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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