Mathematics
200 hours
The changing nature of Mathematics is reflected in the syllabus. The aim is to develop students' mathematical thinking, understanding, competence and confidence in the application of mathematics, their creativity, enjoyment and appreciation for the subject, and their engagement in lifelong learning.
Years 9 and 10 (Stage 5)
The syllabus has been modified for the new courses where 5.1 is a subset of 5,2 which is a subset of 5.3. It is expected that the average student will complete all of 5.1 and 5.2 by the end of Year 10.
Please note:
Students who undertake Pathways 5.1 would look at either undertaking the Standard Mathematics (2 unit) course in Stage 6 or no maths for their HSC,
Students who undertake Pathways 5.2 would undertake the Standard Mathematics (2 unit) course in Stage 6.
Only students who undertake Pathways 5.3 should undertake the Advanced Mathematics (2 unit) course in Stage 6. From these students, a small minority who have excelled in the Stage 5 course and have demonstrated superior problem solving skills and an aptitude for higher order mathematical thinking would pursue one of the Extension courses in Stage 6.
Pathway 5.1
Students who have achieved Stage 5.1 outcomes explain and verify mathematical relationships, ask and explore questions which can be solved using mathematics, and link mathematical ideas to existing knowledge and understanding. They use mathematical language and notation to explain mathematical ideas, and interpret tables, diagrams and text in mathematical situations.
Students apply their knowledge of percentages, fractions and decimals to problems involving consumer situations related to earning and spending money and simple and compound interest. They simplify and evaluate arithmetic expressions using index laws and express numbers in scientific notation using both positive and negative powers often.
Students apply the index laws to simplify algebraic expressions. They determine the midpoint, length and gradient of intervals on the number plane and draw graphs of linear and simple non-linear relationships.
Their statistical skills are extended to include grouping data into class intervals and constructing and interpreting cumulative frequency tables, histograms and polygons. Students determine relative frequency and theoretical probability.
Skills in measurement are further developed to include the use of formulae when calculating the area and perimeter of composite figures. Students apply right-angled triangle trigonometry to practical situations, including those involving angles of elevation and depression.
Pathway 5.2
Students who have achieved the syllabus outcomes up to and including Stage 5.2 outcomes, ask questions that can be explored using mathematics, and use mathematical arguments to reach and justify conclusions. When communicating mathematical ideas, they use appropriate mathematical language and algebraic, statistical and other notations and conventions in written, oral or graphical form. Students use suitable problem-solving strategies which Include selecting and organising key information and they extend their inquiries by identifying and working on related problems.
They can apply their knowledge of percentages, fractions and decimals to problems involving conversion of rates and consumer situations related to compound interest, depreciation and successive discounts. They express recurring decimals as fractions, and round numbers to a specified number of significant figures.
Also, students solve non-routine problems in algebra and apply the index laws to simplify, expand and factorise algebraic expressions. They solve linear equations and simple quadratic equations, inequalities and simultaneous equations. On the number plane they draw and interpret graphs of straight lines, simple parabolas, hyperbolas and graphs of physical phenomena. Formulae are used to find distance, gradient and midpoint.
Statistical skills are extended to include descriptions of distributions and the construction of box-and-whisker plots. Student analysis of data includes determining upper and lower quartiles and standard deviation.
They extend their skills in measurement to calculations of the area and perimeter of complex composite figures, the volume of pyramids, cones, spheres and composite solids, and the surface area of cylinders and composite solids. In geometry, they use deductive reasoning in numerical and non-numerical problems, drawing on their knowledge of the properties of similar and congruent triangles, the angle properties of polygons and the properties of quadrilaterals, including diagonal properties.
Pathway 5.3
The 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 format definitions and generalisations and connect and apply mathematical ideas within and across topics.
They can 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 analysing 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 30°, 45° and 60°, 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.