Pre-Calculus

General Introduction

The transition from algebraic mathematics to calculus is one that involves many new concepts for the student. Without a strong mathematical foundation, the student can have many struggles grasping these and performing well in calculus class. This makes pre-calculus a particularly important subject for serious math students. Pre-calculus takes the algebraic concepts that the student has learned and teaches them in more depth, as well as focuses them towards applications that students will need to understand for calculus.

Instruction Content

I. Number Systems, Polynomials, and Exponents

A. Sets of Numbers

B. Axioms for the Real Number System

C. Properties of Inequalities

D. Absolute Value

E. Complex Numbers

F. Order of Operations

G. Polynomials

H. factoring

I. Exponents

J. Rational and Radical Expressions

II. Equations and Inequalities

III. Systems of Equations and Partial Fractions

IV. Analytic Geometry and Functions

V. Algebraic Functions and Their Graphs

VI. Exponential and Logarithmic Functions

VII. Conic Sections

VIII. Trigonometric Functions

IX. Trigonometric Identities and Trigonometric Inverses

X. Sequences and Series

Homework and Tests 

Homework reviewing the topics covered will be assigned after each lesson. The assignments serve not only as an assessment of the student’s knowledge to make sure he/she fully understands the concepts, but also as a way to allow the student to put their knowledge into practice.

Students will be tested on each general topic before they move on to the next, in order to ensure they have the skills to progress to the next topic.

Prerequisites

Algebra I required. Algebra II recommended. Geometry recommended.