Err, no.
You can buy the book, and most students also pay by the hour -
don't pay up front, it's an unnecessary risk on numerous levels. The marginal saving is not worth the risk of losing that money: flying schools go bust with annoying regularity and you don't want them owing you money when you. I say again
pay as you go!!!.
Ask the school for a copy of the syllabus they're using and pay for it - expect to pay about £15. If they don't use a specific document - there's the AOPA/Pooleys book, Jeremy Pratt's book, Trevor Thom's book, PPLme, .... All perfectly good books, and all saying roughly the same things, so pick one you like.
4 un-logged hours, as I'm sure you really know, is very little although it's hopefully helped you to feel comfortable in the air. With a proper instructor you will be starting at square 1 and following the syllabus in full, because they daren't risk missing anything out. But, you will find as you review your logbook you'll sometimes do an exercise in the syllabus over several hours, and other times do several exercises in one hour. It really ain't linear.
If you are doing the NPPL(SSEA), the syllabus
here will give you a very good idea, or if the NPPL(M), the document
here; for the PPL(SEP),
here. But in all cases the books and DVDs that are available are likely to be much more informative than the basic lists in the published syllabi.
G