Pre-Calculus for Senior High School

Pre-Calculus is a book tailored to comprehensively cover the needs of a present-day grade 11 student in the K to 12 curriculum. This specifi cally provides the necessary background and training essential to students in the Science, Technology, Engineering, and Mathematics strand. This book is organized into three units. Analytic Geometry. This unit provides a detailed discussion on two analytic geometry topics, namely conic sections and system of nonlinear equations. Properties of each type of conic and its degenerates are thoroughly presented through the discussion, examples, and answered exercises. The last section discusses system of nonlinear equations and explains how this system can be solved through substitution and elimination methods, and how the solution is verifi ed through graphs. This chapter also touches on the solution of situational problems using conic sections and systems of nonlinear equations. Sequences, Series, and Mathematical Induction. This unit opens with a general discussion of what sequences and series are, and their different representations. This is followed by an introduction to the Principle of Mathematical Induction which will serve as basis for the proofs of theorems in the succeeding sections. Arithmetic and Geometric sequences and their corresponding series, and the expansion of a power of a binomial and how this can be performed using the Pascal’s Triangle are the focus of the subsequent lessons. This unit is stand-alone and can be discussed independent of Analytic Geometry and Trigonometry. Trigonometry. Unit 3 gives detailed discussions about angles and the circular function values at these angles. These are supplemented with the properties and identities involving circular functions and their inverses. Applications of these concepts are illustrated in several real-world problems which are included in this unit.