slug
IFYSOW
type
Post
status
Published
category
A-Level 9231
date
Mar 5, 2026
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Lectures
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IFY Further Mathematics
Scheme of Work (8 Weeks)
Teacher: Liao Shuguang
Course: IFY Further Mathematics
Duration: 8 Weeks
Lessons per week: 3
Total lessons: 24
Module 1
Complex Numbers and De Moivre’s Theorem
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 1 | L1 | Complex Numbers (Polar & Exponential Form) | Convert between Cartesian, polar and exponential forms | Argand diagram exploration (GeoGebra) | Practice problems |
Week 1 | L2 | De Moivre’s Theorem | Use De Moivre’s theorem to compute powers of complex numbers | Derivation + exam-style examples | Problem set |
Week 1 | L3 | Trigonometric Identities from De Moivre | Expand complex expressions to derive trig identities | Symbolic derivation activity | Identity exercises |
Module 2
Roots of Unity
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 2 | L4 | Roots of Unity | Find nth roots of unity | Argand diagram visualisation | Practice questions |
Week 2 | L5 | Solving Complex Equations | Solve equations of form zn=ωz^n = \omegazn=ω | Worked examples | Problem set |
Week 2 | L6 | Geometry of Roots | Interpret roots geometrically | Polygon patterns exploration | Extension problems |
Module 3
t-Formula (Trigonometric Substitution)
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 3 | L7 | Deriving t-Formula | Derive substitution t=tan(θ/2)t = \tan(\theta/2)t=tan(θ/2) | Guided derivation | Exercises |
Week 3 | L8 | t-Formula Identities | Transform trig identities using substitution | Algebraic manipulation | Practice questions |
Week 3 | L9 | Solving Trig Equations | Solve equations using t-substitution | Exam-style problem solving | Assignment |
Module 4
Advanced Coordinate Geometry
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 4 | L10 | Parabola | Focus-directrix definition | Graph visualisation | Practice |
Week 4 | L11 | Rectangular Hyperbola | Properties and equations | Graphing investigation | Exercises |
Week 4 | L12 | Tangents and Normals | Tangent & normal equations | Calculus application | Problem set |
Module 5
Advanced Integration
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 5 | L13 | Improper Integrals | Evaluate integrals with infinite limits | Limit concept discussion | Practice |
Week 5 | L14 | Reduction Formula | Derive reduction formulae | Proof activity | Exercises |
Week 5 | L15 | Reduction Applications | Apply reduction formulae | Problem solving session | Assignment |
Module 6
Inverse Functions and Hyperbolic Functions
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 6 | L16 | Inverse Trigonometric Derivatives | Differentiate inverse trig functions | Graph interpretation | Exercises |
Week 6 | L17 | Hyperbolic Functions | Understand sinh, cosh, tanh | Graphing activity | Practice |
Week 6 | L18 | Integrals with Inverse Functions | Integrate inverse/hyperbolic functions | Exam practice | Assignment |
Module 7
Applications of Integration
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 7 | L19 | Arc Length | Calculate curve length using integration | Geometric interpretation | Exercises |
Week 7 | L20 | Surface Area of Revolution | Surface area generated by rotation | Visual modelling | Problem set |
Week 7 | L21 | Leibniz & L’Hôpital | Product differentiation and limits | Worked examples | Practice |
Module 8
Differential Equations
Week | Lesson | Topic | Key Learning Objectives | Activities | Homework |
Week 8 | L22 | First-order ODE | Integrating factor method | Guided problem solving | Exercises |
Week 8 | L23 | Second-order ODE | Solve homogeneous equations | Characteristic equation | Practice |
Week 8 | L24 | Non-homogeneous & Coupled ODE | Advanced differential equation models | Application discussion | Final assignment |
Assessment Plan
Assessment Type | Week | Description |
Formative assessment | Weekly | Short quizzes and in-class questions |
Homework assignments | Weekly | Problem sets |
Mid-module test | Week 4 | Coordinate geometry and complex numbers |
Final assessment | Week 8 | Comprehensive test |
Teaching Resources
- GeoGebra / Desmos
- Exam past papers
- Graphing calculators
- Interactive whiteboard
- 作者:现代数学启蒙
- 链接:https://www.math1234567.com/article/IFYSOW
- 声明:本文采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。
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