Tests are usually written. Assignments/assessment tasks are usually combined (e.g. the problem solving methodology requires analysis, design and evaluation which is usually handwritten). Development would probably be the primary phase where the digital part occurs.
It is a good habit to be able to do both. Exams are handwritten so you'll need to know how to handwrite anyway.
Given Units 1 & 2 are school-based (they still follow the study design but in terms of exams/assessment, this occurs at the school level rather than externally), teachers will usually develop their own case study/problem description or get it commercially. It's up to them what assessment is given to you and how it's administered (provided it meets the study design of course)
This might be of assistance to you:
http://vceit.com/wp/computing-units-1-and-2/Additionally, this outlines the 'advice to teachers' section which may provide some help:
http://www.vcaa.vic.edu.au/Pages/vce/adviceforteachers/computing/unit1_overview.aspxThanks