Much of the verbal section of a standardized test is a test of the student's vocabulary. If you know what the words mean, you will easily be able to understand questions that ask for the opposites or the synonyms, and you will understand the analogies. Likewise, if you are unsure of the meaning of the words, you may not even be able to choose an answer. Standardized test books have lists of commonly tested words for the student to study. Flash cards or writing definitions are effective ways to learn new words; however, you must know how to use these words in sentences as well. Be sure to learn the word's part of speech as well as any secondary definitions.
The math portion of standardized tests often involves complicated problems that are really testing basic math skills. Brush up on fractions, decimals, positive and negative integers, basic geometry rules, square roots and story problem language. These will all come in handy when trying to solve a problem that asks for knowledge such as complementary and supplementary angles. A student who has brushed up on math vocabulary and skills will find the math section much easier.
Most standardized tests include an essay portion. In this section, the student will be asked to answer a theoretical question using examples from history and/or literature. Walk into the test with a couple of historical and literary examples already in mind, especially examples that would work with many types of questions. For example, a play like Shakespeare's "Romeo and Juliet" has many thematic ideas present in the story.
Taking practice tests will ensure that you know the directions for each sections, the types of questions you will face and the ones that pose the most difficulty (see Reference 2). To study without having to buy materials, search online for sample questions from whichever standardized test you are scheduled to take.