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Fundamentals II
Fundamentals II Course Overview
Fundamentals II is an intensive program designed for students who have completed Fundamentals I or have a solid grounding in basic algebra, and are preparing for senior mathematics. It bridges the gap between junior and senior maths, covering the essential techniques that Year 11 and 12 courses assume students already know.
Senior mathematics moves fast. From the first week, courses like Mathematical Methods, Specialist Mathematics, and Extension 1 expect fluency with quadratics, index laws, surds, logarithms, and basic trigonometry. Students who aren't comfortable with these topics don't just struggle—they fall behind while simultaneously trying to learn new content. This course prevents that.
Fundamentals II is the recommended preparation for Advanced Mathematics and senior calculus courses. Students receive a detailed course book with explanations, practice questions, and worksheets—an excellent reference throughout Years 11, 12, and beyond.
🔢 Years 8–12
📖 Course book included
👥 Small group tutorials
📝 Examinations
Who Is This Course For?
This course is ideal for students preparing for senior mathematics who want to solidify their foundational skills:
Year 9 Students
Year 10 Students
Year 11 & 12 Students in Advanced Mathematics
Advanced Year 8 Students
What You'll Learn
The course bridges junior and senior mathematics, covering the essential techniques that Year 11 and 12 courses assume students already know:
1. Review of Numbers, Surds and Index Laws
- Adding and subtracting fractions
- Multiplying and dividing fractions
- Introduction to proportions and using proportions
- Introduction to surds and surd laws
- Simplification of surds
- Rationalising the denominator and numerator
- Rationalising the denominator using the difference of two squares
2. Index Laws
- Index Notation
- Index Laws 1, 2, 3, 4 and 5 + the zero power rule
- Negative indices and the fractional representation
- Scientific notation
- Operating with fractional indices and surds
- Operations with indexes and surds
3. Measurement
- Length and perimeter
- The perimeter of triangles
- Area and Volume
- Area of triangles
- Volume and surface area of 3D shapes
- Introduction to π
- Area of a circle
- Perimeter of a circle
- Volume of a cylinder
- Volume of cones
- Volume of spheres
- Surface area of spheres
- Application of measurement
4. Financial Mathematics
- Introduction to money
- Introduction to investments
- Percentage increase and decrease
- Simple interest
- Compound interest
- The problem with credit
- The benefits of investing early
5. Trigonometry and Pythagoras' Theorem
- Introduction to triangles and angles
- The internal sum of a triangle
- Introduction to Pythagoras' theorem
- Introduction to sine, cosine and tangent
- Solving for triangle side lengths
- Solving for angles
- Angle of elevation, angle of depression and bearings
- The sine rule
- The cosine rule
- Graphing trigonometric functions
6. Introduction to Functions and Graphs
- Introduction to linear relationships
- How to graph straight lines
- Introduction to the gradient
- Introduction to the gradient-intercept form (y = mx + c)
- Solving for the equation of a straight line (y = mx + c)
- Solving for the equation of a straight line (General form)
- Finding the midpoint of a line
- The definition of parallel lines
- The definition of perpendicular lines
- Solving for the length of a line segment
7. Algebraic Techniques
- Overview of algebraic terminology (terms, variables and coefficients)
- Expanding brackets, binomials and trinomials
- Expanding brackets
- Factorising simple algebraic fractions
- Factorising binomials and trinomials
- Factorising perfect squares
- Factorising the difference of two squares
- Completing the square
- Complicated algebraic factorisation
- Factorising surds and fractional indices
8. Linear Equations
- Solving simple linear equations
- Solving equations with multiple brackets and pronumerals
- Introduction to simultaneous equations
- Solving simultaneous equations by elimination
- Solving simultaneous equations by substitution
- What does a simultaneous equation represent? The intersection of two lines.
9. Quadratic Equations
- Comparing quadratic and linear equations
- Techniques to solve quadratic equations
- The X and Y intercepts of a quadratic equation
- The intersection points between a quadratic and straight lines
- Sketching quadratic equations
- Solving worded problems algebraically
Questions?
We are always happy to answer any questions you may have. Please do not hesitate to reach out.