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Mathematics

Mathematics possesses a power, value, and beauty that does not need to extend beyond the human mind. However, the applications of mathematics in the wider world are vast. Studying mathematics provides learners with critical mathematical knowledge and skills necessary for quantitative decision making throughout their lives. Mastering higher levels of school mathematics develops the knowledge, skills and dispositions required in further study, and to ultimately work in one of the many quantitative careers that now exist.

Our mathematics program is designed to ensure the development of the learner's ability to remember and recall (know), calculate, reason logically, analyse, think critically, think creatively, be curious and solve non-routine problems. Highly able students joining the College at Year 7 or 8 may apply to study X-Mathematics. X-Mathematics offers both enrichment and acceleration.


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Mathematics 7-10 Overview

In Years 7 – 10 students work to build mathematical skills, and understanding which supports them both in their ability to participate in contemporary society and their study of mathematical subjects at Years 11 and 12. Being numerate is essential for participating successfully in any future workplace. Humans need to reason, calculate, and communicate to solve problems and students are explicitly taught these skills in mathematics.  

Non-routine problem solving (NRPS) is an area of focus within the classroom at Years 7 – 10. These types of questions help students to build their critical and creative thinking skills. We believe that learning through problem-solving helps students when they encounter new situations outside of the classroom. In mathematics, students develop their understanding by listening, discussing, conjecturing, and undertaking tests which are designed to assess and provide feedback about their progress. 

IBDP Subjects and Pathways

Math IB pathways final
Mathematics: analysis and approaches (Standard or Higher Level) Group 5

Course Description and Aims: The Mathematics: analysis and approaches course is broken into the following sections:  Number and Algebra; Functions; Geometry and Trigonometry; Statistics and Probability; Calculus.   

This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL.

The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of choice of course. However, Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments.

Higher Level Distinction 

The Higher Level course covers all of the same core material as the Standard Level course plus additional Higher Level content.

The HL course extends this is several key areas including: 

  • Number and Algebra – mathematical proof, complex numbers, permutations, and combinations.
  • Functions – polynomial, rational and absolute value functions.
  • Geometry and Trigonometry – reciprocal trigonometric functions and vectors.
  • Statistics and Probability – continuous random variables
  • Calculus – differentiation by first principles, limits, integration techniques and Maclaurin series.

Assessment: 

External Assessment (80% SL, 80% HL) 

Examination Paper 1 (40% SL, 30% HL): A combination of short answer and extended response questions on course content. Paper 1 is completed without the use of a graphics calculator.

Examination Paper 2 (40% SL, 30% HL): A combination of short answer and extended response questions on course content. Paper 2 is completed with access to a graphics calculator.

Examination Paper 3 (HL only, 20%): Two extended response problem-solving questions. Paper 3 is completed with access to a graphics calculator.   

Internal Assessment (20% SL, 20% HL) 

The internal assessment (IA) is an exploration task into a mathematical topic chosen by the student. The task is submitted as a report and is 12 – 20 pages in length (with double line spacing).

Mathematics: applications and interpretation (Standard Level only) Group 5

Course Description and Aims: The Mathematics: applications and interpretation course is broken into the following sections:  Number and Algebra; Functions; Geometry and Trigonometry; Statistics and Probability; Calculus.   

This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics.

The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.

This course differs from Mathematics: analysis and approaches in that students are allowed access to a graphics calculator in all assessments undertaken.

Assessment:
External Assessment (80% SL) 
Examination Paper 1 (40% SL): A series of short answer questions on course content.
Examination Paper 2 (40% SL): A series of extended response questions on course content. 

Internal Assessment (20% SL) 

The internal assessment (IA) is an exploration task into a mathematical topic chosen by the student. The task is submitted as a report and is 12 – 20 pages in length (with double line spacing).

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SACE Subjects and Pathways

Math sace pathways final
Stage 1 Mathematical Methods - 20 Credits 

Course Description:   

Stage 1 Mathematical Methods develops student skills and understanding in the topics of trigonometry, functions, calculus, statistics, and using mathematical models. Problem-solving in mathematics builds students’ depth of conceptual understanding and supports development of critical and creative thinking. Skills learned will help students problem solve when they encounter new situations outside of the classroom.  

Stage 1 Mathematical Methods provides the foundation for further study in mathematics in Stage 2 Mathematical Methods. 

Stage 2 Mathematical Methods can lead to tertiary studies of economics, computer sciences, and the sciences. It prepares students for courses and careers that may involve the use of statistics, such as health or social sciences. 

Assessment
 Skills and Assessment Tasks 75%  
Mathematical Investigation 25%  

Assumed Knowledge: 
 This subject builds on the understanding of the concepts and skills taught in Year 10 Advanced Mathematics. Students who have not achieved a minimum of a B grade in Year 10 Advanced Mathematics are likely to find this course challenging. 

Stage 1 Specialist Mathematics - 20 Credits 

Course Description: 
 Stage 1 Specialist Mathematics develops student skills and understanding in the topics of trigonometry, sequences and series, geometry, vectors, matrices and complex numbers.  

Stage 1 Specialist Mathematics provides the foundation for further study in mathematics in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics. Students are advised that this course is beneficial even if they intend to study Mathematical Methods as a stand-alone course at Stage 2.  

Stage 2 Mathematical Methods can lead to tertiary studies of economics, computer sciences, and the sciences. It prepares students for courses and careers that may involve the use of statistics, such as health or social sciences. 

Stage 2 Specialist Mathematics can be a pathway to mathematical sciences, engineering, space science, and laser physics. Specialist Mathematics is designed to be studied in conjunction with Mathematical Methods. 

Assessment
 Skills and Assessment Tasks 75%  
Mathematical Investigation 25%  

Assumed Knowledge: 
This subject builds on the understanding of the concepts and skills taught in Year 10 Advanced Mathematics. Students who have not achieved a minimum of a B grade in Year 10 Advanced Mathematics are likely to find this course challenging. 

Stage 1 Essential Mathematics - 20 Credits 

Course Description:   
Essential Mathematics offers senior secondary students the opportunity to extend their mathematical skills in ways that apply to practical problem-solving in everyday and workplace contexts. Students apply their mathematics to diverse settings, including everyday calculations, financial management, business applications, measurement and geometry, and statistics in social contexts. 

In Essential Mathematics there is an emphasis on developing students’ computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways. 

This subject is intended for students planning to pursue a career in a range of trades or vocations. 

Assessment
Skills and Assessment Tasks 75%  
Mathematical Investigation 25%  

Assumed Knowledge: 
This subject builds on the understanding of the concepts and skills taught in Year 10 Mathematics.  

Stage 1 General Mathematics - 20 Credits 

Course Description: 
General Mathematics extends students’ mathematical skills in ways that apply to practical problem-solving. A problem-based approach is integral to the development of mathematical models and the associated key ideas in the topics.  

Topics studied cover a range of applications of mathematics, including personal financial management, measurement and trigonometry, the statistical investigation process, modelling using linear functions, and discrete modelling using networks and matrices. In this subject, there is an emphasis on consolidating students’ computational and algebraic skills and expanding their ability to reason and analyse mathematically. 

Students extend their mathematical skills in ways that apply to practical problem-solving and mathematical modelling in everyday contexts. A problem-based approach is integral to the development of mathematical skills and the associated key ideas in this subject. 

Assessment
Skills and Assessment Tasks 75%  
Mathematical Investigation 25%  

Assumed Knowledge:
This subject builds on the understanding of the concepts and skills taught in Year 10 Mathematics.  

Stage 2 Mathematical Methods - 20 Credits 

Course description: 
Stage 2 Mathematical Methods develops an increasingly complex and sophisticated understanding of calculus and statistics. By using functions and their derivatives and integrals, and by mathematically modelling physical processes, students develop a deep understanding of the physical world through a sound knowledge of relationships involving rates of change. Students use statistics to describe and analyse phenomena that involve uncertainty and variation. 

Stage 2 Mathematical Methods provides the foundation for further study in mathematics, economics, computer sciences, and the sciences. It prepares students for courses and careers that may involve the use of statistics, such as health or social sciences. When studied together with Specialist Mathematics, this subject can be a pathway to engineering, physical science, and laser physics. 

Assessment
Skills and Assessment Tasks 50%  
Mathematical Investigation 20%  
External Examination 30%  

Prerequisite: 
This subject builds on the understanding of the concepts and skills taught in Stage 1 Mathematical Methods.  

A minimum achievement of a B grade at Stage 1 is recommended for students wishing to pursue Mathematical Methods at Stage 2. Completion of Stage 1 Specialist Mathematics is beneficial. 

Stage 2 Specialist Mathematics - 20 Credits 

Course Description: 
Specialist Mathematics draws on and deepens students’ mathematical knowledge, skills, and understanding, and provides opportunities for students to develop their skills in using rigorous mathematical arguments and proofs, and using mathematical models. It includes the study of functions and calculus. 

The subject leads to study in a range of tertiary courses such as mathematical sciences, engineering, computer science, and physical sciences. Students envisaging careers in related fields will benefit from studying this subject. 

Specialist Mathematics must be studied in conjunction with Mathematical Methods. 

Assessment
Skills and Assessment Tasks 50%  
Mathematical Investigation 20%  
External Examination 30%  

Prerequisite:
This subject builds on the understanding of the concepts and skills taught in Stage 1 Specialist Mathematics.  

A minimum achievement of a B grade at Stage 1 is recommended for students wishing to pursue Specialist Mathematics at Stage 2.  

Stage 2 Essential Mathematics - 20 Credits 

Course Description: 
Essential Mathematics offers senior secondary students the opportunity to extend their mathematical skills in ways that apply to practical problem-solving in everyday and workplace contexts. Students apply their mathematics to diverse settings, including everyday calculations, financial management, business applications, measurement and geometry, and statistics in social contexts. 

In Essential Mathematics there is an emphasis on developing students’ computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways. 

This subject is intended for students planning to pursue a career in a range of trades or vocations. 

Assessment  
Skills and Assessment Tasks 30%  
Mathematical Investigations 40%  
Examination 30% 

Assumed Knowledge:
Stage 2 Essential Mathematics builds on the understanding of the concepts and skills taught in Stage 1 Essential or General Mathematics 

Successful completion of Stage 1 General Mathematics or a minimum B grade in Stage 1 Essential Mathematics is needed to be prepared for passing this Stage 2 subject. 

Stage 2 General Mathematics - 20 Credits 

Course Description:
General Mathematics extends students’ mathematical skills in ways that apply to practical problem-solving. A problem-based approach is integral to the development of mathematical models and the associated key concepts in the topics. These topics cover a diverse range of applications of mathematics, including personal financial management, the statistical investigation process, modelling using linear and non-linear functions, and discrete modelling using networks and matrices.

Successful completion of this subject at Stage 2 prepares students for entry to tertiary courses requiring a non-specialised background in mathematics.

Stage 2 General Mathematics offers students the opportunity to develop a strong understanding of the process of mathematical modelling and its application to problem solving in everyday workplace contexts.

A problem-based approach is integral to the development of both the models and the associated key concepts in the topics. These topics cover a range of mathematical applications, including linear functions, matrices, statistics, finance, and optimisation.

Assessment
Skills and Assessment Tasks 40% 
Mathematical Investigations 30% 
Examination 30%

Assumed Knowledge: 
Stage 2 General Mathematics builds on the understanding of the concepts and skills taught in Stage 1 General Mathematics

A minimum B grade in Stage 1 General Mathematics is needed to be prepared for passing this Stage 2 subject.

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