Possibly you are doing it the wrong way round. You should list the main words and get her to learn them, as many as she can retain a week--say, ten. Then after a couple of weeks, give her the exercise in the book from which you have derived the words to see if she has retained them, as well as regular tests on them. I would use Schonell, however, rather than the AE words. Schonell 3rd includes all the main words from the AE books without the padding!
You are right. Intelligent children can deduce the words in this situation, but are unlike to retain them without a conscious effort. If they are the rare children who can pick up words after just one telling, then they won't need to do these books at all because they will already have a sizeable vocabulary.
Also, in the synonyms test, they sometimes see if the children know their parts of speech so they might give, let's say, the word definite with a choice of : certainty, probable, rare, positive. They need to know or, at the very least, have a feel for parts of speech in order to reject certainty as a noun and go for positive as an adjective.