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ALGEBRA REVIEW AND WORKOUT: Rigorous Preparation for College Mathematics and SAT
Algebra has three governing aims:
- To develop strength in transforming, simplifying, and evaluating algebraic expressions,
and then to put that strength to work in equations and inequalities.
- To build mastery through a deliberate sequence of explanations, worked examples,
demanding exercises of increasing difficulty, and complete solutions.
- To serve students who are willing to work carefully, persist through "productive struggle," and replace fragile familiarity with dependable skill.
This book is not an attempt to survey every topic that has ever appeared under the name elementary algebra.
The aim is depth in the central skills: manipulating expressions, solving the principal families of real equations and inequalities, and explaining each step with precision. This deliberate concentration is not a rejection of breadth but preparation for it. The phrases
College Mathematics and
SAT Algebra in the subtitle identify important destinations for that preparation; they do not claim comprehensive coverage of either college mathematics or every topic classified under SAT Algebra.
The purpose is to make the central algebraic machinery dependable: reading, transforming, simplifying, and evaluating expressions, and solving equations and inequalities.
Many conventional textbooks present algebra in small, relatively isolated increments, often through short expressions and a narrow range of notation. Such practice has value, and this book also begins progressively; however, university texts soon require students to read and manipulate larger expressions, unfamiliar letters, nested structures, and summation,
product, factorial, and binomial notation without hesitation. The explanations and exercises here intentionally accustom readers to that complexity. The exposition follows the disciplined style of a university text while remaining concrete and accessible; it does not assume the abstraction or level of rigor of an advanced text.
The depth of coverage in this book goes well beyond that of a typical high-school elementary algebra course, for an important reason: modern university-level quantitative courses-such as linear algebra, calculus, probability, and statistics-assume that algebraic manipulation has become routine. Undergraduate and, to a much higher degree, graduate courses do not pause to repair students' weak elementary algebra; they use algebra while teaching something harder. For students preparing for advanced or graduate study in a quantitative field, this book is therefore not merely a review. It is important preparation.
The same fluency supports SAT Algebra preparation. This book does not reproduce the examination's format, teach test-taking strategies, or survey every tested topic. Typical SAT preparation emphasizes short, self-contained questions that are less structurally demanding than the sustained problems here. This book deliberately over-prepares: longer expressions, varied notation, and cumulative problems develop greater symbolic control and endurance. Students who handle this work should find corresponding SAT Algebra questions comparatively direct and approach them calmly and efficiently- mathematically "battle-hardened" for demands beyond those normally imposed by the examination.
In 8 chapters, the book covers algebraic expressions, equations and inequalities.
Each chapter has the following structure: Explanation, Examples of Worked Exercises and Exercises for Self-Practice. All Exercises have not only answers, but full solutions.
