# Gwybodaeth Modiwlau

Module Identifier
MA02610
Module Title
Foundations of Mathematics 1
2023/2024
Co-ordinator
Semester
Semester 1
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Problem sheets  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. evaluate powers of a number where the exponent is positive, negative, whole or fractional;
2. simplify algebraic expressions using the rules of exponents;
3. solve linear and quadratic equations;
4. use the function notation, y = f(x);
5. determine the inverse of a function;
6. sketch the graphs of linear and quadratic functions;
7. find the slope of a straight line given any two points on the line;
8. use both notations, f'(x) and dy/dx, for the derivative of a function;
9. differentiate simple polynomial functions and functions of the form f(x) + g(x), f(x)-g(x);
10. evaluate second-order derivatives;
11. describe the use of the exponential function in economic modelling;
12. sketch graphs involving the exponential function;
13. differentiate the exponential and natural logarithm functions;
14. evaluate logarithms in simple cases;
15. use the laws of logarithms to solve equations;
16. determine the annual percentage rate of interest given a nominal rate of interest;
17. find and classify the stationary points of a function;
18. find the maximum and minimum points of an economic function.

### Brief description

This module covers mathematical topics including functions, the concepts and rules of differentiation, optimization of functions of one variable, and integration.

### Aims

To introduce students to some of the elementary but essential mathematical concepts and skills.

### Content

1. ELEMENTARY ALGEBRA. Exponents. Polynomials. Factorization. Solution of linear and quadratic equations. Solution of simultaneous equations.
2. FUNCTIONS. Notation and definitions. Graphs of functions. Inverse functions. Examples.
3. DIFFERENTIATION. The derivative of a function. The derivative of a polynomial. Marginal functions. Higher-order derivatives.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Definitions and properties. Graphs of exponential and logarithmic functions. Derivatives. Solution of logarithmic equations. Interest compounding.
5. OPTIMIZATION OF FUNCTIONS OF A SINGLE VARIABLE. Local and global maxima and minima, points of inflection. Optimization of functions.

### 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 lectures.
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 N/A
Subject Specific Skills Broadens exposure of students to topics in mathematics
Team work Students will be encouraged to work together on questions during problem classes.

### Notes

This module is at CQFW Level 3