Practice to Mastery

Many students understand their precalculus lessons and still get stuck on the test. They know the unit circle, they recognize the formulas, and then a problem changes one number or one condition and they don't know where to start. Practice to Mastery: Solving Classic Problems in High School Precalculus is built to close that gap between understanding the ideas and actually solving problems.

Instead of hundreds of unrelated exercises, this book takes the small number of classic problems that the whole course rests on and works each one all the way through. Its 14 chapters cover the full high school precalculus course: functions, transformations of functions, polynomial and rational functions, exponential and logarithmic functions, angles and the unit circle, graphs of trigonometric functions, trigonometric identities and equations, triangles and vectors, polar coordinates and complex numbers, systems of equations and matrices, conic sections, sequences and series, counting and probability, and a final chapter on limits that builds a bridge to calculus.

Each chapter presents three or four core problems, 44 in all, and every one is taught in the same eight sections:

- The Problem

- What Kind of Problem Is This? - how to recognize the type from its wording and setup

- The General Approach - a step-by-step method that works for the whole family of problems

- Step by Step - a complete solution with nothing skipped

- Now Change One Thing... - variations that change one condition at a time

- More Than One Way - a second method, and when each one saves effort

- Watch Out - the mistakes students make most often

- The Takeaway - what to carry forward

The variations are the heart of the book. One framework is followed from start to finish, so students see which steps stay the same and which ones must change, and learn to handle unfamiliar problems on their own.

Inside you will also find:

- Clear, friendly explanations written for students working on their own, with every step shown

- Common formulas, including the change-of-base formula, the sum and difference formulas, the Law of Sines and the Law of Cosines, the sum of a geometric series, and the Binomial Theorem, derived rather than simply stated, so students can rebuild them if they forget

- Notes on notation that varies between textbooks, such as sin⁻¹x and arcsin x and the different ways to write combinations

- 167 original black-and-white figures, including function graphs, the unit circle, triangles and vectors, polar curves, conic sections, and tree and Venn diagrams

- Original problems and data throughout, with every computation checked

This book is for students taking precalculus, honors precalculus, or AP® Precalculus, for students preparing to move on to calculus, and for parents, tutors, and teachers who want a clear, structured guide to the problems that matter most. It does not replace a textbook or a teacher; it shows students how to think a problem through.

A Chinese-language edition, 美高预备微积分解题手册 (A Bridge to Solving Classic Problems: High School Precalculus), is also available.

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.