Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

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One-thousand-one algebra problems: You must wonder what inspired such an endeavor.

One possibility for the inspiration is 1,001 Arabian Nights . (Okay, I’m really stretching here, but why not?) 1,001 Arabian Nights is a collection of stories and folk tales, compiled over several centuries. Likewise, 1,001 Algebra II Practice Problems For Dummies is a collection of math problems and explanations, and some of them involve interesting stories. This book wasn’t compiled over centuries (though my editors say it seemed to take that long), but the concepts and ideas involved took mathematicians centuries to develop.

Practice makes perfect. Unlike other subjects in which you can just read or listen and absorb the information sufficiently, mathematics takes practice. The only way to figure out how the different algebraic rules work and interact with one another is to get into the problems — get your hands dirty, so to speak. Many problems appear to be the same, on the surface, but different aspects and challenges have been inserted to make the different problems unique. The concepts become more set in your mind when you work with the problems and have the properties confirmed with your solutions.

Yes, whether it’s 1,001 algebra problems or 1,001 mathematical adventures, you’ll find them here. Enjoy!

This book contains 1,001 algebra problems, their answers, and complete solutions to each. There are 17 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. Other times the sets of questions represent the different ways a topic can be presented. In any case, you’re given brief instructions on doing the problems. And sometimes you’re given a particular formula or format to use. Feel free to refer to other algebra books, such as Algebra II For Dummies, to give you ideas on how to solve some of the problems.

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

This workbook is divided into two main parts: questions and answers. But you probably figured that out already.

The questions chapters cover many different topics:

Review of basic operations: The chapter takes you through some of the main concepts from Algebra I that are essential to working in Algebra II. You’ll find problems on powers of binomials and patterns in those powers. Solving linear equations and linear inequalities are fairly straightforward tasks, but it doesn’t hurt to review these types of problems to bring your skill level up to speed. Two other topics covered here are radicals and complex numbers. Each topic is special in its own way, but similarities crop up — such as the use of conjugates when simplifying the expressions.

Solving nonlinear equations and inequalities: Quadratic equations are by far one of the most used and referred-to equation types in secondary mathematics. That’s why you’ll find techniques such as factoring (with the multiplication property of zero), the square root rule, the quadratic formula, and completing the square to be the main methods covered here.Throw in some radical equations (square roots, cube roots) and rational equations (fractional expressions), and you have more tricks and techniques to practice so you can increase your repertoire.

Graphing lines: A line is a very basic structure and is easy to graph when you have two points. You’ll also find lines to graph when you’re given their equations, and then equations to write when you’re given information about the line. You get to consider lines that are parallel to one another and others that are perpendicular. The graphing part is simplified when you recognize the basics: a point on the line and the line’s slope.

Functions: A function in mathematics has a very specific definition. You can have a function when you have a relationship between sets of numbers and the relationship is described with mathematical operations. The operations take input values and produce output values based on the rules created with the operations. What’s particularly special about functions is that there’s only one output for every input. The functions you’ll find include linear, quadratic, polynomial, rational, exponential, and logarithmic. There are more functions out there, but you get a really good start right here.

Systems of equations and inequalities: When you have two or more statements or equations and want to know whether there are any solutions common to both or all of them at the same time, you’re talking about solving systems. The equations can be linear, quadratic, exponential, and so on. You’ll use algebraic techniques as well as matrices to solve some of the linear systems.

Sequences, sets, and counting techniques: When you’re getting ready for future studies in probability and statistics, you’ll want to practice problems involving lists, counting, sets, and set notation. You’ll use Venn diagrams and make lists of elements in sets. You’ll also write the terms in sequences and add up the terms in series.

This part provides not only the answers to all the questions but explanations of the answers as well. So, you get the solution, and you see how to arrive at that solution.