Precalculus Course Structure and Assignment Guide

Course Overview

This course syllabus outlines the structure, assignments, and assessment methods for a college-level Precalculus course. The course is divided into four modules, each containing several lessons that cover foundational and advanced topics in algebra, functions, and introductory calculus concepts. The course includes homework assignments, quizzes, a proctored midterm, and a final exam.

Course Modules and Topics

Module 1: Algebraic Foundations and Graphs

• Review of Algebra Skills

  • Exponents

  • Factoring

  • Rational Expressions

  • Solving Equations

  • Radicals and Rational Exponents

• Distance and Midpoint Formulas

  • Distance between two points: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

  • Midpoint of a segment: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

• Graphs of Equations

• Equations of Lines and Circles

  • General form of a line: $y = mx + b$

  • Circle: $(x - h)^2 + (y - k)^2 = r^2$

Module 2: Functions and Polynomial/Rational Functions

• Functions and Their Graphs

  • Definition of a function

  • Domain and range

  • Common functions (linear, quadratic, etc.)

• Properties of Functions

  • Even and odd functions

  • Increasing/decreasing intervals

  • Maximum and minimum values

• Quadratic Functions and Their Properties

  • Standard form: $f(x) = ax^2 + bx + c$

  • Vertex: $x = -\frac{b}{2a}$

• Polynomial Functions

  • Synthetic division

  • Zeros of polynomials

  • Polynomial inequalities

• Rational Functions

  • Definition: $f(x) = \frac{P(x)}{Q(x)}$ where $Q(x) \neq 0$

  • Asymptotes and discontinuities

Module 3: Advanced Functions and Applications

• Composition of Functions

  • $(f \circ g)(x) = f(g(x))$

• One-to-One and Inverse Functions

  • Definition of one-to-one

  • Finding inverses

• Exponential and Logarithmic Functions

  • Exponential form: $y = a^x$

  • Logarithmic form: $y = \log_a x$

  • Properties of logarithms

  • Solving exponential and logarithmic equations

• Applications

  • Financial models (compound interest, growth/decay)

  • Growth and decay models: $A = A_0 e^{kt}$

Module 4: Systems, Sequences, and the Binomial Theorem

• Solving Linear Systems

  • Substitution and elimination methods

• Partial Fractions

  • Decomposing rational expressions

• Sequences

  • Definition of a sequence

  • Geometric sequences: $a_n = a_1 r^{n-1}$

• Binomial Theorem

  • Expansion: $(a + b)^n = \sum_{k=0}^n {n \choose k} a^{n-k} b^k$

Assignment and Assessment Structure

Homework Assignments

• 23 assignments, due on Fridays

• Each question can be attempted up to 3 times

• Late submissions incur a 15% deduction

• All homework must be completed before the Final Exam window

Quizzes

• 11 quizzes, due on Saturdays

• Each quiz can be retaken once before the due date; the higher score counts

• Quizzes are timed (60 minutes)

• Late submissions incur a 15% deduction

Exams

• Proctored Midterm Exam (covers Lessons 4-11)

• Final Exam (covers Lessons 12-20)

• Strict proctoring and submission rules apply

• Extra credit available for submitting scanned scratch-work

Grading Policy

Component	Weight
Homework Average	30%
Quiz Average	30%
Midterm Exam	20%
Final Exam	20%

Letter Grade	Score Range
A	90 - 100
B	80 - 89.9
C	70 - 79.9
D	60 - 69.9
F	< 60

Support and Resources

• Contact the instructor for virtual appointments if you need help

• Post questions on the Discussion Board

• Visit the Math Lab at your home school or use the virtual tutoring service

Summary Table: Weekly Lesson Topics

Week	Lessons	Main Topics
1	1-3	Algebra Review: Exponents, Factoring, Rational Expressions, Solving Equations, Radicals
2	4-7	Distance, Midpoint, Graphs, Lines, Circles, Functions, Properties of Functions
3	8-11	Quadratic Functions, Polynomial Functions, Rational Functions, Zeros, Inequalities
4	12-13	Composition, One-to-One, Inverse Functions
5	14-18	Exponential/Logarithmic Functions, Properties, Equations, Financial Models
6	19-23	Linear Systems, Partial Fractions, Sequences, Binomial Theorem

Additional info:

• This syllabus covers nearly all major Precalculus topics, including algebraic manipulation, functions, polynomials, rational functions, exponentials, logarithms, systems of equations, sequences, and the binomial theorem.

• Trigonometry and analytic geometry are not explicitly listed in the weekly lessons, but may be included in other course materials.