## Unit description of WACE Maths Methods Unit 2 Year 11 ATAR Course

The algebra section of WACE Maths Methods Unit 2 Year 11 ATAR Course focuses on exponentials. Their graphs are examined and their applications in a wide range of settings are explored.

Arithmetic and geometric sequences are introduced and their applications are studied.

Rates and average rates of change are introduced, and this is followed by the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically, by calculating difference quotients both geometrically as slopes of chords and tangents, and algebraically.

Calculus is developed to study the derivatives of polynomial functions, with simple application of the derivative to curve sketching, the calculation of slopes and equations of tangents, the determination of instantaneous velocities and the solution of optimisation problems. The unit concludes with a brief consideration of anti-differentiation.

## Learning outcomes of WACE Maths Methods Unit 2 Year 11 ATAR Course

By the end of this unit, students:

- understand the concepts and techniques used in algebra, sequences and series, functions, graphs and calculus
- solve problems in algebra, sequences and series, functions, graphs and calculus
- apply reasoning skills in algebra, sequences and series, functions, graphs and calculus
- interpret and evaluate mathematical and statistical information and ascertain the reasonableness of solutions to problems
- communicate arguments and strategies when solving problems.

*referred from Mathematics Methods ATAR Course Year 11 Syllabus Western Australia School Curriculum and Standards Authority 1 January 2015*

#### Exponents

- Significant Figures
- Scientific Notation
- Index Form
- Index Rules
- Solving from Definition
- Solving by Factorise
- Exponential Literal Equations
- Equations involving Indices
- Negative Base
- Equations by Changing the Base
- Reducible to Quadratic Equations
- Expansion
- Expanding Binomial Terms
- Factorise by Common Factors
- Quadratic Factorise
- Simplification
- Simplifying Rational Expressions

#### Geometric Progressions

- Identifying Geometric Sequences
- Finding the First Term and Common Ratio
- Finding a Term from a Rule
- Set up a Rule
- Finding the number of Terms
- Applications
- Compound Interest
- Finding Unknown Values
- Set up a Sum Formula
- Finding the Sum using a Formula
- Finding Number of Terms
- Sigma Notation of Geometric Series
- Finding the Number of Terms
- Finding the Limiting Sum
- Finding the First Term and the Common Ratio
- Recurring Decimals
- Recurring Decimal with an Extra Value