101 Involved Algebra Problems with Answers

Book Description

Sharpen your algebra skills by solving 101 “involved” algebra problems. This book includes separate sections of answers, hints, and full solutions. Prerequisites include multiplying expressions with square roots, systems of equations, the quadratic formula, the equation for a straight line, power rules, factoring, and other standard algebra techniques. A variety of problems are included, such as:

• systems of equations (many are nonstandard, including a quadratic term or a reciprocal, for example)
• simplifying expressions or solving equations that feature square roots
• applying algebra to derive equations
• variables in the denominator
• rules for exponents
• inequalities
• the equation for a straight line
• multiplying, distributing, or factoring expressions
• applications of algebra (such as in classic physics problems)
• transformations of variables
• exposure to techniques such as completing the square, partial fractions, or separation of variables
• cross multiplying
• ratios
• rationalizing the denominator and multiplying by the conjugate

This book is NOT indented to “teach” algebra (though the solutions may be instructive), but is designed to offer practice with a variety of algebra skills (which most students could benefit from) for students who are familiar with the skills listed. The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving algebra problems.

中文：

书名：101 Involved Algebra Problems with Answers

通过解决101道“复杂”的代数问题来磨练你的代数技能。本书包括答案、提示和完整解决方案的单独部分。先决条件包括与平方根相乘的表达式、方程组、二次公式、直线方程、幂规则、因式分解和其他标准代数技巧。其中包括各种问题，例如：

• 方程组(许多是非标准的，例如，包括二次项或倒数)
• 简化以平方根为特征的表达式或求解方程
• 应用代数推导方程
• variables in the denominator
• 关于指数的规则
• 不等式
• 直线的方程式
• 对表达式进行乘法、分布或因子分解
• 代数的应用(如在经典物理问题中)
• 变量的变换
• 接触一些技巧，如完成平方、部分分数或分离变量
• 交叉乘法
• 比率
• 使分母有理，并乘以共轭

这本书并不是为了“教授”代数(尽管其解决方案可能具有指导性)，而是旨在为熟悉所列技能的学生提供各种代数技能的练习(大多数学生可能从中受益)。作者克里斯·麦克马伦(Chris McMullen)博士拥有20多年向物理专业学生教授数学技能的经验。他准备了这本提高你的数学流利性系列的练习册，分享他解决代数问题的策略。