Stage 2 General Mathematics

Stage 2 General Mathematics - Length | Full Year - (20 credit)

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. 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 General Mathematics at Stage 2 prepares students for entry to tertiary courses requiring a non-specialised background in mathematics.

Content

Stage 2 General Mathematics consists of the following six topics:

• Topic 1: Modelling with linear relationships

• Topic 2: Modelling with matrices

• Topic 3: Statistical models

• Topic 4: Financial models

• Topic 5: Discrete models

• Topic 6: Open topic

Students study five topics from the list of six topics above. All students must study Topics 1, 3, 4, and 5.

Topic 1: Modelling with linear relationships

Students review the concepts of continuous linear functions studied in Topic 5: Linear and exponential functions and their graphs in Stage 1 General Mathematics and extend their understanding through the solution of problems involving simultaneous linear equations. Linear programming is introduced as a major application of linear functions.

Topic 2: Modelling with matrices

This topic continues the development of discrete mathematics begun in Topic 6: Matrices and networks in Stage 1 General Mathematics. Students apply matrices to solve problems in practical contexts.

Topic 3: Statistical models

The linear and exponential growth behaviours studied in Topic 5: Linear and exponential functions and their graphs in Stage 1 General Mathematics are observed in bivariate data. By using electronic technology and statistical tools such as scatter plots and regression to analyse such data, students find algebraic models and use them for predictive purposes.

Topic 4: Financial models

In this topic the focus is on the annuity model and its applications to investing and borrowing money. The broad areas of consideration are:

· saving money for a future need by making regular deposits

· repayment of a reducing balance loan

· receiving an income stream from a lump-sum investment

Topic 5: Discrete models

The focus of this topic is on finding optimal solutions for problems involving critical path analysis and assignment. In critical path analysis, students determine the shortest time in which a complex task can be completed and identify the critical components of that task.

Topic 6: Open topic

Schools may choose to develop a topic that is relevant to their own local context. When this option is undertaken, the open topic developed replaces Topic 2: Modelling with matrices.

Assessment

School-based Assessment (70%)

Assessment Type 1: Skills and Applications Tasks (40%)

Assessment Type 2: Mathematical Investigations (30%)

External Assessment (30%)

Assessment Type 3: Examination (30%)