SchoolWise
Advanced Mathematics
Advanced Mathematics Course Overview
Advanced Mathematics is a two-week intensive course designed for highly motivated students preparing for Years 11 and 12. It provides a comprehensive overview of senior mathematics, targeting the higher-level courses across the ACT, NSW, and IB curricula. Taught by the most senior mathematics tutors at Wise Minds, this course is a unique opportunity to get a massive leg up in Year 11 and 12 mathematics.
This is not a simple summer course aiming to boost grades. It reorganises the content the way mathematics should be taught: algebra builds into functions, functions into calculus, probability into statistics. Each concept arrives when students are ready for it, supported by everything that came before.
Students receive a detailed course book with explanations, practice questions, and worksheets—an excellent reference throughout Years 11, 12, and beyond.
📐 Years 10–12
📖 Course book included
👥 Small group tutorials
📝 Examinations
Who Is This Course For?
This course is ideal for advanced Year 10 students, as well as Year 11 and 12 students studying any of the following subjects:
ACT Mathematical Methods
ACT Specialist Methods
HSC Mathematics Advanced
HSC Mathematics Extension 1
HSC Mathematics Extension 2
IB Mathematics SL
IB Mathematics HL
Advanced Year 10 Students
What You'll Learn
The course covers the full breadth of senior mathematics, structured logically to build understanding:
1. Advanced Algebraic Techniques
- Expanding Binomials
- Expanding Trinomials
- Difference of Two Squares
- Perfect Squares
- Solving Quadratics
- Long Division of Polynomials
- Solving Polynomials
2. Numbers and Surds
- Rationalising the Denominator
- Rationalising Binomial Denominators
3. Exponential & Logarithmic Functions
- Logarithm, Logarithm Laws, and Index Laws
- Logarithmic Functions
- Exponential Functions
- Application of Logarithmic and Exponential Functions
4. Coordinate Plane & Polynomials
- Lengths and Midpoints of Intervals
- Gradients and Intervals
- Points of Intersection of Lines and Curves
- The General Solution to These Problems
- Perpendicular Distance
- Sum and Products of Roots (Quadratics)
5. Trigonometry
- The Radian and Degree
- Sine, Cosine, and Tangent
- Cotangent, Secant, and Cosecant
- Problems with Right-Angled Triangles
- The Sine Rule
- The Cosine Rule
- Angles of Elevation, Depression, and Coordinates
- 3-Dimensional Trigonometry
- The Area of a Triangle (Trigonometry)
- Graphing Trigonometric Equations
- Trigonometric Identities
- Basic Trigonometric Equations
- More Complicated Trigonometric Equations
6. Probability & Statistics
- Introduction to Probability Notation
- Sample Spaces
- Conditional Probability
- Discrete Random Variables
- Expected Value, Mean, Variance, and Standard Deviation
- Bernoulli Sequences and the Binomial Probability Distribution
- The Graph, Expectation, and Variance for Binomial Distributions
- Finding the Sample Size of a Binomial Distribution
- Continuous Random Variables
- Measures of Spread
- Properties of the Mean and Variance
- The 68-95-99.7% Rule
- Determining the Normal Probability
- Sampling, Estimation, and Confidence Intervals
7. Sequences & Series
- What is a Series?
- Arithmetic Series
- Summing Arithmetic Sequences
- Geometric Series
- Summing Geometric Sequences
- The Infinite Sum of a Geometric Sequence
- Applying Sequences and Series
8. Calculus: Functions and Review
- What is a Function?
- Function Notation
- Polynomial Functions
- Introduction to Limits
- Review of the Gradient
- Log Laws and Index Laws
9. Calculus: Introduction to Differentiation
- Differentiation by First Principles
- Application of First Principles
- Rule for Polynomial Differentiation
- Derivatives of Negative Indices
- Derivative of Surd Functions
- The Chain Rule
- The Product Rule
- The Quotient Rule
- Differentiation of Exponentials
- Differentiation of Logarithms
- Differentiation of Trigonometric Functions
10. Calculus: Application of Differentiation
- Identifying Turning Points
- Finding x for a Given Gradient
- Equation of the Tangent
- Equation of the Normal
- Second Derivative and Concavity/Inflection
- Maxima and Minima
- Curve Sketching
11. Calculus: Integration
- The Rule for Integration
- Definite Integrals
- Indefinite Integrals
- Areas with Integration
- Areas of Compound Regions
- Integration by Substitution
- Integration by Parts
- Rotation Around the x-y Axis
- Integration of Trigonometric Functions
- Integration of Other Functions
12. Binomial Distribution & Further Probability
- Probability and Sample Spaces
- Venn Diagrams and Probability Notation
- Permutations
- Combinations
- Binomial Probability
Questions?
We are always happy to answer any questions you may have. Please do not hesitate to reach out.