Stage 2 Mathematical Methods

Stage 2 Mathematical Methods - Length | Full Year - (20 credit)

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.

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.

The capabilities for this subject are literacy, numeracy, information and communication technology (ICT) capability, critical and creative thinking, personal and social capability, ethical understanding and intercultural understanding.

Content

Stage 2 Mathematical Methods consists of the following six topics:

Topic 1: Further Differentiation and Applications

1.1 Introductory Differential Calculus

1.2 Differentiation Rules

1.3 Exponential Functions

1.4 Trigonometric Functions

1.5 The second derivative

Topic 2: Discrete Random Variables

2.1 Discrete Random Variables

2.2 The Bernoulli Distribution

2.3 Repeated Bernoulli Trials and the Binomial Distribution

Topic 3: Integral Calculus

3.1 Anti-differentiation

3.2 The Area under Curves

3.3 Fundamental Theorem of Calculus

3.4 Applications of Integration

Topic 4: Logarithmic Functions

4.1 Using logarithms for solving exponential equations

4.2 Logarithmic Functions and their Graphs

4.3 Calculus of Logarithmic Functions

Topic 5: Continuous Random Variable and the Normal Distribution

5.1 Continuous Random Variables

5.2 Normal Distributions

5.3 Sampling

Topic 6: Sampling and Confidence Intervals

6.1 Confidence Intervals for a Population Mean

6.2 Population Proportions

6.3 Confidence Intervals for a Population Proportion.

Assessment

School-based Assessment (70%)

Assessment Type 1: Skills and Applications Tasks (50%)

Assessment Type 2: Mathematical Investigation (20%)

External Assessment (30%)

Assessment Type 3: Examination (30%)