Welcome to On Ramps College Algebra

As the name "Pre-calculus" indicates, this high level course is designed to prepare students for calculus. It is an in-depth study of functions (including trigonometric functions) and relations and their transformations, sequences and series, and additional mathematical representations. Students taking this rigorous course should have a strong background in both algebra and geometry. Our curriculum is grounded in the updated TEKS and will be taught from a curriculum which follows the TEKS. It will be imperative for each student to have and maintain a binder. It's strongly recommended students have a TI-Nspire calculator (or equivalent) to use outside of class. Below are the topics covered in standard Precalculus courses. The sequence may vary to align with the On Ramps Precalculus course to assist with student transfers.

Unit 1 Functions and Graphs

Function Basics

Graphs of Functions

Properties of Functions

Piecewise Functions

Parent Functions

Transformations of Functions

Combinations of Functions

Inverse Functions

Modeling with Functions

Unit 2 Polynomial, Power and Rational Functions

Quadratic Functions & Graphs

Power Functions

Polynomial Functions of Higher Degrees

Real Zeros of Polynomials

Complex Zeros

Graphs of Rational Functions

Analyzing Rational Functions

Solving Rational Equations & Inequalities

Unit 3 Exponential, Logistic and Logarithmic Functions

Exponential & Logistic Functions

Logarithmic Functions & Their Graphs

Properties of Log Functions

Solving Exponential & Log Equations

Analyzing Graphs of Exponential Functions

Unit 4 Trigonometric Functions

Angles & Their Measure

Right Triangle Trigonometry

Arc Length & Circular Motion

The Unit Circle

Properties of Trig Functions

Graphs of Trig Functions

Inverse Trig Functions & Their Graphs

Modeling with Trig Functions

Unit 5 Analytic Trigonometry

Trig Identities

Sum & Difference Formulas

Multiple Angle Identites

Law of Sine & Cosine

Solve Trig Equations

Unit 6 Polar Coordinates & Vectors

Polar Coordinates

Polar Graphs & Equations

The Complex Plane

Vectors in the Plane

Dot Product

Unit 7 Systems of Equations & Matrices

Solving Systems of Equations

Multivariable Linear Systems

Matrices & Systems of Equations

Operations with Matrices

Inverse Matrices

Determinants of Matrices

Partial Fractions

Systems of Non-Linear Systems

Systems of Inequalities

Unit 8 Conic Sections & Analytic Geometry

Parabolas

Circles

Ellipses

Hyperbolas

Parametric Equations

Applications of Parametrics

Unit 9 Sequences & Series

Sequences & Summation Notation

Arithmetic Sequences & Partial Sums

Geometrice Sequences & Series

Mathematical Induction

Unit 10 Introduction to Calculus

Finding Limits Graphically & Analytically

Limits at Infinity & Continuity

The Derivative & Tangent Lines

Derivatives & the Power Rule