To expand on @Albin's answer:
The HTML Agility Pack is a very robust, reliable way to handle this, and really is the way to go.
However, if and only if you can guarantee that your tag is a) already isolated in a string, and b) always of the same format as you've described, you can use this:
static void Main(string[] args)
{
var tag = @"<img src=""/Student/ExaminationImage?name=figuur"" />";
Console.WriteLine("Tag: {0}", tag);
var tagParts = tag.Split(new[] {'"'},StringSplitOptions.RemoveEmptyEntries);
var src = tagParts[1];
Console.WriteLine("Src: {0}", src);
var srcParts = src.Split('?');
Console.WriteLine("Parameters: {0}", srcParts[1]);
Console.ReadLine();
}