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.

AFQT scores are the primary measure of recruit potential. Figure 2.7 indicates the percentage of NPS recruits who scored at or above the 50th percentile (Categories I–IIIA) since FY 1973. Numerical data are in Appendix D, Table D-12. The drop in Category I–IIIA recruits after FY 1976 was due primarily to the miscalibration of the ASVAB. [1] In FY 1976, when new versions of the ASVAB were introduced, an error in calibrating the score scales made the new versions "easier" than the old versions (i.e., applicants received test scores higher than their actual ability). In FY 1980, an independent study of the calibration was made and the test was correctly calibrated. Then, Congress added legal provisions stipulating that no more than 20 percent of accessions could be in Category IV and that such accessions had to be high school diploma graduates. [2] However, as previously stated, Defense Planning Guidance decreases this limit even further, allowing no more than 4 percent of recruits to come from Category IV.
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Whereas recruits who join as officers tend to be upwardly-mobile,[14][15] most enlisted personnel have a childhood background of relative socio-economic deprivation.[16][17][18] For example, after the US suspended conscription in 1973, "the military disproportionately attracted African American men, men from lower-status socioeconomic backgrounds, men who had been in nonacademic high school programs, and men whose high school grades tended to be low".[14]
Capability development, which is often referred to as the military 'strength', is arguably one of the most complex activities known to humanity; because it requires determining: strategic, operational, and tactical capability requirements to counter the identified threats; strategic, operational, and tactical doctrines by which the acquired capabilities will be used; identifying concepts, methods, and systems involved in executing the doctrines; creating design specifications for the manufacturers who would produce these in adequate quantity and quality for their use in combat; purchase the concepts, methods, and systems; create a forces structure that would use the concepts, methods, and systems most effectively and efficiently; integrate these concepts, methods, and systems into the force structure by providing military education, training, and practice that preferably resembles combat environment of intended use; create military logistics systems to allow continued and uninterrupted performance of military organisations under combat conditions, including provision of health services to the personnel, and maintenance for the equipment; the services to assist recovery of wounded personnel, and repair of damaged equipment; and finally, post-conflict demobilisation, and disposal of war stocks surplus to peacetime requirements.
The Student ASVAB is the most flexible of the exams. It is typically provided to high school students to help them assess their skills, job prospects, potential military positions, or college majors. The ASVAB for students is essentially the same as the MET ASVAB exam, only students are not necessarily testing for positions within the military. The students’ school counselors examine their scores and help them decide on what to do after graduating from high school. This test is still an important component of a student’s education because it can help them identify their strengths and weaknesses and help set them on the right track for their future career goals.