Year 11 Advanced Lessons - Mathematics.com.au

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Year 7 and 8 Year 9 and 10 Year 11 and 12 General Year 11 and 12 Advanced

Year 11 and 12 Advanced Lessons

Algebra & Number

Basic Arithmetic & Algebra
1. Calculator Work
2. Percentages
3. Recurring Decimals
4. Surds
5. Simplifying Algebraic Expressions
6. Factorisation
7. Multiplication & Division Of Algebraic Fractions
8. Addition & Subtraction Of Algebraic Fractions

Equations
1. Linear Equations & Inequations
2. Absolute Value Equations & Inequations
3. Equations After Substitution
4. Quadratic Equations
5. Completing The Square
6. Solving Problems Using Quadratic Equations
7. Quadratic Inequations
8. Simultaneous Equations
9. Solving Problems Using Simultaneous Equations
10. Quadratic Identities
11. Equations Reducible To Quadratics

Geometry

Plane Geometry
1. Review Of Earlier Work
2. Isosceles Triangles
3. Polygons & Angles
4. Special Quadrilaterals
5. Numerical Examples
6. Congruent Triangles
7. Similar Triangles
8. Setting Out Proofs

Coordinate Geometry
1. Midpoint, Distance, Gradient Review
2. Mixed Examples I
3. Perpendicular Distance
4. Point-Gradient Formula
5. Mixed Examples II
6. Exam Type Questions

Functions

Real Functions
1. Introducing Functions
2. Domain & Range
3. Odd & Even Functions
4. Absolute Value Graphs
5. Regions Of The Number Plane

Quadratic Functions & Parabola
1. Axis Of Symmetry & Vertex
2. The Discriminant
3. Sum & Product Of Roots
4. Locus
5. The Parabola: Vertex, Focus & Directrix

Log & Exponential Functions
1. Logarithmic Rules & Logarithmic Equations
2. Exponential Equations
3. Differentiation
4. Integration
5. Miscellaneous Integration
6. Area Between Curves
7. Curve Sketching

Calculus

Introductory Calculus
1. Limits
2. Differentiation By First Principles
3. Differentiation Laws
4. Differentiation Methods
5. Further Differentiation
6. Tangents & Normals

Applications Of Calculus
1. Stationary Points
2. Inflexion Points
3. Curve Sketching
4. Graphs & Their Derivatives
5. Maxima & Minima Problems

Integration
1. Integration
2. Further Integration
3. Equation Of A Curve Given Its Derivative
4. Areas Enclosed By The X-Axis
5. Simpsons Rule & Trapezoidal Rule
6. Areas Enclosed By The Y-Axis
7. Area Between Curves
8. Miscellaneous Integration Involving Areas
9. Volumes Of Revolution

Calculus & The Physical World
1. Distance, Velocity & Acceleration
2. Motion Involving Trigonometric Functions
3. Rates
4. Growth & Decay

Trigonometry

Basic Trigonometry
1. Right Angled Triangles
2. Angles Of Elevation & Depression
3. Exact Trigonometric Ratios
4. Trigonometric Identities
5. Trigonometric Equations
6. The Sine Rule
7. The Cosine Rule
8. Area Of A Triangle
9. Compass Bearings
10. Problems Involving Trigonometry
11. Graphs Of Trigonometric Functions

Trigonometric Functions
1. Radian Measure & Solving Trigonometric Equations
2. Trigonometric Differentiation
3. Integrating Trigonometric Functions
4. Sectors & Segments
5. Small Angle Results
6. Sketching Trigonometric Functions

Series & Probability

Series & Their Applications
1. Arithmetic Progressions
2. Geometric Progressions
3. Sigma Notation
4. Mixed Problems
5. Compound Interest
6. Superannuation
7. Time Payment

Probability
1. Using Lists & Venn Diagrams
2. Tree Diagrams
3. Raffle-Type Questions

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