**Course Study** Both semesters, compulsory

**Course Description**

The Year 10 Mathematics course follows the Victorian Mathematics Curriculum and is organised into three strands:

**Number and algebra** – Real numbers; Money and financial mathematics; Patterns and Algebra; Linear and non-linear relationships.

**Measurement and geometry** – Units of measurement; Geometric reasoning; Pythagoras and trigonometry.

**Statistics and probability** – Chance; Data representation and interpretation.

Across these three strands students:

extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical argument and proof in establishing mathematical propositions. Students apply mental, written or technology-assisted forms of computation as appropriate, and routinely use estimation to validate or provide bounds for their answers. They use exponential functions to model compound interest problems.

expand, factorise, simplify and substitute into a wide range of algebraic expressions, including linear, quadratic, and exponential terms and relations, as well as simple algebraic fractions with numerical denominators. They solve related equations, linear inequalities and simultaneous linear equations, with and without the use of digital technology. They explore the connection between tabular, graphical and algebraic representations of non-linear relations, including circles with centres at any location in the Cartesian plane.

solve problems involving surface area and volume for a range of objects and follow proofs of key geometric results involving the application of congruence and similarity. They solve practical problems in two and three dimensions involving right angle triangles, Pythagoras theorem and trigonometry.

extend their work in probability to combinations of up to three events, using lists, tables, Venn diagrams, tree diagrams and grids as applicable to determine probabilities. They explore the concepts of conditional probability and independence, and their application to solving problems involving chance events.

use quartiles and the interquartile range as a measure of spread, and construct and interpret boxplots to compare data sets. They relate box plots to corresponding dot plots and histograms. Students explore the association between two numerical variables using scatterplots, in particular with time as the independent variable. They discuss claims made using statistics in various media articles and other reports, on issues of interest.

There is also scope for students to be extended:

in number and algebra to investigate the structure and properties of number systems, with further analysis of order relations and inequalities. In the study of trigonometry to include an introduction to circular functions and equations, and in the study of indices and exponential functions to include logarithms and logarithmic functions.

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 statistics and probability to explore the concepts of conditionality, dependence and independence in depth, or 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.

**In Semester 1, **students have a choice of two possible courses dependent on their mathematical ability and results from their previous years of study. The Standard Level course follows Level 10 of the Victorian Curriculum, and the Higher Level Course follows Level 10A which includes the extension material listed above.

A small number of students who have achieved at the highest level in Year 9 Mathematics may be invited to study VCE Mathematical Methods Unit 1 and 2 in Year 10.

**In** **Semester 2, **students have a choice of three possible courses dependent on their Semester 1 results and the prerequisites required for Year 11 courses.

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.

Standard Level (Algebra) – 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 – Applications and interpretation HL or Analysis and approaches HL courses 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 Term Test (20%)

3. Classwork (30%)

4. Examination (50%)