Mathematics Courses
Years 11 & 12
Brendon Cant
Mathematics is the universal language used by everyone, everywhere.
Mathematics provides students with the opportunity to develop their knowledge, understanding and skills in numeracy and working mathematically. Students have the opportunity to develop increasingly sophisticated and refined mathematical understanding, fluency, communication, reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing strategies to make informed decisions and solve problems relevant to their present and future needs.
Numeracy
Content Endorsed Course | Non ATAR
The Numeracy Course builds on the knowledge, skills and understanding presented in the K–10 curriculum. It supports students to develop the functional numeracy skills required to become active and successful participants in society.
The Numeracy course is structured as a 2-unit course that allows delivery as a 120-hour course for Year 11, or as a 240-hour course across Years 11 and 12. The course can count towards the Higher School Certificate and appear on the student's Record of School Achievement (RoSA). Where students request a RoSA, the Numeracy course will be listed with their other Stage 6 courses.
This course offers students the opportunity to achieve the HSC minimum standards of numeracy and prepare for post-school options including employment or further training. Students are supported to develop the core numeracy skills required to become active and successful participants in society. These skills are developed through authentic and relevant learning scenarios such as budgeting, shopping, record and account keeping, and a range of real-life activities requiring numeracy.
Assessment tasks will generally be assignments, allowing students the opportunity to reflect on their learning and
Course Number: Year 11 (30130) & Year 12 (30140).
NESA Numeracy Stage 6 Syllabus
Number of Units: Two for each of the Preliminary Course (Year 11) and HSC Course (Year 12)
Minimum Hours: 120 hours of 'face to face' learning per year (4 hours per week).
Marks Available: This is a Content Endorsed Course. There is no external examination and therefore this course does not count in the calculation of the ATAR. It does count toward the attainment of the HSC. Xavier High School will determine student achievement through internal assessment.
Exclusions: Mathematics Advanced, Mathematics Extension 1, Mathematics Extension 2.
Students wishing to receive an ATAR.
Suitability: Students needing to develop and consolidate functional numeracy skills.
More Information
What Students Learn:
In each of the Preliminary and HSC courses students will learn to:
interpret and use numerical information
solve problems using visual, spatial, financial and statistical literacy skills
think mathematically in practical situations
represent and communicate information
use the context to determine the reasonableness of solutions
Main Topics Covered:
Preliminary Course (Year 11)
Module 1:
Whole numbers
Operations with whole numbers
Distance, area and volume
Time
Data, graphs and tables
Module 2:
Fractions and decimals
Operations with fractions and decimals
Metric relationships
Length, mass and capacity
Chance
HSC Course (Year 12)
Module 3:
Percentages
Operations with numbers
Finance
Location, time and temperature
Space and design
Module 4:
Rates and ratios
Statistics and probability
Exploring with Numerical Reasoning and Mathematical Thinking (NRMT)
Particular Course Requirements:
As a Content Endorsed Course, there is no HSC examination for the Numeracy course. Assessment in this course is school-based. Teachers award a grade in Year 11 using the Common Grade Scale and an assessment grade in Year 12 using the Achievement Level Descriptions for reporting achievement.
Costs:
Nil
Mathematics Standard 1
Board Developed Course | Optional ATAR
Preliminary Course (Year 11)
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 HSC Mathematics Standard 1 course or the HSC Mathematics Standard 2 course.
HSC Course (Year 12)
Mathematics Standard 1 is designed to help students improve their numeracy by building their confidence and success in making mathematics meaningful. Numeracy is more than being able to operate with numbers. It requires mathematical knowledge and understanding, mathematical problem-solving skills and literacy skills, as well as positive attitudes. When students become numerate they are able to manage a situation or solve a problem in real contexts, such as everyday life, work or further learning. This course offers students the opportunity to prepare for post-school options of employment or further training.
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.
Course Number: Year 11 (11236) & Year 12 (30125).
Number of Units: Two for each of the Preliminary Course (Year 11) and HSC Course (Year 12).
Minimum Hours: 120 hours of 'face to face' learning per year (4 hours per week).
Marks Available: HSC examination of 100 marks for the HSC Course (Year 12). This is optional for students wishing to use Mathematics towards their HSC.
Exclusions: Mathematics Standard 2, Mathematics Advanced, Mathematics Extension 1, Mathematics Extension 2. Students wishing to receive an ATAR must opt to complete the HSC exam.
Suitability: Students who consistently achieve below a C grade in Year 10 Mathematics Standard or completed the Year 10 Numeracy Pathway.
More Information
What Students Learn:
The Preliminary and HSC courses:
enable students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely
provide 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
provide an appropriate mathematical background for students entering the workforce and/or undertaking further community and workplace training
Main Topics Covered:
Preliminary Course (Year 11)
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
HSC Course (Year 12)
Topic: Algebra
Types of Relationships
Topic: Measurement
Right Angled Triangles
Rates
Scale Drawings
Topic: Financial Mathematics
Investment
Depreciation & Loans
Topic: Statistical Analysis
Further Statistical Analysis
Topic: Networks
Networks and Paths
Particular Course Requirements:
The Mathematics Standard course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus. It is assumed that students have a sound knowledge in the following areas.
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
Costs:
Nil
Mathematics Standard 2
Board Developed Course | ATAR
Preliminary Course (Year 11)
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 HSC Mathematics Standard 1 course or the HSC Mathematics Standard 2 course .
HSC Course (Year 12)
Mathematics Standard 2 is designed for those students who want to extend their mathematical skills beyond Year 10 but are not seeking the in-depth knowledge of higher mathematics that the study of calculus would provide. This course offers students the opportunity to prepare for a wide range of educational and employment aspirations, including continuing their studies at a tertiary level.
Course Number: Year 11 (11236) & Year 12 (15236).
NESA Mathematics Stage 6 Syllabus
Number of Units: Two for each of the Preliminary Course (Year 11) and HSC Course (Year 12).
Minimum Hours: 120 hours of 'face to face' learning per year (4 hours per week).
Marks Available: 100 marks for the HSC Course (Year 12).
Exclusions: Mathematics Standard 1, Mathematics Advanced, Mathematics Extension 1, Mathematics Extension 2.
Suitability: Students who consistently achieve a C or B grade in Year 10 Mathematics Standard or who achieve lower than a B grade in Year 10 Mathematics Advanced.
More Information
What Students Learn:
The Preliminary and HSC courses:
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
Main Topics Covered:
Preliminary Course (Year 11)
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
HSC Course (Year 12)
Topic: Algebra
Types of Relationships
Topic: Measurement
Non-right angled Trigonometry
Rates and Ratios
Topic: Financial Mathematics
Investments & Loans
Annuities
Topic: Statistical Analysis
Bivariate Data Analysis
The Normal Distribution
Topic: Networks
Network Concepts
Critical Path Analysis
Particular Course Requirements:
The Mathematics Standard course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus. It is assumed that students have a sound knowledge in the following areas.
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
Costs:
Nil
Mathematics Advanced
Board Developed Course | ATAR
The Mathematics Advanced course is focused on enabling students to appreciate that mathematics is 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 Advanced course provides a basis for further studies in disciplines in which mathematics and the skills that constitute thinking mathematically have an important role. It is designed for those students whose future pathways may involve mathematics and its applications in a range of disciplines at the tertiary level.
Students intending to go to university to study any kind of STEAM degree (Science, Technology, Engineering, Arts and Mathematics) should choose Mathematics Advanced and are strongly advised to include Mathematics Extension 1 in Years 11 and 12 if possible. Students aiming to study STEAM degrees and degrees which include STEAM subjects (such as economics, psychology and commerce), are advised to choose the highest level of mathematics in Years 11 and 12 of which they might be capable.
Course Number: Year 11 (11255) & Year 12 (15255).
NESA Mathematics Advanced Stage 6 Syllabus
Number of Units: Two for each of the Preliminary Course (Year 11) and HSC Course (Year 12).
Minimum Hours: 120 hours of 'face to face' learning per year (4 hours per week).
Marks Available: 100 marks for the HSC Course (Year 12).
Exclusions: Numeracy, Mathematics Standard 1, Mathematics Standard 2
Suitability: Students who consistently achieve a B or A grade in Year 10 Mathematics Advanced.
More Information
What Students Learn:
The Preliminary and HSC courses:
enable students to develop their knowledge, understanding and skills in working mathematically and in communicating concisely and precisely
provide 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
provide opportunities for students to develop ways of thinking in which problems are explored through observation, reflection and reasoning
provide a basis for further studies in disciplines in which mathematics and the skills that constitute thinking mathematically have an important role
provide an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in a range of disciplines at the tertiary level
Main Topics Covered:
Preliminary Course (Year 11)
Topic: Functions
Working with Functions
Topic: Trigonometric Functions
Trigonometry and Measure of Angles
Trigonometric Functions & Identities
Topic: Calculus
Introduction to Differentiation
Topic: Exponential & Logarithmic Functions
Logarithms & Exponentials
Topic: Statistical Analysis
Probability and Discrete Probability Distributions
HSC Course (Year 12)
Topic: Functions
Graphing Techniques
Topic: Trigonometric Functions
Trigonometric Functions & 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
Particular Course Requirements:
The Mathematical Advanced course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus. It is assumed that students have a sound knowledge in the following areas:
Algebraic techniques
Surds and indices
Equations
Linear relationships
Trigonometry and Pythagoras’ theorem
Single variable data analysis
Non-linear relationships (partial knowledge expected)
Properties of Geometrical Shapes (partial knowledge expected)
Costs:
Nil
Mathematics Extension 1
Board Developed Course | ATAR
Mathematics 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. Students of Mathematics Extension 1 will be able to develop an appreciation of the interconnected nature of mathematics, its beauty and its functionality.
Mathematics Extension 1 provides a basis for progression to further study in Mathematics or related disciplines in which Mathematics has a vital role at a tertiary level. An understanding and exploration of Mathematics Extension 1 is also advantageous for further studies in such areas as science, engineering, finance and economics.
Course Number: Year 11 (11250) & Year 12 (15250).
NESA Mathematics Extension 1 Stage 6 Syllabus
Number of Units: One for each of the Preliminary Course (Year 11) and HSC Course (Year 12).
Minimum Hours: 60 hours of 'face to face' learning per year (2 hours per week).
Marks Available: 50 marks for the HSC Course (Year 12).
Exclusions: Numeracy, Mathematics Standard 1, Mathematics Standard 2.
Suitability: Students who consistently achieve an A grade in Year 10 Mathematics Advanced.
More Information
What Students Learn:
The Preliminary and HSC courses:
enable students to develop thorough knowledge, understanding and skills in working mathematically and in communicating concisely and precisely
provide opportunities for students to develop rigorous mathematical arguments and proofs, and to use mathematical models extensively
provide opportunities for students to develop their awareness of the interconnected nature of mathematics, its beauty and its functionality
provide a basis for progression to further study in mathematics or related disciplines and in which mathematics has a vital role at tertiary level
provide an appropriate mathematical background for students whose future pathways may involve mathematics and its applications in such areas as science, engineering, finance and economics
Main Topics Covered:
Preliminary Course (Year 11)
Topic: Functions
Further Work with Functions
Polynomials
Topic: Trigonometric Functions
Inverse Trigonometric Functions
Further Trigonometric Identities
Topic: Calculus
Rates of Change
Topic: Combinatorics
Working with Combinatorics
HSC Course (Year 12)
Topic: Proof
Proof by Mathematical Induction
Topic: Vectors
Introduction to Vectors
Topic: Calculus
Further Calculus Skills
Applications of Calculus
Integral Calculus
Topic: Statistical Analysis
The Binomial Distribution
Particular Course Requirements:
The Mathematical Advanced course has been developed on the assumption that students have studied the content and achieved the outcomes of the NSW Mathematics Years 7–10 Syllabus. It is assumed that students have a sound knowledge in the following areas.
Polynomials
Logarithms
Functions and Other Graphs
Circle Geometry
Costs:
Nil
