Precalculus is the field of mathematics that contains the fundamental mathematical areas needed for the study of calculus. The two main subjects included in precalculus are algebra and trigonometry. Anyone planning on studying calculus or other branches of mathematically intensive fields (e.g., economics, physics or engineering) needs a strong background in precalculus. The good news is that you do not have to shell out hard-earned cash to obtain a working knowledge of precalculus.

Borrow some books on precalculus. Because precalculus is important in a wide range of disciplines, finding a calculus book in your local library will not require digging through a pile of books; any library with a math section should have books on precalculus. Do not limit yourself to borrowing books labeled as “precalculus” either, because books on algebra and trigonometry can teach you the same material contained in a precalculus book.

Take notes while reading. If your intent is to learn for free, you will need to return your library books. This means it is important for you to write down any important concepts or techniques you encounter in the books. You can return to your notes any time you need to review.

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Read before going to bed every night. The key to mastering a subject is studying frequently. If you study for two or three hours every night, you can become proficient in precalculus much more quickly than by studying without a schedule. Studying before sleeping also minimizes interference, allowing you to retain information more efficiently.

Audit precalculus courses. Universities and community colleges are two common places where precalculus courses are offered. These schools often allow auditing, i.e., attending class for free, provided that you obtain the professor’s permission. Even if you do not have a text and therefore cannot do the homework the professor assigns, you can still attend lectures and ask questions. Of course, taking notes in class is also advantageous.

Take practice tests to measure your skills. Test yourself with the tests and quizzes provided in your precalculus books. You can also find practice precalculus tests online (see Resources). If you find you are consistently wrong on certain types of problems, return to your notes to review.