Jiazheng Chen
Many students understand calculus in class and still freeze on a test. They can explain that a derivative is a slope and an integral is an area, but when the function changes or one condition is different, they do not know where to start. Practice to Mastery: Solving Classic Problems in High School Calculus is built to close that gap. It is not a problem bank. Instead, it takes the 42 classic problems that the whole course rests on and works each one all the way through.The book covers all of high school calculus, the full scope of AP® Calculus AB and BC, in 12 chapters and three parts:Part I, Limits and Derivatives: limits and continuity, derivative rules, the chain rule and implicit differentiation, analyzing functions, and applications of derivatives.Part II, Integration and Differential Equations: the Fundamental Theorem, techniques of integration, applications of integration, and differential equations.Part III, Parametric Curves, Polar Curves, and Series: parametric, polar, and vector-valued functions; sequences and series; and Taylor series.Every core problem follows the same eight steps: The Problem; What Kind of Problem Is This?; The General Approach; Step by Step, with every derivative, substitution, and limit written out; Now Change One Thing..., which changes one condition at a time; More Than One Way; Watch Out, the mistakes students make most often; and The Takeaway. More than 150 variations show which steps stay the same and which have to change. Chapter 4 takes a single function and asks it every standard question, from tangent lines and extrema to concavity, graphing, the Mean Value Theorem, and L’Hôpital’s Rule. Chapter 8 takes a single region and finds its area and the volumes of the solids formed by disks, washers, and shells about different axes.Formulas and theorems are explained rather than simply stated, and their hypotheses are always spelled out, because many calculus mistakes come from using a theorem whose conditions are not met. Decimal answers are generally given to three places, places that need a graphing calculator are pointed out, and 65 original black-and-white figures appear where a graph, Riemann sum, solid of revolution, slope field, or parametric or polar curve is genuinely needed. All problems are original.Use it alongside any high school calculus course, Honors Calculus, or AP® Calculus AB or BC, for self-study, or for review before a unit test or final exam. A Chinese edition is also available as 美高微积分解题手册 (A Bridge to Solving Classic Problems: High School Calculus).AP® and Advanced Placement® are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, this product.
