Stage 1 Mathematical Methods

Stage 1 Mathematical Methods - Length | Full year 20 credits

Mathematical Methods is a 10 Credit subject or a 20 Credit subject at Stage 1 and a 20 Credit Subject at Stage 2.

Mathematical Methods develops an increasingly complex and sophisticated understanding of calculus and statistics. 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.

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 healthy or social sciences.

When studied together with Specialist Mathematics, this subject can be a pathway to engineering, space science and laser physics.

Learning Requirements

The learning requirements summarise the knowledge, skills and understanding that students are expected to develop and demonstrate through their learning in Stage 1 Mathematical Methods.

Students are expected to:

· Understand mathematical concepts, demonstrate mathematical skills and apply mathematical techniques

· Investigate and analyse mathematical information in a variety of contexts

· Think mathematically by posing questions and solving problems including making and testing conjectures

· Interpret results, draw conclusions and determine the reasonableness of solutions in context

· Make discerning use of electronic technology

· Communicate mathematically and present mathematical information in a variety of ways

Content

Stage 1 Mathematical Methods may be studied as a 10 Credit subject or a 20 Credit subject.

Mathematical Methods at Stage 1 builds on the mathematical knowledge, understanding and skills that students have developed in Number and Algebra, Measurement and Geometry, Statistics and Probability during Year 10.

Stage 1 Mathematical Methods is organised into topics that broaden students’ mathematical experience and provide a variety of contexts for incorporating mathematical arguments and problem solving. The topics provide a blending of algebraic and geometric thinking. In this subject, there is a progression of content, applications and level of sophistication and abstraction.

Topics

Stage 1 Mathematical Methods consists of the following list of six topics:

Topic 1: Functions and Graphs

1.1 Lines and Linear Relationships

1.2 Inverse Relationships

1.3 Relations

1.4 Functions

Topic 2: Polynomials

2.1 Quadratic Relationships

2.2 Cubic and Quartic Polynomials

Topic 3: Trigonometry

3.1 Cosine and Sine Rules

3.2 Circular Measure and Radian Measure

3.3 Trigonometric Functions

Topic 4: Counting and Statistics

4.1 Counting

4.2 Discrete and Continuous Random Data

4.3 Samples and Statistical Measures

4.4 Normal Distributions

Topic 5: Growth and Decay

5.1 Indices and Index Laws

5.2 Exponential Functions

5.3 Logarithmic Functions

Topic 6: Introduction to Differential Calculus

6.1 Rate of Change

6.2 The Concept of a Derivative

6.3 Computations of Derivatives

6.4 Properties of Derivatives

6.5 Applications of Derivatives.

Assessment

Each semester students are required to complete:

Assessment Type 1: 3 Skills and Applications Tasks (75%)

Assessment Type 2: 1 Folio Task (25%)