Essential Algebra for Advanced High School Math and SAT

The Essential Algebra for Advanced High School and SAT is a 241-page math book in the Mathematical Reasoning series and is an ‘essential’ resource for building the foundation of ongoing excellence in mathematics. This book offers an in-depth approach to teaching math skills focusing on important algebraic concepts that are vital to a student’s success in advanced high school mathematics. This book is broken down into ten algebraic concepts:

• Understanding Terms and Order of Operations


• Understanding the Family of Real Numbers


• Rationals and Irrationals


• Working with Terms and Polynomials


• Polynomial Division, Factoring, and Rational Expressions


• Solving Equations and Inequalities


• Ratio, Proportion, and Percent


• How Algebra is Used in Geometry


• Understanding Functions


• Working With Quadratic Equations and Functions

Algebra is essentially the language of all advanced mathematics courses. It is generalized arithmetic, so the rules that apply when we are working with number and fraction operations—including the knowledge of factors and multiples—also apply when we are working with algebra.

Without this knowledge and these skills, students often struggle or even fail in advanced mathematics courses. Imagine a good high school student who sees a problem like 3•x•y•4 and hesitates to write 12xy because he or she is unsure of the rules that govern multiplication. Or they don't understand how to add 2x to 1/4y to combine it into one entire fraction. Or why –62 is different than (–6)2. It is easy to see that not having a strong understanding of the foundational rules of algebra can stop even the smartest students from succeeding in advanced high school math courses.

The lessons within this book teach fundamental arithmetic principles that govern algebra so that students can apply them, as needed, in advanced mathematical courses and in life. The book begins with the definition of a "term" and the facts of when you can cancel and when you cannot. It discusses the importance of factors and multiples and integer rules. It teaches addition, subtraction, multiplication, and division of fractions – not by doing the problems up and down like they are mostly done in elementary school, but by doing them sideways just like they are done later in algebra and in higher-level math. This helps make everything so much easier down the road!

The explanations are clear and followed with basic step-by-step procedures to show students how to master and apply those fraction concepts, negative number operations, exponent rules, work with square roots, and doing real life percent problems with charts and tables, just like those on the SATs. Concepts are purposefully repeated in different settings, so students will keep re-applying what they learn throughout the book. The language is friendly to put students at ease and increase their confidence while learning concepts that are often confusing.

This book reviews the necessary reading strategies needed to translate word problems, but it is not the primary focus of the book. The book Understanding Algegra I  (also part of the Mathematical Reasoning series) devotes large sections to many types of word problems and many useful strategies if deeper study of this topic is desired.

In the last two chapters of the book, students are asked to apply the algebra they have just learned to an overview of problems in geometry. Also included is review of some important techniques that students frequently struggle with involving both linear and quadratic equations.

This book also includes an appendix of topics used as a review, but also includes new information that can be considered enrichment for students who may want to learn more. Teaching support and answers are also included.