Module 1: Prerequisites (Chapter 1)

It’s a cold day in Antarctica. In fact, it’s always a cold day in Antarctica. The coldest temperature ever recorded, over one hundred degrees below zero on the Celsius scale, was recorded by remote satellite. It is no surprise then, that no native human population can survive the harsh conditions. Only explorers and scientists brave the environment for any length of time.

Measuring and recording the characteristics of weather conditions in Antarctica requires a use of different kinds of numbers. For tens of thousands of years, humans have undertaken methods to tally, track, and record numerical information. While we don't know much about their usage, the Lebombo Bone (dated to about 35,000 BCE) and the Ishango Bone (dated to about 20,000 BCE) are among the earliest mathematical artifacts. Found in Africa, their clearly deliberate groupings of notches may have been used to track time, moon cycles, or other information. Performing calculations with them and using the results to make predictions requires an understanding of relationships among numbers. In this chapter, we will review sets of numbers and properties of operations used to manipulate numbers. This understanding will serve as prerequisite knowledge throughout our study of algebra.

Image Caption: Earth’s southernmost continent, Antarctica experiences the coldest, driest, and windiest conditions known. (Credit: Andreas Kambanls)

(Content & Image Source: Chapter 1 Introduction, Algebra and Trigonometry 2e, Jay Abramson, OpenStax, CC BY 4.0 License)

• Classify a real number as a natural, whole, integer, rational, or irrational number. (CLO #)
• Perform calculations using order of operations.
• Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity.
• Evaluate algebraic expressions.
• Simplify algebraic expressions.

• Use the product rule of exponents.
• Use the quotient rule of exponents.
• Use the power rule of exponents.
• Use the zero exponent rule of exponents.
• Use the negative rule of exponents.
• Find the power of a product and a quotient.
• Simplify exponential expressions.
• Use scientific notation.

• Evaluate square roots.
• Use the product rule to simplify square roots.
• Use the quotient rule to simplify square roots.
• Add and subtract square roots.
• Rationalize denominators.
• Use rational roots.

• Identify the degree and leading coefficient of polynomials.
• Add and subtract polynomials.
• Multiply polynomials.
• Perform operations with polynomials of several variables.

• Factor the greatest common factor of a polynomial.
• Factor a trinomial.
• Factor by grouping.
• Factor a perfect square trinomial.
• Factor a difference of squares.
• Factor the sum and difference of cubes.
• Factor expressions using fractional or negative exponents.

• Simplify rational expressions.
• Multiply rational expressions.
• Divide rational expressions.
• Add and subtract rational expressions.
• Simplify complex rational expressions.

1. Read the Module 1 Introduction (see above).
   
2. Read Sections 1.1 - 1.6 of Chapter 1: Prerequisites in College Algebra (links to each Section provided below)
   • At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
     
3. Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
   
4. Practice the problems on the Chapter 1 Review Exercises, checking the solutions provided (link provided below)
   
5. View the Chapter 1 Practice Test (link provided below)
7. Complete the MyOpenMath Quiz for Chapter 1 (link provided below) - This is graded!
8. Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
9. Post in the Chapter 1 Q&A Discussion Forum - link provided below.

Module Pressbooks Resources and Activities