Module Information
Course Delivery
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Assessment | Coursework Mark based on attendance at lectures and tutorials and submitted assignments | 20% |
| Semester Exam | 2 Hours (Written Examination) | 80% |
| Supplementary Exam | 2 Hours (Written Examination) | 100% |
Learning Outcomes
On successful completion of this module students should be able to:
1. identify simple loci analytically and geometrically;
2. find equations of angular bisectors;
3. determine lengths of tangents to a circle;
4. identify the type of a conic from its equation;
5. determine the equations of the tangents and normals to conics;
6. express the coordinates of a general point of certain curves parametrically;
7. use vectors to solve elementary problems in geometry;
8. compute scalar and vector products of two vectors;
9. compute scalar and vector triple products of three vectors;
10. determine the vector equations of lines and planes;
11. determine the angle between two planes and the shortest distance from a point to a plane;
12. solve elementary problems in kinematics.
Brief description
This module introduces some of the fundamental notions of geometry - points, lines, curves, planes and surfaces - analytically, in the language of coordinate geometry. Conics are classified in terms of their equations and geometric properties. The concepts of tangent and normal are developed.
Aims
To develop geometric intuition and the ability to view geometric problems analytically and vice versa.
Content
- COORDINATE GEOMETRY IN THE REAL PLANE: The straight line. Loci. Conics - particular forms and the general form. Identification of centres, foci and major and minor axes. The general equation of the tangent. Families of lines and conics. Parametric plane curves. Tangents and the use of derivatives. Polar coordinates.
- INTRODUCTION TO VECTOR METHODS: Unit vectors. Scalar and vector products, angles. Position vectors. Linearly independent vectors. Vector equations of lines and planes. Introduction to kinematics.
Module Skills
| Skills Type | Skills details |
|---|---|
| Adaptability and resilience | Completion of tasks (assignments) to set deadlines will aid personal development. |
| Creative Problem Solving | The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills. |
| Digital capability | Use of Blackboard and internet resources |
| Professional communication | Written answers to exercises must be clear and well structured. |
| Subject Specific Skills | Broadens exposure of students to topics in mathematics. |
Notes
This module is at CQFW Level 4