SUBJECTS / YEAR 12
MATHEMATICS EXTENSION 1
Vectors, induction and differential equations — we build the intuition first, then the exam technique, so the hard questions start to feel routine.
OUR TRACK RECORD
99.95 top ATAR · 100 perfect mark in Maths Ext 1 · 5.0★ on Google
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WHO THIS COURSE IS FOR
Built for Year 12 students pushing beyond Advanced
A continuation of our Year 11 Extension 1 program, covering the full HSC Extension 1 course (Advanced content is also covered). Every topic is taught from first principles and drilled to exam standard — with the exam technique, past-paper practice and marking feedback that turn understanding into an E4.
You want to genuinely understand maths — not just memorise it
You learn best through discussion in a relaxed, informal classroom
You want the structure and accountability of a weekly lesson
You appreciate extra support — in class and long after it ends
FACE-TO-FACE LESSONS
$100 / lesson
Billed termly, everything included. Averages to $40 an hour before any applicable discounts are applied.
WAYS TO SAVE
First lesson free · loyalty discount after your first term · multi-subject & sibling discounts
Every lesson includes
You bring the pen. We bring the rest.
2.5-hour weekly lessons — small class, taught systematically
Course notes — comprehensive, structured for note taking & revision
Curated workbooks — hand-picked, challenging questions
HSC101 access — thousands of videos, on-demand 24/7
Progress tracking — quizzes & homework monitoring
Out-of-hours support — always here and ready to help!
COURSE MAP
Every facet of the syllabus
-
Numbers and Algebra
+ Overview of the Number System
+ Surds
+ Terms and Factors
+ Expanding Brackets
+ Linear Equations
+ Linear Inequations
+ Factorisation
+ Quadratic Equations
+ Algebraic Fractions
+ Simultaneous Equations -
Functions
+ 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 -
Trigonometry
+ 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 -
Sequences and Series
+ 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 -
Differentiation
+ Limits
+ Continuity and Differentiability
+ First Principle of Differentiation
+ Rules of Differentiation
+ Tangents and Normals
+ Implicit Differentiation (Optional) -
Geometrical Applications of the Derivative
+ Geometric Definition of the Derivative
+ Stationary Points
+ The Second Derivative
+ Global Maximum and Minimum
+ Maximisation and Minimisation -
Integration
+ Primitive Functions
+ Constant of Integration
+ Area Bounded between the Coordinate Axes
+ Compound Areas
+ Properties of Definite Integrals
+ Trapezoidal Rule -
Statistics and Probability
+ Sets and Venn Diagram
+ Theoretical Probability including conditional probability
+ Discrete Random Variables
+ Continuous Random Variables
+ Bivariate Data Analysis including linear regression
+ The Normal Distribution -
Further Calculus
+ Logarithmic, Exponential and Trigonometric Functions
+ Differentiation and Integration of Functions involving Logarithms
+ Differentiation and Integration of Exponential Functions
+ Differential and Integration of Trigonometric Functions -
Physical Applications of Calculus
+ Gradient as a Rate
+ Natural Growth and Decay
+ Kinematics: Differentiation
+ Kinematics: Integration -
Mathematical Induction (X1)
+ Principle of Induction
+ Summation and Divisibility Induction -
Further Functions (X1)
+ Further Inequations
+ Sketching Curves by Addition of Ordinates
+ Sketching Reciprocal Functions
+ Sketching Absolute Value Transformations
+ Sketching Square Root Transformations
+ Parametric Representation of Functions
+ Inverse Functions -
Further Trigonometry (X1)
+ Compound Angle Formula
+ Double Angle Formula
+ Triple Angle Formula
+ Further Trigonometric Equations
+ Sum of Sine and Cosine Functions -
Inverse Trigonometric Functions (X1)
+ Inverse Trigonometric Functions
+ Differentiating Inverse Trigonometric Functions -
Polynomials (X1)
+ Introduction to Polynomials
+ Division of Polynomials
+ Remainder Theorem
+ Factor Theorem
+ Graphs of Polynomial Functions
+ Consequences of the Factor Theorem
+ Multiple Root Theorem
+ Relationship between Roots and Coefficients -
Binomial Theorem (X1)
+ Factorial Notation
+ Binomial Expansions
+ Binomial Theorem
+ Binomial Identities -
Permutations and Combinations (X1)
+ Ordered Arrangements without Repetition
+ Ordered Arrangements with Repetition
+ Counting with Identical Elements
+ Unordered Arrangements
+ Circular Arrangements -
Vectors (X1)
+ Introduction to Vectors
+ Vector Operations
+ Dot Product
+ Projections
+ Vector Geometry
+ Physical Applications of Vectors -
Further Calculus (X1)
+ Volume of Solids of Revolution
+ Further Differentiation of Trigonometric Functions
+ Further Integration of Trigonometric Functions
+ Integration by Substitution
+ Integrating Functions associated with Inverse Trigonometric Functions -
Differential Equations (X1)
+ Introduction to Differential Equations
+ Slope Fields
+ Separable Differential Equations
+ Autonomous Differential Equations
+ Applications of Differential Equations -
Further Probability (X1)
+ Further Probability, including with counting
+ Binomial Probability
+ The Binomial Distribution
+ The Normal Distribution as an Approximation
+ Sample Proportions -
Further Physical Applications of Calculus (X1)
+ Related Rates of Change
+ Modified Growth and Decay
+ Projectile Motion
E4’s are made week by week
Come sit in on a lesson. It’s free.
No commitment, no payment details — just experience the class for yourself and see if we’re the right fit. Over 90% of students who try us stay for their whole HSC journey.
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