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Graphs, Trigonometry and Probability
In this unit students study the relationships between variable quantities and how their functions can be applied to graphs. Trigonometry starts with the consideration of the unit circle and how degrees, radians and graphical representations of trigonemetric functions are related. The fundamentals of probability are introduced which includes the concepts of conditional probability and independence.
- 1 Functions and Graphs
- Lines and Linear Relationships
- Quadratic Relationships
- Inverse Relationships
- Polynomials and Powers
- Graphs of Relations
- 2 Trigonometric Functions
- 3 Counting and Probability
Exponential Functions; Sequences and Series; and Differential Calculus
Students identify and use the core properties of exponential functions and their graphs. Geometric sequences are examined which includes assessing recursive definitions. The concept of a derivative being the instantaneous rate of change is introduced and students work with derivatives quantitatively, graphically and algebraically. Derivative work is applied contextually to solving equations of tangents, calculation of instantaneous velocities and optimisation.
- 4 Exponential Functions
- 5 Arithmetic and Geometric Sequences and Series
- 6 Introduction to Differential Calculus
- Rates of Change
- The Concept of the Derivative
- Computation of Derivatives
- Properties of Derivatives
- Applications of Derivatives