**Course Study** Both semesters, compulsory

**Course Description**

The Year 10 Mathematics course follows the Australian Mathematics Curriculum and is organised into six strands:

**Number **– Indices, exponentials, logarithms, and surds.

**Algebra **– .Algebra, equations, and linear relationships; Quadratic expressions and equations; Parabolas and rates of change.

**Measurement **– Geometry and Trigonometry.

**Space** – Graph theory and Networks.

**Statistics **– Data representation and interpretation.

**Probability** – Probability and counting techniques.

Across these six strands students:

- investigate the accuracy of decimal approximations to irrational real numbers; consider the accuracy of computation with real numbers in context and the use of logarithmic scales to deal with phenomena involving small and large quantities and change
- apply numerical, graphical and algebraic approaches to analyse the behaviour of pairs of linear equations and linear inequalities in 2 variables
- generalise and extend their repertoire of algebraic techniques involving quadratic and exponential algebraic expressions
- use mathematical modelling to solve problems in applied situations exhibiting growth or decay using linear, quadratic, and exponential functions; and solve related equations, numerically, graphically and algebraically, with the use of digital tools as applicable
- solve measurement problems involving the surface area and volume of common objects, composite objects, and irregular objects; use Pythagoras’ theorem and trigonometry of right-angled triangles to solve spatial problems in two- and three-dimensions, and manipulate images of their representations using digital tools
- apply geometric theorems to deduce results and solve problems involving plane shapes, and interpret networks and network diagrams in authentic contexts
- investigate conditional probability and its relation to dependent and independent events, including sampling with and without replacement; devise and use simulations to test intuitions involving chance events that may or may not be independent
- compare different ways of representing the distribution of continuous data and interpret key features of the distribution; explore association between pairs of variables, decide the form of representation, interpret the data with respect to the context and discuss possible conclusions; use scatterplots to informally discuss and consider association between 2 numerical variables and informally consider lines of good fit by eye, interpolation, extrapolation, and limitations.

There is also scope for students to be extended:

- in number to investigate the structure and properties of number systems, with further analysis of order relations and inequalities
- in algebra to include polynomials, functions, and graphs
- in the study of indices and exponential functions to include logarithms and logarithmic functions
- in the study of trigonometry to include an introduction to circular functions and equations
- in measurement and geometry towards proving a broader range of geometric propositions solving trigonometric problems in non-right angles triangles or solving three dimensional problems involving surface area and volume of cones, spheres and composite shapes
- in probability to explore the concepts of conditionality, dependence, and independence in depth
- and, in statistics to consider how various measures of location and spread can be used to describe the distribution of a data set and investigate how robust these are with respect to variation in the data, in particular with respect to measurement error

Students will be placed in one of three possible courses dependent on their mathematical ability as determined by standardised testing and results from their previous years of study. There is opportunity for movement between courses if students feel they have not been placed appropriately. The Standard Level course follows Level 10 of the Australian curriculum, permitting access to resource materials and technology for all assessments, to improve accessibility for students who find Maths challenging. The Algebra Level course follows Level 10 of the Australian Curriculum, with a strong focus on algebraic techniques, and the Higher-Level Course includes a variety of extension material for the strongest mathematicians.

A small number of students may be identified as candidates for acceleration and may be invited to study VCE Mathematical Methods Unit 1 and 2 in Year 10.

**Standard Level** – Provides opportunities for students to complete the Year 10 course, without an emphasis on algebraic skills. It is focused on preparing students to study the VCE Foundation and General Mathematics courses in year 11 and 12. There is no pathway to the IB for students studying this course.

**Algebra Level **– Provides opportunities for students to enhance and extend their algebraic skills. It is focused on preparing students to study VCE Mathematical Methods or IB – Applications and interpretation SL or Analysis and approaches SL courses in year 11 and 12.

**Higher Level** – Provides opportunities for students to continue to study extension materials. It is focused on preparing students to study VCE Specialist Mathematics in addition to Mathematical Methods or IB – Analysis and approaches HL in year 11 and 12.

In each of the Mathematics courses, students are required to: learn, practise and apply mathematical routines and techniques and use them to find solutions to standard problems; creatively solve problems in unfamiliar situations; and communicate mathematics and mathematical findings in an effective manner.

**ASSESSMENT**

1. Course Tests (50%)

2. Examination (50%)