Mathematics Specialist

Conrad HoggNovember 30, 2017February 28, 2024

Mathematics Specialist has been designed to be taken in conjunction with Mathematics Methods. The subject contains topics in functions, calculus, probability and statistics that build on and deepen the ideas presented in Mathematics Methods, and demonstrate their application in many areas. Vectors, complex numbers and matrices are introduced. Mathematics Specialist is designed for students with a strong interest in mathematics, including those intending to study mathematics, statistics, all sciences and associated fields, economics or engineering at university.

Year 11 ATAR Course

Unit 1

The three topics in Unit 1 complement the content of the Mathematics Methods ATAR course. The proficiency strand of Reasoning, from the Years 7–10 curriculum, is continued explicitly in the topic Geometry through a discussion of developing mathematical arguments. This topic also provides the opportunity to summarise and extend students’ studies in Euclidean Geometry, knowledge which is of great benefit in the later study of topics such as vectors and complex numbers. The topic Combinatorics provides techniques that are very useful in many areas of mathematics, including probability and algebra. The topic Vectors in the Plane provides new perspectives on working with two-dimensional space and serves as an introduction to techniques which can be extended to three-dimensional space in Unit 3. These three topics considerably broaden students’ mathematical experiences and therefore begin an awakening to the breadth and utility of the subject. They also enable students to increase their mathematical flexibility and versatility.

Unit 2

In Unit 2, Matrices provide new perspectives for working with two-dimensional space and Real and Complex Numbers provides a continuation of the study of numbers. The topic Trigonometry contains techniques that are used in other topics in both this unit and Units 3 and 4. All topics develop students’ ability to construct mathematical arguments. The technique of proof by the principle of mathematical induction is introduced in this unit.

Assessments

Response
Students respond using knowledge of mathematical facts, concepts and terminology, applying problem-solving skills and algorithms.

Response tasks can include: tests, assignments, quizzes and observation checklists. Tests are administered under controlled and timed conditions.
Investigation
Students plan, research, conduct and communicate the findings of an investigation. They can investigate problems to identify the underlying mathematics, or select, adapt and apply models and procedures to solve problems. This assessment type provides for the assessment of general inquiry skills, course-related knowledge and skills, and modeling skills.
Examination
Students apply mathematical understanding and skills to analyse, interpret and respond to questions and situations. Examinations provide for the assessment of conceptual understandings, knowledge of mathematical facts and terminology, problem-solving skills, and the use of algorithms.

Year 12 ATAR Course

Unit 3

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

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.

Assessments

Response
Students respond using knowledge of mathematical facts, concepts and terminology, applying problem-solving skills and algorithms.

Response tasks can include: tests, assignments, quizzes and observation checklists. Tests are administered under controlled and timed conditions.
Investigation
Students plan, research, conduct and communicate the findings of an investigation. They can investigate problems to identify the underlying mathematics, or select, adapt and apply models and procedures to solve problems. This assessment type provides for the assessment of general inquiry skills, course-related knowledge and skills, and modeling skills.
Examination
Students apply mathematical understanding and skills to analyse, interpret and respond to questions and situations. Examinations provide for the assessment of conceptual understandings, knowledge of mathematical facts and terminology, problem-solving skills, and the use of algorithms.

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