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MATHEMATICS ADVANCED
Board Developed Course
Course number(s):
11255 Mathematics Advanced (2 units – Year 11)
15255 Mathematics Advanced (2 units – Year 12)
Prerequisites: The Mathematics Advanced Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus and in particular, the content and outcomes of all substrands of Stage 5.1 and Stage 5.2, and the following substrands of Stage 5.3:
Algebraic techniques
Surds and indices
Equations
Linear relationships
Trigonometry and Pythagoras’ theorem
Single variable data analysis
and at least some of the content from the following substrands of Stage 5.3:
Non-linear relationships
Properties of Geometrical Shapes.
Corequisites: Nil
Eligibility: Nil
Study via self-tuition: Yes
Exclusions:
11236 Mathematics Standard (2 units – Year 11)
15231 Mathematics Standard 1 (2 units – Year 12)
15232 Mathematics Standard 1 (Exam) (2 units – Year 12)
15236 Mathematics Standard 2 (2 units – Year 12)
16611 Mathematics Life Skills (2 units – Year 11)
16611 Mathematics Life Skills (2 units – Year 12)
Course description
The Mathematics Advanced course is a calculus-based course focused on developing student awareness of mathematics as a unique and powerful way of viewing the world to investigate order, relation, pattern, uncertainty and generality. The course provides students with the opportunity to develop ways of thinking in which problems are explored through observation, reflection and reasoning.
The Mathematics Extension 1 Year 11 course includes the Mathematics Advanced Year 11 course. The Mathematics Extension 1 Year 12 course includes the Mathematics Advanced Year 12 course.
All students studying the Mathematics Advanced course will sit for an HSC examination.
What students learn
The study of Mathematics Advanced in Stage 6:
enables students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely
provides opportunities for students to consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling and use these models to solve problems related to their present and future needs
provides opportunities for students to develop ways of thinking in which problems are explored through observation, reflection and reasoning
provides a basis for further studies in disciplines in which mathematics and the skills that constitute thinking mathematically have an important role
provides an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in a range of disciplines at the tertiary level.
Year 11 course
The Mathematics Advanced Year 11 course content comprises five Topics, with the Topics divided into Subtopics.
Topic: Functions
Working with Functions
Topic: Trigonometric Functions
Trigonometry and Measure of Angles
Trigonometric Functions and Identities
Topic: Calculus
Introduction to Differentiation
Topic: Exponential and Logarithmic Functions
Logarithms and Exponentials
Topic: Statistical Analysis
Probability and Discrete Probability Distributions
Year 12 course
The Mathematics Advanced Year 12 course content includes four of the same Topics and the Topic ‘Financial Mathematics’ in place of ‘Exponential and Logarithmic Functions’.
Topic: Functions
Graphing Techniques
Topic: Trigonometric Functions
Trigonometric Functions and Graphs
Topic: Calculus
Differential Calculus
The Second Derivative
Integral Calculus
Topic: Financial Mathematics
Modelling Financial Situations
Topic: Statistical Analysis
Descriptive Statistics and Bivariate Data Analysis
Random Variables

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MATHEMATICS CURRICULUM IN AUSTRALIA
They begin mathematics in Kindergarten. They divide Mathematics in to parts: From Kindergarten to Year 10 and Years 11-12.
Years
Early Stage 1 (Kindergarten)
Stage 1 ( Years 1-2)
Stage 2 ( Years 3-4)
Stage 3 ( Years 5-6)
Stage 4(  Years 7-8)
Stage 5 ( Years 9-10)
Stage 6 ( Years 11-12)

STAGE 5 ( YEARS 9-10)
For Kindergarten to Year 10, educational programs are based on the outcomes of syllabuses. The content provides detail about how the outcomes can be interpreted and used, and the intended learning appropriate for the stage. In considering meaningful learning within local contexts, teachers will make decisions about the sequence, the emphasis to be given to particular areas of content, and any adjustments required based on the needs, interests and abilities of their students.
K–10 Curriculum
The NSW Education Standards Authority (NESA) syllabuses are developed with respect to some overarching views about education. These include the NESA K–10 Curriculum Framework and Statement of Equity Principles and the Melbourne Declaration on Educational Goals for Young Australians (December 2008).
NESA syllabuses include agreed Australian Curriculum content and content that clarifies the scope, breadth and depth of learning. The Australian Curriculum achievement standards underpin the syllabus outcomes and the Stage statements for Early Stage 1 to Stage 5.
In accordance with the K–10 Curriculum Framework and the Statement of Equity Principles, the syllabus takes into account the diverse needs of all students. It identifies essential knowledge, understanding, skills, values and attitudes. It outlines clear standards of what students are expected to know and be able to do in K–10. It provides structures and processes by which teachers can provide continuity of study for all students.
The framework also provides a set of broad learning outcomes that summarise the knowledge, understanding, skills, values and attitudes essential for all students in all learning areas to succeed in and beyond their schooling.
The continued relevance of the K–10 Curriculum Framework is consistent with the intent of the Melbourne Declaration on Educational Goals for Young Australians (December 2008), which sets the direction for Australian schooling for the next 10 years. There are two broad goals:
 Goal 1: Australian schooling promotes equity and excellence
 Goal 2: All young Australians become successful learners, confident and creative individuals, and active and informed citizens.
The way in which learning in the Mathematics K–10 Syllabus will contribute to the curriculum and to students’ achievement of the broad learning outcomes is outlined in the syllabus rationale.
COURSE  CONTENT
To see the content please click on the link.
https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/content

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MATHEMATICS EXTENSION 2
Board Developed Course
Course number(s):
 15260 Mathematics Extension 2 (1 unit – Year 12)
Prerequisites: The Mathematics Extension 2 Year 12 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Advanced Year 11 course and the Mathematics Extension 1 Year 11 course. The Mathematics Extension 2 Year 12 course has also been constructed on the assumption that students are concurrently studying the Mathematics Advanced Year 12 course and the Mathematics Extension 1 Year 12 course.
Corequisites:
 11255 Mathematics Advanced (2 units – Year 11)
 15255 Mathematics Advanced (2 units – Year 12)
 11250 Mathematics Extension (1 unit – Year 11)
 15250 Mathematics Extension 1 (1 unit – Year 12)
Eligibility: Nil
Study via self-tuition: Yes
Exclusions:
 11236 Mathematics Standard (2 units – Year 11)
 15231 Mathematics Standard 1 (2 units – Year 12)
 15232 Mathematics Standard 1 (Exam) (2 units – Year 12)
 15236 Mathematics Standard 2 (2 units – Year 12)
 16611 Mathematics Life Skills (2 units – Year 11)
 16611 Mathematics Life Skills (2 units – Year 12)
Course description
Mathematics Extension 2 provides students with the opportunity to develop strong mathematical manipulative skills and a deep understanding of the fundamental ideas of algebra and calculus, as well as an appreciation of mathematics as an activity with its own intrinsic value, involving invention, intuition and exploration. Mathematics Extension 2 extends students’ conceptual knowledge and understanding through exploration of new areas of mathematics not previously seen.
The Mathematics Extension 2 Year 12 course includes the Mathematics Extension 1 Year 12 course and the Mathematics Advanced Year 12 course.
The Mathematics Advanced, Mathematics Extension 1 and Mathematics Extension 2 Stage 6 courses form a continuum.
All students studying the Mathematics Extension 2 course will sit for an HSC examination.
What students learn
The study of Mathematics Extension 2 in Stage 6:
 enables students to develop strong knowledge, understanding and skills in working mathematically and in communicating concisely and precisely
 provides opportunities to develop strong mathematical manipulative skills and a deep understanding of the fundamental ideas of algebra and calculus, as well as an awareness of mathematics as an activity with its own intrinsic value, involving invention, intuition and exploration
 provides opportunities at progressively higher levels for students to acquire knowledge, understanding and skills in relation to concepts within areas of mathematics that have applications in an increasing number of contexts
 provides a basis for progression to further study in mathematics or related disciplines and in which mathematics has a vital role at tertiary level
 provides an appropriate mathematical background for students whose future pathways will be founded in mathematics and its applications in such areas as science, engineering, finance and economics.
Year 12 course
The Mathematics Extension 2 course comprises five Topics, with the Topics divided into Subtopics.
Topic: Proof
 The Nature of Proof
 Further Proof by Mathematical Induction
Topic: Vectors
 Further Work with Vectors
Topic: Complex Numbers
 Introduction to Complex Numbers
 Using Complex Numbers
Topic: Calculus
 Further Integration
Topic: Mechanics
 Applications of Calculus to Mechanics

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MATHEMATICS EXTENSION 1Board Developed CourseCourse number(s):11250 Mathematics Extension (1 unit – Year 11)15250 Mathematics Extension 1 (1 unit – Year 12)Prerequisites: The Mathematics Extension 1 Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus and, in particular, the content and outcomes of all substrands of Stage 5.1, Stage 5.2 and Stage 5.3, including the optional substrands:PolynomialsLogarithmsFunctions and Other GraphsCircle Geometry.Corequisites:11255 Mathematics Advanced (2 units – Year 11)15255 Mathematics Advanced (2 units – Year 12)Eligibility: NilStudy via self-tuition: YesExclusions:11236 Mathematics Standard (2 units – Year 11)15231 Mathematics Standard 1 (2 units – Year 12)15232 Mathematics Standard 1 (Exam) (2 units – Year 12)15236 Mathematics Standard 2 (2 units – Year 12)16611 Mathematics Life Skills (2 units – Year 11)16611 Mathematics Life Skills (2 units – Year 12)Course descriptionMathematics Extension 1 is focused on enabling students to develop a thorough understanding of and competence in further aspects of mathematics. The course provides opportunities to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively.The Mathematics Extension 1 Year 11 course includes the Mathematics Advanced Year 11 course. The Mathematics Extension 1 Year 12 course includes the Mathematics Advanced Year 12 course.The Mathematics Extension 2 Year 12 course includes the Mathematics Extension 1 Year 12 course, and therefore also the Mathematics Advanced Year 12 course.All students studying the Mathematics Extension 1 course will sit for an HSC examination.What students learnThe study of Mathematics Extension 1 in Stage 6:enables students to develop thorough knowledge, understanding and skills in working mathematically and in communicating concisely and preciselyprovides opportunities for students to develop rigorous mathematical arguments and proofs, and to use mathematical models extensivelyprovides opportunities for students to develop their awareness of the interconnected nature of mathematics, its beauty and its functionalityprovides a basis for progression to further study in mathematics or related disciplines and in which mathematics has a vital role at tertiary levelprovides an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in such areas as science, engineering, finance and economics.Year 11 courseThe Mathematics Extension 1 Year 11 course content is comprised of four Topics, with the Topics divided into Subtopics.Topic: FunctionsFurther Work with FunctionsPolynomialsTopic: Trigonometric FunctionsInverse Trigonometric FunctionsFurther Trigonometric IdentitiesTopic: CalculusRates of ChangeTopic: CombinatoricsWorking with CombinatoricsYear 12 courseThe Mathematics Extension 1 Year 12 course content includes the Topics ‘Trigonometric Functions’ and ‘Calculus’ continued from Year 11 and introduces three different Topics.Topic: ProofProof by Mathematical InductionTopic: VectorsIntroduction to VectorsTopic: Trigonometric FunctionsTrigonometric EquationsTopic: CalculusFurther Calculus SkillsApplications of CalculusTopic: Statistical AnalysisThe Binomial Distribution

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MATHEMATICS EXTENSION 1Board Developed CourseCourse number(s):11250 Mathematics Extension (1 unit – Year 11)15250 Mathematics Extension 1 (1 unit – Year 12)Prerequisites: The Mathematics Extension 1 Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus and, in particular, the content and outcomes of all substrands of Stage 5.1, Stage 5.2 and Stage 5.3, including the optional substrands:PolynomialsLogarithmsFunctions and Other GraphsCircle Geometry.Corequisites:11255 Mathematics Advanced (2 units – Year 11)15255 Mathematics Advanced (2 units – Year 12)Eligibility: NilStudy via self-tuition: YesExclusions:11236 Mathematics Standard (2 units – Year 11)15231 Mathematics Standard 1 (2 units – Year 12)15232 Mathematics Standard 1 (Exam) (2 units – Year 12)15236 Mathematics Standard 2 (2 units – Year 12)16611 Mathematics Life Skills (2 units – Year 11)16611 Mathematics Life Skills (2 units – Year 12)Course descriptionMathematics Extension 1 is focused on enabling students to develop a thorough understanding of and competence in further aspects of mathematics. The course provides opportunities to develop rigorous mathematical arguments and proofs, and to use mathematical models more extensively.The Mathematics Extension 1 Year 11 course includes the Mathematics Advanced Year 11 course. The Mathematics Extension 1 Year 12 course includes the Mathematics Advanced Year 12 course.The Mathematics Extension 2 Year 12 course includes the Mathematics Extension 1 Year 12 course, and therefore also the Mathematics Advanced Year 12 course.All students studying the Mathematics Extension 1 course will sit for an HSC examination.What students learnThe study of Mathematics Extension 1 in Stage 6:enables students to develop thorough knowledge, understanding and skills in working mathematically and in communicating concisely and preciselyprovides opportunities for students to develop rigorous mathematical arguments and proofs, and to use mathematical models extensivelyprovides opportunities for students to develop their awareness of the interconnected nature of mathematics, its beauty and its functionalityprovides a basis for progression to further study in mathematics or related disciplines and in which mathematics has a vital role at tertiary levelprovides an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in such areas as science, engineering, finance and economics.Year 11 courseThe Mathematics Extension 1 Year 11 course content is comprised of four Topics, with the Topics divided into Subtopics.Topic: FunctionsFurther Work with FunctionsPolynomialsTopic: Trigonometric FunctionsInverse Trigonometric FunctionsFurther Trigonometric IdentitiesTopic: CalculusRates of ChangeTopic: CombinatoricsWorking with CombinatoricsYear 12 courseThe Mathematics Extension 1 Year 12 course content includes the Topics ‘Trigonometric Functions’ and ‘Calculus’ continued from Year 11 and introduces three different Topics.Topic: ProofProof by Mathematical InductionTopic: VectorsIntroduction to VectorsTopic: Trigonometric FunctionsTrigonometric EquationsTopic: CalculusFurther Calculus SkillsApplications of CalculusTopic: Statistical AnalysisThe Binomial Distribution

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YEAR 11- YEAR 12

MATHEMATICS STAGE 6

The Mathematics Stage 6 syllabuses are designed to offer opportunities for students to think mathematically through questioning, communicating, reasoning and reflecting. They promote development of 21st-century knowledge, skills, understanding, values and attitudes and provide challenge. Students generalise, find connections, think critically and creatively, using appropriate technology to support mathematical activity.

MATHEMATICS STANDARD

Mathematics Standard 1

Board Developed Course

Course number(s):

▪ 11236 Mathematics Standard (2 units – Year 11)

▪ 15231 Mathematics Standard 1 (2 units – Year 12)

Optional examination: Mathematics Standard students who intend to undertake the optional HSC examination must also be enrolled in this course:

▪ 15232 Mathematics Standard 1 (2 units – Year 12)

Prerequisites: The Mathematics Standard 1 Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus and, in particular, the content and outcomes of all substrands of Stage 5.1 and the following substrands of Stage 5.2:

▪ Area and surface area

▪ Financial mathematics

▪ Linear relationships

▪ Non-linear relationships

▪ Right-angled triangles (Trigonometry)

▪ Single variable data analysis

▪ Volume

▪ some content from Equations

▪ some content from Probability.

Corequisites: Nil

Eligibility: Nil

Study via self-tuition: Yes

Exclusions:

▪ 15236 Mathematics Standard 2 (2 units – Year 12)

▪ 11255 Mathematics Advanced (2 units – Year 11)

▪ 15255 Mathematics Advanced (2 units – Year 12)

▪ 11250 Mathematics Extension (1 unit – Year 11)

▪ 15250 Mathematics Extension 1 (1 unit – Year 12)

▪ 15260 Mathematics Extension 2 (1 unit – Year 12)

▪ 16611 Mathematics Life Skills (2 units – Year 11)

▪ 16611 Mathematics Life Skills (2 units – Year 12)

Course description

Mathematics Standard students use mathematics to make informed decisions in their daily lives. Students develop understanding and competence in mathematics through real-world applications. These skills can be used in a range of concurrent HSC subjects.

Mathematics Standard 1 improves numeracy by building student confidence and making mathematics meaningful. Numerate students can manage situations or solve problems in everyday life, work or further learning.

What students learn

The study of Mathematics Standard 1 in Stage 6:

▪ enables students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely

▪ provides opportunities for students to consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling and use these models to solve problems related to their present and future needs

▪ provides an appropriate mathematical background for students entering the workforce and/or undertaking further community and workplace training.

Year 11 course

The Mathematics Standard Year 11 course content comprises four Topics, with the Topics divided into Subtopics.

Topic: Algebra

▪ Formulae and Equations

▪ Linear Relationships

Topic: Measurement

▪ Applications of Measurement

▪ Working with Time

Topic: Financial Mathematics

▪ Money Matters

Topic: Statistical Analysis

▪ Data Analysis

▪ Relative Frequency and Probability

Year 12 course

The Mathematics Standard 1 Year 12 course content includes the same four Topics and the additional Topic ‘Networks’. The Topics and Subtopics are:

Topic: Algebra

▪ Types of Relationships

Topic: Measurement

▪ Right-angled Triangles

▪ Rates

▪ Scale Drawings

Topic: Financial Mathematics

▪ Investment

▪ Depreciation and Loans

Topic: Statistical Analysis

▪ Further Statistical Analysis

Topic: Networks

▪ Networks and Paths

The Mathematics Standard Year 11 course is a common course for all students studying the Mathematics Standard syllabus. In Year 12 students can elect to study either the Mathematics Standard 1 Year 12 course (Category B) or the Mathematics Standard 2 Year 12 course (Category A).

Mathematics Standard Year 11 course content that is essential for Mathematics Standard 1 Year 12 is identified by the symbol .

Students studying the Mathematics Standard 1 course may elect to undertake an optional HSC examination.

To be eligible for an ATAR, students studying the Mathematics Standard 1 course must undertake a pattern of study to satisfy the ATAR requirements and complete the optional HSC examination. For the purposes of calculating the ATAR, no more than 2 units from Category B courses can be included.

All students studying the Mathematics Standard course in Stage 6 have the opportunity to enhance their numeracy skills and capabilities. The content of the course aligns with Level 3 of the Australian Core Skills Framework.

Mathematics Standard 2

Board Developed Course

Course number(s):

▪ 11236 Mathematics Standard (2 units – Year 11)

▪ 15236 Mathematics Standard 2 (2 units – Year 12)

Prerequisites: The Mathematics Standard 2 Year 11 course has been developed on the assumption that students have studied the content and achieved the outcomes of the Mathematics Years 7–10 Syllabus and, in particular, the content and outcomes of all substrands of Stage 5.1 and the following substrands of Stage 5.2:

▪ Area and surface area

▪ Financial mathematics

▪ Linear relationships

▪ Non-linear relationships

▪ Right-angled triangles (Trigonometry)

▪ Single variable data analysis

▪ Volume

▪ some content from Equations

▪ some content from Probability.

Corequisites: Nil

Eligibility:Nil

Study via self-tuition: Yes

Exclusions:

▪ 15231 Mathematics Standard 1 (2 units – Year 12)

▪ 15232 Mathematics Standard 1 (Exam) (2 units – Year 12)

▪ 11255 Mathematics Advanced (2 units – Year 11)

▪ 15255 Mathematics Advanced (2 units – Year 12)

▪ 11250 Mathematics Extension (1 unit – Year 11)

▪ 15250 Mathematics Extension 1 (1 unit – Year 12)

▪ 15260 Mathematics Extension 2 (1 unit – Year 12)

▪ 16611 Mathematics Life Skills (2 units – Year 11)

▪ 16611 Mathematics Life Skills (2 units – Year 12)

Students who have followed the Mathematics Standard  pathway in Year 11 are encouraged to study the Mathematics Standard 1 Year 12 course.

Course description

Mathematics Standard students use mathematics to make informed decisions in their daily lives. Students develop understanding and competence in mathematics through real-world applications. These skills can be used in a range of concurrent HSC subjects.

In Mathematics Standard 2 students extend their mathematical skills beyond Stage 5 without the in-depth knowledge of higher mathematics that the study of calculus would provide. This course prepares students for a wide range of educational and employment aspirations, including continuing their studies at a tertiary level.

What students learn

The study of Mathematics Standard 2 in Stage 6:

▪ enables students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely

▪ provides opportunities for students to consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling and use these models to solve problems related to their present and future needs

▪ provides opportunities for students to develop an understanding of and skills in further aspects of mathematics for concurrent HSC studies

▪ provides an appropriate mathematical background for students entering the workforce or undertaking further tertiary training.

Year 11 course

The Mathematics Standard Year 11 course comprises four Topics, with the Topics divided into Subtopics.

Topic: Algebra

▪ Formulae and Equations

▪ Linear Relationships

Topic: Measurement

▪ Applications of Measurement

▪ Working with Time

Topic: Financial Mathematics

▪ Money Matters

Topic: Statistical Analysis

▪ Data Analysis

▪ Relative Frequency and Probability

Year 12 course

The Mathematics Standard 2 Year 12 course content includes the same four Topics and the additional Topic ‘Networks’.

Topic: Algebra

▪ Types of Relationships

Topic: Measurement

▪ Non-right-angled Trigonometry

▪ Rates and Ratios

Topic: Financial Mathematics

▪ Investments and Loans

▪ Annuities

Topic: Statistical Analysis

▪ Bivariate Data Analysis

▪ The Normal Distribution

Topic: Networks

▪ Network Concepts

▪ Critical Path Analysis

▪ The Mathematics Standard Year 11 course is a common course for all students studying the Mathematics Standard syllabus. In Year 12 students can elect to study either the Mathematics Standard 1 Year 12 course (Category B) or the Mathematics Standard 2 Year 12 course (Category A).

▪ All students studying the Mathematics Standard 2 course will sit for an HSC examination.

▪ All students studying the Mathematics Standard course in Stage 6 have the opportunity to enhance their numeracy skills and capabilities. The content of the course aligns with Level 3 of the Australian Core Skills Framework.