Are we talking about a digital zoom or pre-digital as in film (Remember that stuff?) Also is the lens manual or autofocus?
One of my pet hates is that the DOF Scale on digital zoom lenses is ether none existant or less than useless. To be fair the problem really started with autofocus film lenses anyway, when the DOF Scale suddenly began to disappear.
Anyway I have two zoom lenses the 17-85mm EF-S and the 100-400L and neither has any DOF Scale at all! Even my 50mm 1.4 only has a DOF Scale with a marking for f32, so it's pretty useless anyway.
It's almost impossible to answer your question, good as it is, without seeing a pic of the lens markings. In the pre autofocus days you got a continuous curved red line extending down the lens barrel to show the changing infra red index mark at various focal lengths and often two others, usually white, to show the DOF index marks for differing focal lengths. It's interesting to see you say that zooms 'usually' have a DOF Scale, as it's been my experience that very few have since the inception of autofocus when we suddenly got that silly little window to view the distance scale through.
No doubt Canon and Nikon et al would tell you to use the DOF preview button, but I far preferred being able to set the hyperfocal distance using a proper DOF Scale showing ALL apertures. It's quite probable also that the lens manual has DOF tables in it, or the manufactures will publish them separately, but it's no substitute for a proper scale on the lens barrel which is a really sad loss IMO!