Foundations of College Algebra


A Note about Formatting

  • The MS Word version of each lesson handout is the best for people with visual impairments. The Microsoft Word “Read Out Loud” feature provides the most correct reading of mathematics.
  • The PDF version is best for printing. It has the cleanest format. It is not fully ADA compliant, so please be careful.

Lesson List

  1. Review of Arithmetic, Introduction to Fractions, Prime factorization
  2. Simplifying, Multiplying, and Dividing Fractions
  3. Adding and Subtracting Fractions
  4. Conclusion of Fractions, Introduction to Decimals
  5. Operations with Decimals
  6. Ratios, Proportions, and Percentage
  7. Exam 1
  8. Using Percentages
  9. Geometry Formulas
  10. Pythagorean Theorem, Sets of Numbers, Variables
  11. Operations with Signed Numbers
  12. Algebra Introduction
  13. Rules for Solving Equations
  14. Exam 2
  15. Solving Linear Equations
  16. Problem Solving and Formulas
  17. Linear Inequalities, The Coordinate Plane
  18. Graphing Linear Equations, Intercepts
  19. Slope, Rates of Change, Equations of Lines
    1. Worksheet - PDF - Word
  20. Functions and Exponents
    1. Worksheet - PDF - Word
  21. Exam 3
  22. Introduction to Polynomials, Adding and Subtracting Polynomials
  23. Multiplying Polynomials
  24. Greatest Common Factor and Factoring by Grouping
    1. Worksheet - PDF - Word
  25. Factoring Trinomials of the Form x^2+bx+c
    1. Worksheet - PDF - Word
  26. Factoring Trinomials of the form ax^2+bx+c
    1. Worksheet - PDF - Word
  27. Special Factoring, Solving Quadratic Equations by Factoring
  28. Additional Topics in Algebra
  29. Exam 4
  30. Review

Teaching Resources

KCTCS Competencies

Upon completion of this course, the student can:
  1. Perform operations on integers and decimals.
  2. Find the prime factorization and least common multiple of whole numbers.
  3. Add, subtract, multiply, divide, and simplify fractions.
  4. Simplify ratios and rates, and solve application problems involving proportions.
  5. Convert between decimals and percents, and calculate percent change.
  6. Simplify radicals and find decimal approximations.
  7. Apply common units for length, area, volume, time, currency, or speed.
  8. Simplify numeric expressions using the order of operations.
  9. Simplify algebraic expressions.
  10. Solve linear equations in one variable.
  11. Solve a formula for a given variable.
  12. Solve linear inequalities in one variable. Write the solution set, including compound inequalities, in interval notation and set builder notation.
  13. Identify and plot points in the Cartesian coordinate system.
  14. Find the slope of a line.
  15. Graph lines using a table of solutions, slope-intercept form, and intercepts.
  16. Add, subtract, and multiply polynomials.
  17. Factor polynomials by factoring common factors, grouping, and special products; and factor general trinomials.
  18. Simplify rational expressions.
  19. Solve quadratic equations by factoring.
  20. Identify and evaluate linear, polynomial, rational, and exponential functions.
  21. Solve application problems based on the above competencies.

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