I have already served in the military years ago. But I wondered if there was a primer that might have helped me improve my test scores. I think this book would help. Unfortunately it's hard to learn enough from a book to do well on the math and reading comprehension of the ASBAB test. Study hard in math and English class in high school. It's hard to cram from a book to pass a comprehensive test that covers many topics. I think it may give you a few extra points, however.
How good is your vocabulary? It’s never too late to brush up by using “vocabulary builders” you find on Google, reading a variety of books, manuals and magazines, and using practice tests to identify words that you’re not sure of. The WK section tests your word knowledge in several ways. First, it tests whether you can recognize correct and incorrect spellings of words. For this type of question, you may want to review words that are often spelled incorrectly, and make sure you know how to spell them. You will also need to know the definitions of words, and be able to use them in a sentence. The more you practice, the better you will be at automatically recognizing the right spelling of a word, and the easier it will be to know it’s precise meaning when it’s used in a sentence.

The four most important sections of the test—Word Knowledge, Paragraph Comprehension, Arithmetic Reasoning, and Mathematics Knowledge-make up your Armed Forces Qualifications Test (AFQT) score. Your AFQT score ranges from 0 to 100 and determines if you are able to enlist in the military and which jobs and programs you may qualify for when you are in.

Mathematics Knowledge tests the ability to solve problems by applying knowledge of mathematical concepts and applications. The problems focus on concepts and algorithms, and involve number theory, numeration, algebraic operations and equations, geometry, measurement and probability. Mathematics Knowledge is one factor that characterizes mathematics comprehension; it also assesses logical thinking.