the special quadrilaterals
- congruence proofs
- similarity proofs
- properties of intercepts on parallel lines
Coordinate Geometry (3)
- distance, midpoint, gradient and angle of inclination
- equations of lines
- parallel and perpendicular lines
- perpendicular distance from a point to a line
- equation of a line through the point of intersection of two lines
Trigonometry (5)
- the reciprocal ratios (cosec, sec and cot)
- exact values
- complementary results
- angles of any magnitude
- graphs of the trigonometric functions
- Pythagorean identities and the tan/cot relations
- trigonometric equations
- sine rule
- cosine rule
- area of a triangle
Differential Calculus (4)
- differentiation by first principles
- differentiation by rule
- tangents and normals
- chain rule, product rule and quotient rule
- continuity and differentiability at a point
Quadratic Polynomial (3)
- the discriminant of a quadratic function
- definite and indefinite quadratics
- equations reducible to quadratics
- sum and product of roots
- quadratic identities
Locus (1.5)
- general locus problems
- locus and the parabola
- translations of the parabola
Extension – 1 Course (14 lessons)
Further Algebra and Inequalities (0.5)
- inequalities with x in the denominator
Further Trigonometry (4)
- compound angle identities
- double angle identities
- t results
- auxiliary angle method
Further Coordinate Geometry (1)
- division of an interval in a given ratio (internal and external)
- angle between two lines
Polynomials (4.5)
- definition of a polynomial
- adding, subtracting and multiplying polynomials
- the division transformation
- graphs of polynomial functions
- factor theorem
- remainder theorem
- consequences of the factor and remainder theorems
- relationship between roots and coefficients
Circle Geometry (4)
- chord properties
- angle properties
- cyclic quadrilateral properties
- tangent properties
- further chord, tangent and secant properties