Your CV should always be accompanied by a cover letter. The cover letter may be typed or handwritten, unless specified handwritten, consider typed as it is much easier to read.
For specific advice for mature students, check the Prospects website.
Tips for Compelling Cover Letters:
Your cover letter's only job is to get your CV read.
Always written to a named person. You know their names and titles as you've done the research!
You must inspire and grab their attention in 3-4 paragraphs.
You need to round it off with a call to action that is polite and firm but not pushy.
Your letter should project a professional image and can be structured as follows:
Introductory paragraph, outlining who you are and what you are applying for. If someone has referred you to the company, mention them by name here.
Outlines why you are interested in the job and the company. Highlight your particular qualifications / skills and experience or competencies in line with what they are looking for. Tell the company/organisation you have what they want.
Final paragraph express your interest in helping the company do more and the part you would play in their ongoing success. Convey to them you want to work for them not just anyone in the industry. Finally round it off by thanking the reader for taking the time to consider your application and advising of your availability for interview.
Keep a copy of the letter for reference.