 Mathematics

Mathematics

Mathematics - 1MAM10 & 1MAS10*

1MAM10 Pre-Methods Mathematics

1MAS10* Pre-Specialist Mathematics (*GSLC Code)

Students who choose Pre-Specialist Mathematics must also choose Pre-Methods Mathematics.

Mathematics develops an increasingly complex and sophisticated understanding of calculus, statistics, mathematical arguments, and proofs, and using mathematical models. By using functions, 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 1 Mathematics provides the foundation for further study in mathematics in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics. Students who complete this subject with a C– or better will meet the numeracy requirement of the SACE.

Mathematical Methods can lead to tertiary studies of, for example, 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.

Specialist Mathematics can be a pathway to mathematical sciences, engineering, and physical sciences. Specialist Mathematics is designed to be studied in conjunction with Mathematical Methods.

Stage 1 Pre-Mathematical Methods Possible Topics

• Functions and graphs
• Polynomials
• Trigonometry
• Counting and Statistics
• Growth and Decay
• Introduction to Differential Calculus

Stage 1 Pre-Specialist Mathematics Possible Topics

• Arithmetic and Geometric Sequences and Series
• Geometry
• Vectors in the Plane
• Further Trigonometry
• Matrices
• Real and Complex Numbers

Stage 1 Assessment

Students demonstrate their evidence of their learning through the following assessment types.

• Mathematical Investigation

Mathematical Methods - 2MHS20

Mathematical Methods further extends students’ mathematical knowledge, skills, and understanding, and includes the study of calculus and statistics. By using functions and their derivatives and integrals, and by mathematically modelling physical processes, students extend their understanding of aspects of the physical world based on relationships involving rates of change. Students use statistics to describe and analyse phenomena that involve uncertainty and variation. Mathematical Methods provides the foundation for further study in mathematics, economics, computer sciences, the sciences, 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.

Stage 2 Topics

• Further Differentiation and Applications
• Discrete Random Variables
• Integral Calculus
• Logarithmic Functions
• Continuous Random Variables and the Normal Distribution
• Sampling and Confidence Intervals

Stage 2 Assessment

 School-based Assessment Weighting Skills and Applications Tasks 50% Folio 20% External Assessment 130-Minute Examination 30%

Specialist Mathematics - 2MSC20

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 is designed to be studied in conjunction with Mathematical Methods.

The topics extend students’ mathematical experience and their mathematical flexibility and versatility, in particular, in the areas of complex numbers and vectors. The general theory of functions, differential equations, and dynamic systems provides opportunities to analyse the consequences of more complex laws of interaction. Specialist Mathematics topics provide different scenarios for incorporating mathematical arguments, proofs, and problem-solving.

Stage 2 Topics

• Mathematical Induction
• Complex Numbers
• Functions and Sketching Graphs
• Vectors in Three Dimensions
• Integration Techniques and Applications
• Rates of Change and Differential Equations

Stage 2 Assessment (Stage 1 Assessment mirrors the requirements of Stage 2)

 School-based Assessment Weighting Weighting Skills and Applications Tasks 50% Folio 20% External Assessment 130-Minute Examination 30%

General Mathematics - 1MGM10 and 2MGM20

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 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 diverse range of applications of mathematics, including personal financial management, measurement and trigonometry, 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 into tertiary courses requiring a non-specialised background in mathematics.

Stage 1 Topics

• Investing and borrowing
• Measurement
• Statistical investigation
• Applications of trigonometry
• Linear and exponential functions and their graphs
• Matrices and networks
• Open topic

Stage 2 Topics

• Modelling with linear relationships
• Modelling with matrices
• Statistical models
• Financial models
• Discrete models
• Open topic

Stage 2 Assessment (Stage 1 Assessment mirrors the requirements for Stage 2)

 School-based Assessment Weighting Skills and Applications Tasks 40% Mathematical Investigations 30% External Assessment 130-Minute Examination 30%

Essential Mathematics - 1MEM10 & 2MEM20

Stage 2 Essential Mathematics is only available to students undertaking the Career Acceleration Pathway (CAP).

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 students developing their computational skills and expanding their ability to apply their mathematical skills in flexible and resourceful ways. This subject is valuable for students planning to pursue a career in a range of trades or vocations. Students who complete this subject with a C– or better will meet the numeracy requirement of the SACE.

Stage 1 Topics

• Calculations, time and ratio
• Earning and spending
• Geometry
• Data in Context
• Measurement
• Investing

Stage 2 Topics

• Scales, Plans and Models
• Measurement