Overview
Further Mathematics develops algebraic, analytical, graphical, numerical, and applied techniques required for advanced study in calculus, applied mathematics, statistics, physics, economics, and computing. Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions; transformations and composition; complex numbers; systems of equations; vectors; sequences and series; limits and continuity; and introductory differential and integral calculus.
Students apply differentiation to rates of change and optimization, and integration to area and accumulation. Selected topics in matrices, parametric equations, differential equations, and mathematical modelling extend the course according to programme requirements. Emphasis is placed on selecting efficient methods, interpreting models, evaluating assumptions, and communicating solutions using accurate notation and justified reasoning.
Learning Outcomes
- Analyze and graph families of polynomial, rational, exponential, logarithmic, and trigonometric functions using symbolic, graphical, and numerical methods.
- Manipulate and solve equations, inequalities, and systems using efficient algebraic and analytical techniques.
- Apply transformations, composition, inverse functions, complex numbers, vectors, sequences, and series to solve mathematical problems.
- Evaluate limits and continuity and apply differentiation to rates of change, curve analysis, and optimization.
- Apply integration techniques to determine areas, accumulation, and solutions to standard applied problems.
- Construct and interpret mathematical models, and evaluate their assumptions, limitations, and suitability for stated applications.
- Select and justify appropriate techniques for unfamiliar problems and present solutions with correct notation, logical structure, and mathematical reasoning.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 3 hours | Weekly | All semester |
| Tutorial | 2 hours | Weekly | All semester |
| Lab | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Problem-solving assignments (4 × 5%) | 20.00% |
| Quiz | Online quizzes (5 × 2%) | 10.00% |
| Test | Mid-semester test | 20.00% |
| Deliverable | Applied mathematical modelling project | 15.00% |
| Test | Practical problem-solving test | 15.00% |
| Exam | Final examination | 20.00% |
Prerequisites
- Requirement 14 NCEA Level 2 Mathematics credits, externally assessed
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.
