The results of the diagnostic will help you efficiently focus your study efforts (unlike the multiweek survey courses offered by, say, Kaplan or the Princeton Review).

Study your areas of weakness exposed by the diagnostic test. A good study manual or private tutor will likely provide sufficient instruction.

Note that having solid mathematical aptitudes will not necessarily get you a good score on a standardized test. These tests require special tactics and skills. You will find these tactics in any good study manual. Some of them are (in outline):

• Know your strengths and weaknesses. For each question, decide, after reading it, whether you will tackle it right away, save it for later, or eliminate obviously wrong answers and guess. Remember, you don’t have to work every question on a test to get a good score.

• Eliminate obviously wrong answers, especially those that are clearly too big or too small. Sometimes this strategy is called process of elimination.

• Practice using Desmos (for the SAT at least) or a calculator of your choice.

• On multiple choice questions, especially those involving algebra, use the answers to your advantage. There are at least two ways to do this: (i) on some questions, you can try the answers one by one to see which work; and (ii) on some algebra questions, a more elaborate technique involves substituting small numbers for the variables (like 2, 3, and 4), and sometimes larger numbers (10, 100), to find specific values for algebraic expressions. Then compare these values to those you get doing the same for the answers. Doing so, allows you to avoid some fairly complicated algebra.

• Slow Down! Again, you don’t have to work every question to get a good score (unless you are aiming for a perfect score). Take your time and make sure you work the easy questions correctly.

• Don’t be fooled by negatives: always take special care and check your work when working with problems involving negative numbers.

Once you have an understanding of all or most of the material covered by the exam, there is no substitute for working practice problems like those on the exam and taking practice tests. Just like you would practice a musical score before a major performance, you must practice taking exams.