Mathematics 5.3
Mathematics is a mandatory course that is studied substantially in each of Years 7–10 with at least 400 hours to be completed by the end of Year 10. This is a requirement for eligibility for the award of the School Certificate.
Course Description
Mathematics is used to identify, describe and apply patterns and relationships. It provides a precise means of communication and is a powerful tool for solving problems both within and beyond mathematics. In addition to its practical applications, the study of mathematics is a valuable pursuit in its own right, providing opportunities for originality, challenge and leisure.
The aim of Mathematics in K–10 is to develop students’ mathematical thinking, understanding, competence and confidence in the application of mathematics, their creativity, enjoyment and appreciation of the subject, and their engagement in lifelong learning.
In order to meet students’ vocational and other learning needs beyond the compulsory years, a variety of mathematical learning experiences are required in Years 9 and 10. The arrangement of content in Stage 5 acknowledges the wide range of achievement of students in Mathematics as they enter the last two years of their compulsory years of schooling. Stage 5.1 content is designed to meet the needs of students who achieve Stage 4 outcomes during Year 9 or Year 10. Stage 5.2 content builds on and includes the content of Stage 5.1 and is designed for students who have achieved Stage 4 content generally by the end of Year 8 or early in Year 9. Stage 5.3 content includes the content for 5.1 and 5.2 and is designed for students who have achieved Stage 4 outcomes probably before the end of Year 8.
What will students learn about?
Students study Number, Patterns and Algebra, Data, Measurement, Space and Geometry. Within each of these strands they will cover a range of topics including:
- fractions
- decimals
- percentages
- consumer arithmetic
- probability
- algebraic techniques
- coordinate geometry
- graphing and interpreting data
- perimeter
- area
- surface area and volume
- trigonometry
- properties of solids
- geometrical figures
- deductive geometry
What will students learn to do?
Students learn to ask questions in relation to mathematical situations and their mathematical experiences; develop, select and use a range of strategies, including the use of technology, to explore and solve problems; develop and use appropriate language and representations to communicate mathematical ideas; develop and use processes for exploring relationships, checking solutions and giving reasons to support their conclusions; and make connections with their existing knowledge and understanding and with the use of mathematics in the real world.
Students who have achieved the syllabus outcomes, up to and including Stage 5.3 outcomes, use deductive reasoning in problem solving and in presenting arguments and formal proofs. They interpret and apply formal definitions and generalisations and connect and apply mathematical ideas within and across topics.
Students calculate the probability of compound events, operate with irrational numbers and extend their knowledge of the number system to include all real numbers. They apply algebra to analyzing and describing physical phenomena and rates of change. Algebraic skills are extended to expanding binomial products, factorising quadratic expressions, and solving literal equations, inequalities, quadratic and simultaneous equations. They generate, describe and graph equations of straight lines, parabolas, cubics, hyperbolas, circles and exponential functions, and are able to graph regions determined by inequalities.
Students calculate the surface areas of pyramids, cones and spheres and explore and use similarity relationships for area and volume. They determine exact trigonometric ratios for 30º, 45º and 60º, extend trigonometric ratios to obtuse angles and sketch sine and cosine curves. Students apply the sine and cosine rules for finding unknown angles and/or sides in non-right-angled triangles.
Their knowledge of a wide range of geometrical facts and relationships is used to prove general statements in geometry, extending the concepts of similarity and congruence to a more generalised application. Students prove Pythagoras’ theorem and the properties of triangles and quadrilaterals.
School Certificate
Satisfactory completion of the mandatory study of Mathematics during Stage 5 (Years 9 and 10) will be recorded with a grade on the student’s School Certificate Record of Achievement Part A. In Year 10, students undertaking the Board Developed Course in Mathematics sit for the Mathematics School Certificate test.