Toán math 12

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Board Developed Courses

Board Developed Life Skills Courses

Content Endorsed Courses

Board Developed Courses

Mathematics Standard 1

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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 lớn 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 nội dung 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 & surface areaFinancial mathematicsLinear relationshipsNon-linear relationshipsRight-angled triangles (Trigonometry)Single variable data analysisVolumesome nội dung from Equationssome content from Probability.

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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 & 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 và 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 khổng lồ develop their knowledge, understanding and skills in working mathematically and in communicating concisely and preciselyprovides opportunities for students to lớn consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling & use these models to lớn solve problems related lớn their present and future needsprovides 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 nội dung comprises four Topics, with the Topics divided into Subtopics.

Topic: Algebra

Formulae and EquationsLinear Relationships

Topic: Measurement

Applications of MeasurementWorking with Time

Topic: Financial Mathematics

Money Matters

Topic: Statistical Analysis

Data AnalysisRelative Frequency và ProbabilityYear 12 course

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

Topic: Algebra

Types of Relationships

Topic: Measurement

Right-angled TrianglesRatesScale Drawings

Topic: Financial Mathematics

InvestmentDepreciation và Loans

Topic: Statistical Analysis

Further Statistical Analysis

Topic: Networks

Networks & Paths

Course requirements

Nil

RoSA & HSC

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 lớn 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 lớn 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 & 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 màn chơi 3 of the Australian vi xử lý core Skills Framework.

Mathematics Standard 2

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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 và the following substrands of Stage 5.2:

Area and surface areaFinancial mathematicsLinear relationshipsNon-linear relationshipsRight-angled triangles (Trigonometry)Single variable data analysisVolumesome nội dung from Equationssome nội dung 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 lớn make informed decisions in their daily lives. Students develop understanding và 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 khổng lồ develop their knowledge, understanding & skills in working mathematically & in communicating concisely và preciselyprovides opportunities for students to lớn consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling và use these models to solve problems related lớn their present & future needsprovides opportunities for students khổng lồ develop an understanding of and skills in further aspects of mathematics for concurrent HSC studiesprovides 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 và EquationsLinear Relationships

Topic: Measurement

Applications of MeasurementWorking with Time

Topic: Financial Mathematics

Money Matters

Topic: Statistical Analysis

Data AnalysisRelative Frequency và ProbabilityYear 12 course

The Mathematics Standard 2 Year 12 course nội dung includes the same four Topics và the additional Topic ‘Networks’.

Topic: Algebra

Types of Relationships

Topic: Measurement

Non-right-angled TrigonometryRates & Ratios

Topic: Financial Mathematics

Investments và LoansAnnuities

Topic: Statistical Analysis

Bivariate Data AnalysisThe Normal Distribution

Topic: Networks

Network ConceptsCritical Path Analysis

Course requirements

Nil

RoSA và HSC

The Mathematics Standard Year 11 course is a common course for all students studying the Mathematics Standard syllabus. In Year 12 students can elect lớn 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 bộ vi xử lý core Skills Framework.

Mathematics Advanced

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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 & in particular, the nội dung and outcomes of all substrands of Stage 5.1 and Stage 5.2, and the following substrands of Stage 5.3:

Algebraic techniquesSurds & indicesEquationsLinear relationshipsTrigonometry and Pythagoras’ theoremSingle variable data analysis

and at least some of the nội dung from the following substrands of Stage 5.3:

Non-linear relationshipsProperties 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 lớn investigate order, relation, pattern, uncertainty & 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 khổng lồ develop their knowledge, understanding and skills in working mathematically and in communicating concisely và preciselyprovides opportunities for students khổng lồ consider various applications of mathematics in a broad range of contemporary contexts through the use of mathematical modelling & use these models to solve problems related to their present and future needsprovides opportunities for students to develop ways of thinking in which problems are explored through observation, reflection and reasoningprovides a basis for further studies in disciplines in which mathematics & the skills that constitute thinking mathematically have an important roleprovides 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 nội dung comprises five Topics, with the Topics divided into Subtopics.

Topic: Functions

Working with Functions

Topic: Trigonometric Functions

Trigonometry and Measure of AnglesTrigonometric Functions và Identities

Topic: Calculus

Introduction lớn Differentiation

Topic: Exponential và Logarithmic Functions

Logarithms & Exponentials

Topic: Statistical Analysis

Probability và Discrete Probability DistributionsYear 12 course

The Mathematics Advanced Year 12 course content includes four of the same Topics & the Topic ‘Financial Mathematics’ in place of ‘Exponential và Logarithmic Functions’.

Topic: Functions

Graphing Techniques

Topic: Trigonometric Functions

Trigonometric Functions và Graphs

Topic: Calculus

Differential CalculusThe Second DerivativeIntegral Calculus

Topic: Financial Mathematics

Modelling Financial Situations

Topic: Statistical Analysis

Descriptive Statistics và Bivariate Data AnalysisRandom Variables

Course requirements

Nil

RoSA and HSC

Mathematics Extension 1

View course

Board Developed Course

Course 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 nội dung 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 và Stage 5.3, including the optional substrands:

PolynomialsLogarithmsFunctions & Other GraphsCircle Geometry.

Corequisites:

11255 Mathematics Advanced (2 units – Year 11)15255 Mathematics Advanced (2 units – 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 1 is focused on enabling students khổng lồ develop a thorough understanding of & competence in further aspects of mathematics. The course provides opportunities khổng lồ develop rigorous mathematical arguments & proofs, & 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, và therefore also the Mathematics Advanced Year 12 course.

All students studying the Mathematics Extension 1 course will sit for an HSC examination.

What students learn

The study of Mathematics Extension 1 in Stage 6:

enables students to develop thorough knowledge, understanding & skills in working mathematically & in communicating concisely và preciselyprovides opportunities for students to lớn develop rigorous mathematical arguments and proofs, và to use mathematical models extensivelyprovides opportunities for students to lớn develop their awareness of the interconnected nature of mathematics, its beauty & its functionalityprovides a basis for progression to lớn further study in mathematics or related disciplines và 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 và economics.Year 11 course

The Mathematics Extension 1 Year 11 course nội dung is comprised of four Topics, with the Topics divided into Subtopics.

Topic: Functions

Further Work with FunctionsPolynomials

Topic: Trigonometric Functions

Inverse Trigonometric FunctionsFurther Trigonometric Identities

Topic: Calculus

Rates of Change

Topic: Combinatorics

Working with CombinatoricsYear 12 course

The Mathematics Extension 1 Year 12 course content includes the Topics ‘Trigonometric Functions’ và ‘Calculus’ continued from Year 11 & introduces three different Topics.

Topic: Proof

Proof by Mathematical Induction

Topic: Vectors

Introduction to Vectors

Topic: Trigonometric Functions

Trigonometric Equations

Topic: Calculus

Further Calculus SkillsApplications of Calculus

Topic: Statistical Analysis

The Binomial Distribution

Course requirements

Nil

RoSA và HSC

Mathematics Extension 2

View course

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 nội dung 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 & 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 lớn develop strong mathematical manipulative skills & a deep understanding of the fundamental ideas of algebra và 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 & 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 & Mathematics Extension 2 Stage 6 courses khung 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 khổng lồ develop strong knowledge, understanding & skills in working mathematically and in communicating concisely và preciselyprovides opportunities to lớn develop strong mathematical manipulative skills & a deep understanding of the fundamental ideas of algebra & calculus, as well as an awareness of mathematics as an activity with its own intrinsic value, involving invention, intuition & explorationprovides opportunities at progressively higher levels for students khổng lồ acquire knowledge, understanding và skills in relation khổng lồ concepts within areas of mathematics that have applications in an increasing number of contextsprovides a basis for progression to further study in mathematics or related disciplines & in which mathematics has a vital role at tertiary levelprovides an appropriate mathematical background for students whose future pathways will be founded in mathematics & its applications in such areas as science, engineering, finance và economics.Year 12 course

The Mathematics Extension 2 course comprises five Topics, with the Topics divided into Subtopics.

Topic: Proof

The Nature of ProofFurther Proof by Mathematical Induction

Topic: Vectors

Further Work with Vectors

Topic: Complex Numbers

Introduction khổng lồ Complex NumbersUsing Complex Numbers

Topic: Calculus

Further Integration

Topic: Mechanics

Applications of Calculus khổng lồ Mechanics

Course requirements

Nil

RoSA và HSC

Board Developed Life Skills Courses

Mathematics Life Skills

View course

Board Developed Course

Course number(s):

16611 Mathematics Life Skills (2 units – Year 11)16611 Mathematics Life Skills (2 units – Year 12)

Prerequisites: A student studying any Stage 6 Life Skills course will usually have completed one or more courses based on Life Skills outcomes and nội dung in Years 7–10, except under special circumstances.

Corequisites: Nil

Eligibility: Life Skills Eligibility

Study via self-tuition: No

Exclusions:

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 11)15260 Mathematics Extension 2 (1 unit – Year 12)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)

Course description

The Mathematics Life Skills Stage 6 course aligns with the rationale, aim and objectives of the Mathematics Standard Stage 6 course. The Life Skills content has been developed from the Mathematics Standard syllabus khổng lồ provide opportunities for integrated delivery.

The Mathematics Life Skills Stage 6 course focuses on the development of students’ ability to lớn apply mathematics in a variety of contexts in order lớn enhance and encourage their participation in post-school contexts.

Students are provided with opportunities to apply mathematical operations to practical situations and develop problem-solving in real-life situations. They develop their practical skills in measurement, calculating with money, statistics and using plans & maps. Students also have the opportunity to lớn explore the concepts of earning & spending money & apply their understanding in a range of financial decision-making contexts.

Study in the Mathematics Life Skills Stage 6 course enhances students’ access to lớn community living, further education, training và employment.

What students learn

The structure of the Mathematics Life Skills Stage 6 course allows teachers to provide a broad và balanced program that reflects the needs of students within the context of the collaborative curriculum planning process.

The course is organised into the following topics & subtopics:

Topic: Number and Modelling (Algebra)

Review of Number PropertiesMathematical Modelling

Topic: Measurement

Everyday MeasurementMeasuring Two-Dimensional & Three-Dimensional Shapes

Topic: Financial Mathematics

Decimals, Percentages và MoneyEarning MoneySpending Money

Topic: Statistics và Probability (Statistical analysis)

StatisticsProbability

Topic: Plans, Maps và Networks (Networks)

Using Plans, Maps & Networks

The Topics provide possible frameworks for addressing the Mathematics Life Skills Stage 6 outcomes and content, và are suggestions only. The course provides flexibility to develop programs appropriate to the needs, strengths, goals, interests & prior learning of students.

Course requirements

On entering students for the Mathematics Life Skills Stage 6 course, the principal is certifying that the student is eligible & the decision is the result of the collaborative curriculum planning process.

Students are expected to address or achieve one or more of the Mathematics Life Skills Stage 6 outcomes. They need not address or complete all of the content to demonstrate achievement of an outcome.

RoSA & HSC

Content Endorsed Courses

Numeracy

View course

Content Endorsed Course

Course number(s):

30130 Numeracy (2 units – Year 11) 30140 Numeracy (2 units – Year 12)

Prerequisites: Nil

Co-requisites: Nil

Eligibility: Nil

Study via self-tuition: No

Exclusions: Nil

It is anticipated that students undertaking Mathematics Advanced or higher courses have already consolidated essential numeracy skills and would not benefit from studying this course.

Course description

The Numeracy course builds on the knowledge, skills & understanding presented in the K–10 curriculum. It supports students khổng lồ develop the functional numeracy skills required to lớn become active and successful participants in society.

The Numeracy Stage 6 CEC Syllabus is designed lớn offer opportunities for students to reason numerically & think mathematically. Numerical reasoning and mathematical thinking are supported by an atmosphere of questioning, communicating, reasoning and reflecting và are engendered by opportunities khổng lồ generalise, challenge, find connections & to think critically và creatively.

The Numeracy course provides opportunities for students to lớn develop 21st-century knowledge, skills, understanding, values and attitudes. As part of this, students are encouraged to learn lớn use appropriate công nghệ as an effective support for numerical & mathematical activities.

What students learn

The study of Numeracy in Stage 6 enables students to build on existing numeracy skills and to develop & improve their capability to:

interpret & use numerical information solve problems using visual, spatial, financial & statistical literacy skills think mathematically in practical situations represent & communicate information use the context to determine the reasonableness of solutions

in order to manage situations & solve problems relating khổng lồ their present và future needs.

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Year 11 course

Module 1:

1: Whole numbers 2: Operations with whole numbers 3: Distance, area & volume 4: Time 5: Data, graphs and tables

Module 2:

1: Fractions and decimals 2: Operations with fractions và decimals 3: Metric relationships 4: Length, mass & capacity 5: ChanceYear 12 course

The Numeracy Year 12 course nội dung comprises 2 modules. The modules are divided into content areas.

Module 3:

1: Percentages 2: Operations with numbers 3: Finance 4: Location, time và temperature 5: Space & design

Module 4:

1: Rates & ratios 2: Statistics & probability 3: Exploring with NRMT

Course requirements

Nil