SUBJECTS / YEAR 11
MATHEMATICS ADVANCED
Functions, trigonometry and the first steps of calculus — the foundations Year 12 is built on, laid properly.
Who is this course for?
Specifically developed for Year 11 students studying Mathematics Advanced for the HSC. Full list of topics covered in both Year 11 and Year 12 is given below. The course begins in Term 4 of Year 10 and transitions into Year 12 Mathematics Advanced in Term 4 of Year 11 (no change in timetable normally).
Through this course, we aim to give students an in-depth understanding of the topics and develop their maths abilities. We will work to strengthen foundational skills, improve critical thinking and problem solving skills, and learn how to synthesise different techniques to tackle complicated examination-style questions.
Recommended for students who:
✔ want to improve their maths skills and don’t mind an occasional challenge
✔ enjoy interpersonal interactions and in-class discussions in an informal environment
✔ desire the structure and accountability of weekly lessons
✔ appreciate additional support while in class
Face-to-Face Lessons
$100 per lesson (billed termly)
DISCOUNTS AVAILABLE!
✔ 2.5-hour weekly lessons through our teaching term
✔ Top quality teaching makes difficult concepts easier to grasp
✔ Topics are taught systematically and comprehensively
✔ Amazing learning experience
✔ Small class size allows for flexible topic schedule
✔ Comprehensive course notes for you to note-take and personalise
✔ 24/7 access to HSC101 for on-demand streaming of thousands of learning videos
✔ AI driven practices to help you master course content
✔ Workbooks with careful curation of challenging questions to help you go that extra mile
✔ Progress tracking to identify and overcome any challenges
✔ Always here and ready to help!
List of Topics (YEAR 11+12)
-
+ Overview of the Number System
+ Surds
+ Terms and Factors
+ Expanding Brackets
+ Linear Equations
+ Linear Inequations
+ Factorisation
+ Quadratic Equations
+ Algebraic Fractions
+ Simultaneous Equations -
+ Introduction to Functions
+ Domain and Range
+ Odd and Even Functions
+ Linear Functions
+ Quadratic Functions
+ Further Quadratic Equations
+ Sketching Polynomial Functions
+ Graphs of Some Other Basic Curves
+ Absolute Value Functions
+ Curve Sketching Techniques - Translations / Reflections / Dilations / Combinations of Transformations
+ Composite Functions
+ Rational Functions
+ Graphical Solutions and Basic Inequations
+ Regions in the Number Plane -
+ Introduction to Trigonometry
+ Special Angles and Angles of any Magnitude
+ Sine Rule, Cosine Rule and Area of Triangle
+ Radians
+ Arc length, Sectors and Segments
+ Trigonometric Identities
+ Trigonometric Graphs
+ Trigonometric Equations
+ 3D Trigonometry -
+ Introduction to Sequences
+ Sigma Notation and Partial Sum
+ Arithmetic Sequences and Series
+ Geometric Sequences and Series, and Limiting Sum
+ Simple Applications of APs and GPs
+ Arithmetic and Geometric Means
+ Revision of Basic Financial Mathematics
+ Investment Schemes
+ Time Payments -
+ Limits
+ Continuity and Differentiability
+ First Principle of Differentiation
+ Rules of Differentiation
+ Tangents and Normals
+ Implicit Differentiation (Optional) -
+ Geometric Definition of the Derivative
+ Stationary Points
+ The Second Derivative
+ Global Maximum and Minimum
+ Maximisation and Minimisation -
+ Primitive Functions
+ Constant of Integration
+ Area Bounded between the Coordinate Axes
+ Compound Areas
+ Properties of Definite Integrals
+ Trapezoidal Rule -
+ Sets and Venn Diagram
+ Theoretical Probability including conditional probability
+ Discrete Random Variables
+ Continuous Random Variables
+ Bivariate Data Analysis including linear regression
+ The Normal Distribution -
+ Logarithmic, Exponential and Trigonometric Functions
+ Differentiation and Integration of Functions involving Logarithms
+ Differentiation and Integration of Exponential Functions
+ Differential and Integration of Trigonometric Functions -
+ Gradient as a Rate
+ Natural Growth and Decay
+ Kinematics: Differentiation
+ Kinematics: Integration
Please note that the topics above are not necessarily covered in chronological order. We run a flexible schedule based on the students’ need. Please contact us for specific details.