Mathematics Specialist (Units 3 & 4) - ATAR

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Course Code:
ATMAS
Pathway:
University Pathway
Pre-requisites:
Grade C or better in Mathematics Specialist (Units 1 & 2) - ATAR
Course Description:
The Year 12 syllabus is divided into two units which are delivered as a pair. In this course there is a progression of content, applications, level of sophistication and abstraction. For example, vectors in the plane are introduced in Year 11 Unit 1 and then in Year 12 Unit 3, they are studied for three-dimensional space. In Unit 3, the topic ‘Vectors in three dimensions’ leads to the establishment of the equations of lines and planes, and this in turn, prepares students for solving simultaneous equations in three variables.
 
Unit 3
This unit contains the three topics:
 
  • Complex numbers
  • Functions and sketching graphs
  • Vectors in three dimensions
 
The Cartesian form of complex numbers was introduced in Unit 2, and in Unit 3, the study of complex numbers is extended to the polar form. The study of functions and techniques of calculus begun in the Mathematics Methods ATAR course is extended and utilised in the sketching of graphs and the solution of problems involving integration. The study of vectors begun in Unit 1, which focused on vectors in one-and two-dimensional space, is extended in Unit 3 to three-dimensional vectors, vector equations and vector calculus, with the latter building on students’ knowledge of calculus from the Mathematics Methods ATAR course. Cartesian and vector equations, together with equations of planes, enables students to solve geometric problems and to solve problems involving motion in three-dimensional space.
 
Unit 4
This unit contains the three topics:
 
  • Integration and applications of integration
  • Rates of change and differential equations
  • Statistical inference
 
In this unit, the study of differentiation and integration of functions is continued, and the techniques developed from this and previous topics in calculus are applied to the area of simple differential equations, in particular in biology and kinematics. These topics serve to demonstrate the applicability of the mathematics learnt throughout this course. Also in this unit, all of the students’ previous experience in statistics is drawn together in the study of the distribution of sample means. This is a topic that demonstrates the utility and power of statistics.
Course Assessment:
Response - 40%
Investigation - 20%
Examination - 40%
Additional Information:
This course is suitable for students who require the strongest mathematical preparation for tertiary studies. It is the most appropriate preparation for courses such as mathematics, computing, engineering and the physical sciences. Students who enjoy studying mathematics and intending to study biological, social or management science at tertiary level would also gain great benefit from this unit selection.