Maths (general advanced-extension)

General Mathematics

Board Endorsed Course This is a NON ATAR 2 Unit course

Prerequisites:
The course is constructed on the assumption that students have achieved the
outcomes of Advanced Mathematics, OR demonstrated a high level of competence in
Intermediate Mathematics.
Course Description:
General Mathematics focuses on mathematical skills and techniques, which have
direct application to everyday activity. The course content is written in five areas of
study, with an emphasis on application of specific skills and on tasks that involve
integrating mathematical skills and techniques across a range of familiar and
unfamiliar situations. These tasks may draw from more than one area of study, and
encourage transfer of knowledge across the entire course, as well as linking with study
in other Stage 6 subjects. The course is fully prescribed, and is designed to support
TAFE and other vocational courses.

General Mathematics

Financial Mathematics
Preliminary Course HSC Course
You will learn about... You will learn about...

• Earning Money • Annuities and Loan
• Investing Money Repayments
• Taxation • Credit and Borrowing
• Depreciation

General Mathematics

Data Analysis

• Statistics and Society • Interpreting Sets of Data
• Data Collection and Sampling • The Normal Distribution
• Displaying Single Data Sets • Correlation

General Mathematics

Measurement

• Units of Measurement and • Further Applications of Area
Applications and Volume
• Applications of Area and • Applications of Trigonometry
Volume • Spherical Geometry
• Similarity of 2D Figures
• Right Angled Triangles

General Mathematics

Probability

• The Language of Chance • Multi Stage Events
• Relative Frequency and • Applications of Probability
Probability

General Mathematics

Algebra and Modelling

• Basic Algebraic Skills • Further Algebraic Skills and
• Modelling Linear Relationships Techniques
• Modelling Linear and Non
Linear Relationships

Mathematics


Prerequisites:
The School Certificate in Mathematics
Course Description:
The course is constructed on the assumption that the students have achieved the
outcomes, and, demonstrated a high level of competence in Stage 5.3 Mathematics.
This course further develops the understanding and competence in the aspects of
Mathematics that follow.

Mathematics

Preliminary Course
Basic Arithmetic and Algebra
You will learn about…

• Rationals and Surds
• Absolute Value
• Algebraic Expressions
• Linear Equations and Inequalities

Mathematics

Preliminary Course
Real Functions

• Real Functions
• Graphs
• Algebraic Representations
• Regions

Mathematics

Preliminary Course
Trigonometry

• Trigonometric Ratios
• Trigonometric Identities
• Applied Trigonometry

Mathematics

Preliminary Course
Linear Functions

• The Linear Function
• The Gradient of a Line
• Interval Formulae

Mathematics

Preliminary Course
The Quadratic Polynomial and
The Parabola

• The Quadratic Function
• The Quadratic Equation
• Other Quadratics
• The Parabola as a Locus

Mathematics

Preliminary Course
Plane Geometry

• Notations and Symbols
• Definition, Recognition, and Properties
• Congruence and Similarity
• Intercept Theorems
• Measurement

Mathematics

Preliminary Course
Tangent to a Curve and Derivative of a
Function

• Continuity and Limits
• Secants and Tangents
• Differential Rules
• Equation of the Tangent

Mathematics

HSC Course
Geometrical Applications of
Differentiation

• Sign of the Derivative
• The Second Derivative
• Applications to Problem Solving
• Primitive Functions

Mathematics

HSC Course
Integration

• The Definite Integral
• Area and Volume
• Approximate Methods

Mathematics

HSC Course
Trigonometric Functions

• Circular Measurement
• Graphs
• Limits
• Differentiation
• Integration

Mathematics

HSC Course
Logarithmic and Exponential Functions

• The Log Function
• The Exponential Function
• Graphs
• Differentiation
• Integration

Mathematics

HSC Course
Applications of Calculus to
the Physical World

• Simple Rates of Change
• Motion of a Particle with Respect to Time

Mathematics

HSC Course
Probability

• Random and Complementary Events
• Tree Diagrams
• Mutually and Non Mutually Exclusive Outcomes
• Multi Stage Events

Mathematics

HSC Course
Series and Series Applications

• General Series
• Arithmetic Series
• Geometric Series

Extension 1 Mathematics

Board Endorsed Course This is an ATAR 1 Unit course

1 Unit additional to 2 Unit Mathematics in each of Preliminary and HSC
Prerequisites:
Before selecting this course, students need to have demonstrated a significant
aptitude for Mathematics at Stage 5.3 level. Students must also pass an entrance exam
and obtain written approval from the Head Teacher of Mathematics

Course Description:
The course runs concurrently with the Stage 6 Mathematics Course.

It is constructed on the assumption that students are highly proficient in all Stage 5
outcomes, and, have demonstrated a mastery of the skills in Stage 5.3 Mathematics. It
further develops the understanding and competence in the aspects of Mathematics.


Preliminary Course
Other Inequalities

• Unknown in the Denominator


Preliminary Course
Further Plane Geometry

• Theoretical Problems with more than One Step of Reasoning


Preliminary Course
Circle Geometry

• Chord Properties
• Angle Properties
• Tangent Properties
• Theoretical Problems with more than One Step of Reasoning


Preliminary Course
Further Trigonometry

• Sums and Differences
• Half Angles
• Double Angles
• T-Substitutions
• Solution Methods
• 3D Applied Trigonometry Problems


Preliminary Course
Permutations and Combinations

• Counting Techniques
• Factorial Notation


Preliminary Course
Polynomials

• Operations
• Remainder Theorem
• Factor Theorem
• Graphs


Preliminary Course
Angle Between Two Lines
&
Internal and External Division of Lines
into Given Ratios

• Applications of the Formula


HSC Course
Methods of Integration

• Substitution Methods
• Trig Substitution
• Primitives of sin²x and cos²x


HSC Course
Further Exponential/Log Functions

• Integration involving Partial Fractions
• Newton’s Law of Cooling


HSC Course
Applications of Calculus to
the Physical World

• Related Rages of Change
• Velocity and Acceleration as Functions of the Displacement
• Projectile Motion
• Simple Harmonic Motion


HSC Course
Inverse Functions and
Inverse Trigonometric Functions

• Graphs
• Differentiation and Integration


HSC Course
Binomial Theorem

• Pascal’s Triangle
• General Binomial Theorem
• Further Probability


HSC Course
Iterative Method for
Estimation of Roots

• Halving the Interval Theorem
• Newton’s Method


HSC Course
Mathematical Induction

• Summation Style
• Divisibility Test
• Inequalities
• Other Contexts


1 Unit additional to the Mathematics Extension 1 course, for the HSC
Prerequisites:
Before selecting this course, students need to have demonstrated a significant
aptitude for Mathematics at Extension 1 level. Students must also obtain written
approval from the Head Teacher of Mathematics
Course Description:
This course is run concurrently with Stage 6 Mathematics and Extension 1.

It is constructed on the assumption that students are highly proficient in all
Preliminary outcomes, and, have demonstrated a mastery of the skills in Extension 1
Mathematics. It further develops the understanding and competence in aspects of
Mathematics.


HSC Course only


Please refer to the Board of Studies Website for Topics and Detailed
Syllabus Notes

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/mathematics-advanced.html

Maths (general advanced-extension)

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