Module Information

Module Identifier
Module Title
Mathematics Tutorial
Academic Year
Semester 2 (Taught over 2 semesters)
Reading List
Other Staff

Course Delivery



Assessment Type Assessment length / details Proportion
Semester Assessment Coursework  Mark based on attendance at tutorials and submitted assignments  30%
Semester Exam 2 Hours   Exam  (Written Examination)  70%
Supplementary Exam 2 Hours   Written Examination  100%

Learning Outcomes

On successful completion of this module students should be able to:

Solve polynomials of small degree; obtain and use relations between the roots and coefficients of polynomials.

Simplify algebraic expressions and inequalities.

Compute with trigonometric functions and use trigonometric identities.

Apply basic set operations; explain the difference between integers, rational and irrational numbers.

Manipulate vectors and evaluate their products. Translate between Cartesian and polar coordinates.

Represent complex numbers in different forms and apply algebraic operations to them.

Define a function and its domain and range; sketch graphs of simple functions.

Determine properties of sequences and series

Manipulate expressions involving the exponential and logarithmic functions.

Prove simple theorems about numbers.

Brief description

The module consists of a weekly two hour problem class, throughout both
semesters, at which students are required to work, individually or in groups, on
set problems. Difficulties arising in other Year 0 mathematics modules will be
discussed and resolved.


The aims of this module are to increase awareness in the technical skills
associated with basic mathematics; to develop analytical skills; to develop an
appreciation of the need for logical order and precision; to increase confidence
in understanding and solving mathematical problems.


1. BASIC ALGEBRA, SETS, INEQUALITIES. Manipulation of mathematical expressions, introduction to set theory, number sets, solving inequalities.

2. SURDS, LOGARITHMS, EXPONENTIAL FUNCTION. Simplification of surds, laws of exponentials and logarithms.

3. POLYNOMIALS. Factors and roots. Completing the square, Vieta's Theorem, Factor and Remainder Theorems.

4. TRIGONOMETRY. Trigonometric functions and identities. Graphs of trigonometric functions. Trigonometric equations.

5. FUNCTIONS AND SEQUENCES. Domain, codomain, image, composition and inverse of functions. Arithmetic and geometric sequences and series.

6. COORDINATE AND VECTOR GEOMETRY. 2D and 3D vector arithmetic. Cartesian and polar coordinate systems.

7. COMPLEX NUMBERS. Complex number representations. Real and imaginary parts, modulus and argument, De Moivre's Theorem, complex roots.

8. PROOFS. Introduction to proofs in number theory.

Module Skills

Skills Type Skills details
Application of Number Required throughout the course.
Communication Written answers to exercises must be clear and well structured.
Improving own Learning and Performance Students are expected to develop their own approach to time-management regarding the completion of assignments on time and preparation between classes.
Information Technology Use of Blackboard
Personal Development and Career planning Completion of task (assignments) to set deadlines will aid personal development.
Problem solving The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Research skills
Subject Specific Skills Broadens exposure of students to topics in mathematics.
Team work


This module is at CQFW Level 3