# Gwybodaeth Modiwlau

Module Identifier
MA01020
Module Title
Mathematics Tutorial
2022/2023
Co-ordinator
Semester
Semester 2 (Taught over 2 semesters)
Other Staff

#### Assessment

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 completion of this module, students should be able to:
1. solve certain polynomials of small degree;
2. obtain and use relations between the roots and coefficients of polynomials;
3. simplify algebraic expressions and inequalities;
4. compute with trigonometric functions and use trigonometric identities;
5. explain the difference between integers, rational and irrational numbers;
6. manipulate complex numbers using operations of algebra;
7. define a function and its domain and range;
8. manipulate expressions involving the exponential and logarithmic functions;
9. differentiate polynomials, logarithmic and exponential functions;
10. integrate polynomials and calculate areas.

### 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.

### Aims

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.

### Content

1. POLYNOMIALS. Factors and roots. The Remainder Theorem. Relations
between roots and coefficients of a polynomial. Inequalities.

2. TRIGONOMETRY. Trigonometric functions and identities. Graphs of
trigonometric functions.

3. REPRESENTATION OF NUMBERS. Natural numbers, integers, fractions,
decimals, the law of indices, exponents, logarithms.

4. COMPLEX NUMBERS. Real and imaginary parts, modulus and argument,
representation on the Argand diagram.

5. FUNCTIONS. Definition of a function. Domain, range. Exponential and
logarithmic functions. Inverse functions.

6. CALCULUS. Introduction to curves, tangents and the derivative of a
function, the rules of differentiation, rates of change. Integration as
anti-derivative. Calculating areas by integration.

### 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

### Notes

This module is at CQFW Level 3