Study-Unit Description

Study-Unit Description


CODE IFS0012

 
TITLE Coordinate Geometry, Matrices and Probability

 
UM LEVEL 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus

 
MQF LEVEL 4

 
ECTS CREDITS 5

 
DEPARTMENT Engineering and ICT

 
DESCRIPTION This study-unit introduces mathematical concepts to provide an introduction to two and three dimensional Cartesian coordinate geometry, polar coordinates and polar curve sketching, probability, matrices and transformations. The tools and techniques developed in this study-unit will enable the students to formulate a mathematical representation of a real life situation and to solve it by using rigorous methods and procedures.

Study-unit Aims:

To provide:

- A review of the Cartesian coordinate system and an extension of this through an elementary treatment of lines, circles and curves;
- An introductory overview to matrix algebra;
- An outline of the applications of coordinate geometry, polar coordinate geometry, probability and matrices.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:

- Describe the terms distances, angles, direction ratios, lines, and curves used in two and three dimensional Cartesian coordinate systems;
- Convert between Cartesian and polar coordinates;
- Sketch polar curves and determine the area enclosed by a polar curve;
- Describe the rules underlying the algebra of matrices;
- Recognise the matrices associated with standard linear transformations;
- Identify the relationship between composition of transformations and matrix multiplication;
- Describe the possible solution sets of a system of up to three linear equations in three unknowns and give their geometrical interpretation;
- Describe probability, permutations, combinations, probability trees and Venn Diagrams.

2. Skills:

By the end of the study-unit the student will be able to:

- Construct the Cartesian equations of lines, circles and curves;
- Convert between polar and Cartestian coordinates;
- Sketch polar curves and determine the area enclosed by a polar curve;
- Add, subtract, and multiply matrices and find the determinants of matrices;
- Find the inverse of a matrix both by elementary row operations and by the adjoint method;
- Find the matrix associated with a linear transformation and vice-versa;
- Solve a system of up to three linear equations in three unknowns by using matrices;
- Solve simple counting problems involving permutations and combinations;
- Calculate probabilities of an event, the complement of an event, and the union and intersection of two events;
- Use Venn diagrams and tree diagrams to solve problems in probability.

Main Text/s and any supplementary readings:

- L. Bostock and S. Chandler (2014). Mathematics The Core Course for A-Level. Stanley Thornes. ISBN: 9780859503068.
- L. Bostock, S. Chandler and C. Rourke (1982). Further Pure Mathematics. Stanley Thornes. ISBN: 9780859501033.

 
ADDITIONAL NOTES Please note that a pass in the Examination component is obligatory for an overall pass mark to be awarded.

 
STUDY-UNIT TYPE Lecture, Independent Study & Tutorial

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Oral and Written Exercises SEM2 No 20%
Examination [See Add. Notes] (2 Hours) SEM2 Yes 80%

 
LECTURER/S Agnetha Agius

 

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit