Pre-Calculus for Senior High School – (PDF/EPUB Version)

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.