Advanced Mathematics
KLA: MATHEMATICS
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Advanced Mathematics - 2 Units for each Preliminary and HSC
Advanced Mathematics - 2 Units for each Preliminary and HSC
[Board Developed Course]
[Board Developed Course]
Exclusions: Students may not study the Stage 6 Preliminary Standard Mathematics course in conjunction with the Preliminary Mathematics Advanced course, nor the Stage 6 HSC Standard Mathematics course in conjunction with the HSC Mathematics Advanced course.
Exclusions: Students may not study the Stage 6 Preliminary Standard Mathematics course in conjunction with the Preliminary Mathematics Advanced course, nor the Stage 6 HSC Standard Mathematics course in conjunction with the HSC Mathematics Advanced course.
Course Description:
Course Description:
The Advanced course places a considerable emphasis on the more abstract concepts that are contained in the areas of algebra, functions and calculus.
The course is intended to give students who have demonstrated some competence in the 5.3 pathway at Year 10, and therefore attained an A or B grade in that course, an understanding of and competence in some further aspects of mathematics which are applicable to the real world. It is essential that students have developed the mathematical thinking skills required for an A or B grade at Stage 5, as students will be required to employ these problem-solving skills throughout the study of the Advanced course.
Advanced Mathematics has general educational merit and is also useful for concurrent studies in science and commerce. The course is a sufficient basis for further studies in mathematics as a minor discipline at tertiary level in support of courses such as the life sciences or commerce. Students who require substantial mathematics at a tertiary level, supporting the physical sciences, computer science or engineering, should undertake the Mathematics Extension 1 course or both the Mathematics Extension 1 and Mathematics Extension 2 course.
The Mathematics Advanced course is the first basic part of a continuum of Mathematics that provides opportunities for students to study at progressively higher levels and to acquire knowledge, skills and understanding in relation to concepts within the area of mathematics that have applications in an increasing number of contexts. The concepts and techniques of differential and integral calculus form a strong basis of the course, and are developed and used in a range of applications and in increasing complexity.
Students who choose to undertake the Extension Mathematics course will study the Advanced Mathematics course concurrently.
Preliminary Course - Category A - 2 Units
Preliminary Course - Category A - 2 Units
[Board Developed Course]
[Board Developed Course]
Students who have attained a high B (B8) or above in Year 10 Mathematics are able to successfully study the Preliminary Mathematics Advanced course.
Students who have attained a high B (B8) or above in Year 10 Mathematics are able to successfully study the Preliminary Mathematics Advanced course.
Main Topics Covered
Main Topics Covered
The topics that are studied in the Preliminary Course are:
Functions
Working with Functions
Algebraic Techniques
Introduction to Functions
Linear, Quadratics and Cubic Functions
Further functions and relations
Trigonomic Functions
Trigonometry & Measure of Angles
Trigonometry
Radians
Trigonometric Functions & Identities
Calculus
Introduction to Differentiation
Gradients of Tangents
Difference Quotients
The derivative function and its graph
Calculating with derivatives
Exponential and Logarithmic Functions
Logarithms & Exponentials
Introducing logarithms
Logarithmic laws and applications
The exponential function and natural logarithms
Graphs and applications of exponential and logarithm functions
Statistical Analysis
Probability & Discrete Probability Distributions
Probability and Venn diagrams
Discrete Probability Distributions
The textbook that is used at Marian Catholic College is the Pearson Publication: New Senior Mathematics Advanced Years 11 & 12.
Assessment: Preliminary Course Only
Assessment: Preliminary Course Only
Students in the Preliminary Advanced course are assessed through the use of:
Formal assessment tasks, as outlined in the assessment booklet
Informal assessment tasks: homework, classwork and discussion, topic tests, quizzes…
Formal Assessment
The following formal assessment is completed by students in the Advanced Mathematics course. This allows students to demonstrate their competence in the outcomes that are being assessed by the task.
Task 1
In-class Assessment (Test) (30%)
Task 2
Investigation/Assignment (30%)
Task 3
End of Preliminary Examination (40%)
Informal Assessment
Informal assessment occurs regularly in the classroom through the use of discussions, exercises, quizzes, homework tasks and smaller topic tests.
Students can use this assessment to help track their progression during the learning phase, so that they are able to monitor and address any weaknesses that they may have. This means that students are able to make changes to improve their results and learning.
Teachers use this assessment to plan learning activities and monitor student understanding and engagement. This allows for teachers to build a more comprehensive picture of the student as a learner in the Mathematics course.
Continuation to the HSC
Continuation to the HSC
Students who attain a Band 1, 2 or 3 are advised to complete the HSC Standard 2 course.
The Preliminary Standard Mathematics course is significantly different to the Preliminary Advanced Mathematics course. Students that wish to move to the Standard Course will be required to complete additional work to catch up on content that is unique to the Standard Course.
Students who attain a Band 4, 5 or 6 are advised to complete the HSC Advanced course.
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