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MATHEMATICS
MATHEMATICS SUBJECTS - YEAR 10 TO YEAR 12
MATHEMATICS Learning Leader: Mr Andrew John
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STAGE 1 SPECIALIST MATHEMATICS
Possible progression Likely progression STAGE 1 MATHEMATICAL METHODS (3 SEMESTERS)
STAGE 2 SPECIALIST MATHEMATICS
STAGE 2 MATHEMATICAL METHODS
STAGE 2 GENERAL MATHEMATICS
YEAR 10YEAR 10 GERMAN ESSENTIAL MATHEMATICS STAGE 1 ESSENTIAL MATHEMATICS STAGE 2 ESSENTIAL MATHEMATICS
Year 10 Mathematics
Length of Course: 2 semesters (compulsory)
There are 3 groupings for Mathematics at Year 10 as shown in the flowchart. Students are placed according to their choice of future pathway and their performance throughout their middle years’ study of mathematics.
Extension Mathematics including Enrichment Mathematics – is the required selection for students planning to undertake Specialist Mathematics and/ or Mathematical Methods at Stage 1 and Specialist Mathematics and/or Mathematical Methods at Stage 2.
General Mathematics – Students studying this course would be precluded from Mathematical Methods and Specialist Mathematics at Stage 1. It is expected that students undertaking this course will study General Mathematics at Stage 1.
Essential Mathematics – Essential Mathematics will continue for those students who require greater support, modified content and assessment. Students studying this course would not be precluded from General Mathematics at Stage 1 if they have a proven high level of achievement and teacher recommendation. It is important, however, to recognise that they will not have been extended to the same extent as for the General Mathematics course. For the majority of students undertaking this course it is expected that they will study Essential Mathematics at Stage 1. All three courses follow the Australian Curriculum. All courses include common topics but the Extension course will cover additional concepts.
Each student’s progress will continue to be monitored and reviewed regularly. Class changes can be made using the evidence of results and with appropriate consultation, generally at the end of a term.
Aims: Revise, revisit, strengthen and extend concepts studied in the earlier years of the Australian Curriculum. Introduce new concepts in line with the Australian Curriculum year level descriptions for Year 10. Address the proficiency strands of: understanding, fluency problem-solving and reasoning. Provide appropriate and varied pathways to Stage 1 Mathematics.
Content: • Number and Algebra • Measurement and Geometry • Statistics and Probability
Topics: • Algebra • Probability • Linear Equations • Coordinate Geometry • Surds and Index Laws • Simultaneous Equations • Measurement • Pythagoras and Trigonometry • Financial Mathematics • Quadratics
MATHEMATICS SUBJECTS - YEAR 10 TO YEAR 12
Year 10 Enrichment Mathematics
Enrichment Mathematics is a course for students keen to challenge and enhance their mathematical knowledge and understanding of abstract, complex and sophisticated concepts. Students study this course in conjunction with Year 10 Extension Mathematics. This course allows for extension of Year 10 concepts and introduction of Year 11 content which comprehensively prepares students for Specialist Mathematics and/or Mathematical Methods at Stage 1 and 2. Students also experienced double Mathematics in one of the two semesters of Year 10.
Enrichment Mathematics must be chosen from the preference subject list as the first preference should students intend to study Specialist Mathematics and/ or Mathematical Methods at Stage 1. It is anticipated that all students currently in an Extension class have the option to study Enrichment Mathematics.
Prerequisites: Students need to achieve a C+ in Year 9 Extension Mathematics or a B+ grade or higher and teacher recommendation in Year 9 General Mathematics to be considered for Year 10 Enrichment Mathematics. Aims: • Revise, revisit, strengthen and extend concepts studied in the earlier years of the Australian
Curriculum. • Introduce new concepts in line with the
Australian Curriculum year level descriptions for
Year 10. • Introduce new concepts in line with the
Australian Curriculum year level descriptions for
Year 11. • Address the proficiency strands of: understanding, fluency problem-solving and reasoning. • Provide appropriate and varied pathways to Stage 1 Mathematics.
Content: Number and Algebra Measurement and Geometry Statistics and Probability
Topics: • Further Trigonometry • Geometrical Reasoning • Exponentials and Logarithms
NOTE: The study of a Mathematics subject is compulsory at Stage 1. Students must achieve a C grade or higher in at least one semester to qualify for the SACE.
Stage 1 Mathematical Methods
Length of Course: Equivalent of 3 semesters (30 credits)
These 3 units form the necessary basis for the study of Stage 2 Mathematical Methods. Students may exit this combination after completion of one semester of Stage 1 Mathematical Methods A & C if the course proves too difficult they may not enter Stage 1 Mathematical Methods B, Stage 2 Mathematical Methods or Stage 2 Specialist Mathematics without first successfully completing Stage 1 Mathematical Methods A and C.
Mathematical Methods is organised into topics that broaden students’ mathematical experience, and provide a variety of contexts for incorporating mathematical arguments and problem-solving. The topics provide a merging of algebraic and geometric thinking. In this subject there is a progression of content, application, and level of complexity and abstraction. Stage 1 Mathematical Methods provides a foundation for further study in Mathematics in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics. Prerequisites: A C+ grade or higher in Year 10 Extension and Enrichment Mathematics, along with a teacher recommendation.
Content: • Functions and Graphs • Trigonometry • Counting and Statistics • Growth and Decay • Introduction to Differential Calculus • Matrices • Geometry • Sequences and Series • Polynomials
Assessment: Summative assessment includes four assessment tasks, at least 2 SATs (tests) and at least 1 Investigation per semester. Formative assessment occurs on a continuous basis and includes an examination which is held at the end of each semester.
Stage 1 Specialist Mathematics
Length of Course: 1 semester (10 credits)
This unit is necessary for the study of Stage 2 Specialist Mathematics. Students who study Stage 1 Specialist Mathematics must also study Stage 1 Mathematical Methods.
Specialist Mathematics develops an increasingly complex and sophisticated understanding of trigonometric functions, vectors in 2-dimensions, mathematical arguments, and proof, and using mathematical models. Stage 1 Specialist Mathematics provides a foundation for further study in mathematics in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics. Prerequisites: B grade or higher in Year 10 Extension and Enrichment Mathematics, Semester 1 Stage 1 Mathematical Methods, and a teacher recommendation.
Content: • Further Trigonometry • Vectors in the Plane • Real and Complex Numbers • Mathematical Induction
Assessment: Summative assessment includes four assessment tasks, at least 2 SATs (tests) and at least 1 Investigation per semester. Formative assessment occurs on a continuous basis. An examination is held at the end of the semester.
MATHEMATICS SUBJECTS - YEAR 10 TO YEAR 12
Stage 1 General Mathematics
Length of Course: 1 or 2 semesters (10 credits or 20 credits)
General Mathematics extends students’ mathematical skills in ways that apply to practical problem solving. Topics cover a diverse range of applications of mathematics, including personal financial management, measurement and trigonometry, the statistical investigation process, modelling using linear and non-linear functions, and networks and matrices.
Prerequisites: Successful completion of Year 10 Extension Mathematics or Year 10 General Mathematics. Content: • Investing and Borrowing • Measurement • Statistical Investigation Process • Applications of Trigonometry • Linear and Exponential Functions and their
Graphs • Matrices and Networks
Assessment: Summative assessment includes four assessment tasks, at least 2 SATs (tests) and 1 Investigation per semester. Formative assessment occurs on a continuous basis. An examination is held at the end of each semester.
Content: • Calculations, Time and Ratio • Earning and Spending • Measurement • Data in Context • Geometry • Investing
Assessment: Summative assessment includes four assessment tasks, at least 2 SATs (tests) and 1 Investigation per semester. Formative assessment occurs on a continuous basis. An examination is held at the end of each semester.
Stage 1 Essential Mathematics
Length of Course: 1 or 2 semesters (10 credits or 20 credits)
Stage 1 Essential Mathematics is designed for a range of students, including those who are seeking to meet the SACE numeracy requirement, and students who are planning to pursue a career in a range of trades or vocational pathways. There is an emphasis on extending student’s mathematical skills in ways that apply to practical problem-solving in everyday and workplace contexts, in flexible and resourceful ways.
Prerequisites: Completion of Year 10 Mathematics
Stage 2 Mathematical Methods
Length of Course: 2 semesters (20 credits)
Mathematical Methods develops an increasingly complex and sophisticated understanding on calculus and statistics. By using functions and their derivatives and integrals, and by mathematically modelling physical processes, students develop a deep understanding of the physical world through a sound knowledge of relationships involving rates of change. Students use statistics to describe and analyse phenomena that involve uncertainty and variation.
Prerequisites: A C+ grade or higher in Stage 1 Mathematical Methods, along with a teacher recommendation.
Stage 2 Specialist Mathematics
Length of Course: Length of course: 2 semesters (20 credits)
Specialist Mathematics draws on and deepens students’ mathematical knowledge, skills and understanding, and provides opportunities for students to develop their skills in using rigorous mathematical arguments and proofs, and using mathematical models. It includes the study of functions and calculus.
Specialist Mathematics must be studied in conjunction with Stage 2 Mathematical Methods.
Prerequisites: A B grade or higher in Stage 1 Mathematical Methods and Stage 1 Specialist Mathematics, along with teacher recommendation. Content: • Mathematical Induction • Complex Numbers • Functions and Sketching Graphs • Vectors in Three Dimensions • Integration Techniques and Applications • Rates of Change and Differential Equations
Assessment: Consists of the following components: • Skills and Applications Tasks (50%) • Mathematical Investigation (20%) • Examination – external (30%)
Content: • Further Differentiation and Applications • Discrete Radom Variables • Integral Calculus • Logarithmic Functions • Continuous Random Variables and the Normal
Distribution • Sampling and Confidence Intervals
Assessment: Consists of the following components • Skills and Applications Tasks (50%) • Mathematical Investigation (20%) • Examination – external (30%)
MATHEMATICS SUBJECTS - YEAR 10 TO YEAR 12
Stage 2 General Mathematics
Length of Course: 2 semesters (20 credits)
General Mathematics extends students’ mathematical skills in ways that apply to practical problem solving. A problem-based approach is integral to the development of mathematical models and the associated key concerts in the topics. These topics cover a diverse range of applications of mathematics, including personal financial management, the statistical investigation process, modelling using linear and non-linear functions and discrete modelling using networks and matrices.
Prerequisites: A C grade or higher in Stage 1 General Mathematics, along with teacher recommendation. Content: Modelling with Linear Relationships Modelling with Matrices Statistical Models * Financial Models * Discrete Models * * Indicates examined topics
Assessment: Consists of the following components Skills and Applications Tasks (40%) Mathematical Investigation (30%) Examination – external (30%)
Stage 2 Essential Mathematics
Length of Course: 2 semesters (20 credits)
Essential Mathematics offers senior secondary students the opportunity to extend their mathematical skills in ways that apply to practical problem-solving in everyday and workplace contexts. Students apply their mathematics to diverse settings, including every day calculations, financial management, business applications, measurement and geometry, and statistics in social contexts.
In Essential Mathematics there is an emphasis on developing students’ computational skills and expanding their ability to apply their mathematical skills to flexible and resourceful ways. Prerequisites: A B- grade or higher in Stage 1 Essential Mathematics, along with teacher recommendation.
Content: • Scales, Plans and Models • Business Applications • Measurement * • Statistics * • Investments and Loans * * Indicates examined topics
Assessment: Consists of the following components • Skills and Applications Tasks (30%) • Folio (40%) • Examination – external (2 hours) (30%)
