Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

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Pre-calculus is a rather difficult topic to define or describe. There’s a little bit of this, a lot of that, and a smattering of something else. But you need the mathematics considered to be pre-calculus to proceed to what changed me into a math major: calculus! Yes, believe it or not, I started out as a biology major — inspired by my high school biology teacher. Then I got to the semester where I was taking invertebrate zoology, chemistry, and calculus. (Yes, all at the same time.) All of a sudden, there was a bright light! An awakening! “So this is what mathematics can be!” Haven’t turned back since. Calculus did it for me, and my great preparation for calculus made the adventure wonderful.

Pre-calculus contains a lot of algebra, some trigonometry, some geometry, and some analytic geometry. These topics all get tied together, mixed up, and realigned until out pops the mathematics you’ll use when working with calculus. I keep telling my calculus students that “calculus is 60 percent algebra.” Maybe my figures are off a bit, but believe me, you can’t succeed in calculus without a good background in algebra (and trigonometry). The geometry is very helpful, too.

Why would you do 1,001 pre-calculus problems? Because practice makes perfect. Unlike other subjects where you can just read or listen and absorb the information sufficiently, mathematics takes practice. The only way to figure out how the different algebraic and trigonometric rules work and interact with one another, or how measurements in degrees and radians fit into the big picture, is to get into the problems — get your hands dirty, so to speak. Many problems given here may appear to be the same on the surface, but different aspects and challenges have been inserted to make them unique. The concepts become more set in your mind when you work with the problems and have your solutions confirm the properties.

This book contains 1,001 pre-calculus problems, their answers, and complete solutions to each. There are 16 problem chapters, and each chapter has many different sets of questions. The sets of questions are sometimes in a logical, sequential order, going from one part of a topic to the next and then to the next. Or sometimes the sets of questions represent the different ways a topic can be presented. In any case, you’ll get instructions on doing the problems. And sometimes you’ll get a particular formula or format to use. Feel free to refer to other mathematics books, such as Yang Kuang and Elleyne Kase’s Pre-Calculus For Dummies , my Algebra II For Dummies , or my Trigonometry For Dummies (all published by Wiley) for even more ideas on how to solve some of the problems.

Instead of just having answers to the problems, you’ll find a worked-out solution for each and every one. Flip to the last chapter of this book for the step-by-step processes needed to solve the problems. The solutions include verbal explanations inserted in the work where necessary. Sometimes, the explanation may offer an alternative procedure. Not everyone does algebra and trigonometry problems exactly the same way, but this book tries to provide the most understandable and success-promoting process to use when solving the problems presented.

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