# Module Information

#### Course Delivery

#### 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

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