I also agree that the AE Vocab books are very good.
However depending on the type of test, the child will need to memorise lists of vocab and synonyms too - you could take the main words from the books, or use other lists such as those in Schonell or First Aid English.
If you start Book 7 the November before the test, and complete 2 units per week, you should finish Book 12 before the test (assuming it is November, as it is here in Birmingham!). This is what I have been doing with the children I work with. And despite being very bright, many of the words even in Book 7 were new to them.
The real serious vocab starts in Book 9 to be honest, but for an average-vocab child, starting them straight on this could well traumatise them