Module R: Review Topics

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Competencies needed for MAT151

To enroll in College Algebra (MAT150/151) you must understand the following topics.  

Need to review a topic?   Watch a video or read a summary of the topic below!


  1. Use function notation.                  (Questions scattered throughout)
  2. Solve quadratic equations by factoring, completing the square, and the quadratic formula.    

    Factoring:  Trinomials using Trial and Error  Factoring a Trinomial  Completing the Square  Completing the Square Method Explained  Using the Quadratic Formula   Completing the Square & Quadratic Formula

              (Factoring: Questions 1 & 3; Comp. Square: # 2; Quad. Form: 4, 8, 9, 7 (a+bi))
  3. Solve equations quadratic in form.    Solve Equations in Quadratic Form by Factoring   Solve Quadratic in Form Equations  (Questions 9, 10)
  4. Solve rational and radical equations.   Solve Rational Equations    Solve Rational Equation     Solve a Rational Equation - Alternative Method         Solve Rational Equation – Example   

    Solve Radical Equations with One Radical       Solve Radical Equations with Two Radicals

        (Questions 11-13)
  5. Perform operations on complex numbers.   Complex Number Operations            (Questions 14 - 16)
  6. Perform operations on radical and rational expressions.  Adding and Subtracting Radicals      Multiplying Radicals    Dividing Radicals   Multiplying and Dividing Rational Expressions    Adding and Subtracting Rational Expressions       (Rationals: Questions 17 - 20; Radicals: 21 - 24)
  7. Simplify rational and radical expressions.    Simplify Rational Expressions       Simplify Radical Expressions    Radicals Intro      (Questions 25 - 26)
  8. Simplify expressions involving rational exponents.  Rational Exponents    Rational Exponents    (Question 27)
  9. Graph quadratic, exponential, and logarithmic functions.   Graph Quadratic Functions in Standard (Vertex) Form   Graph Quadratic Functions in General Form   Graph Exponential Functions   Graph an Exponential Function and Logarithmic Function
            (Questions 28 - 30)    
  10. Identify the domain of quadratic, rational, radical, exponential, and logarithmic functions.  Find domain and range from a graph  Find Domain and Range from a Graph   Find Domain and Range of a Rational and Radical Function     Domain of Rational Function      Find Domain of Logarithmic Function    (Question 31 - 34) 
  11. Rewrite logarithmic expressions using the properties of logarithms.  

    Properties of Logarithms    Logarithms: Change of Base Formula     Logarithm Review      Properties of Logarithms          (Questions 35-37)

  12. Evaluate formulas involving exponential or logarithmic expressions. 

    Compound Interest    Continuous Interest       Exponential Growth Function - Population      Exponential Growth Function - Bacterial Growth                                      

     Continuous and Compound Interest Formula   (Questions 38-40) 
  13. Model and solve real-world problems using quadratic, rational, radical, exponential, and logarithmic equations.  

    Introduction to Regression Analysis      Quadratic Regression on TI84 - Stopping Distance      Quadratic Function - Time and Vertical Height      Find Size of Cardboard Needed to Make a Box with Given Volume    Rational Equation - Painting Together     Rational Equation - Plane and Car Traveling the Same Time     Rational Equation - Fill a Pool with Drain Open      Rational Equation - Two Bikers Riding Different Distances      Radical Equation - Vehicle Speed from Skid Mark Length     The Pythagorean Theorem      Find the Length of the Leg of a Right Triangle     Find the Distance Between Two Points    

    How to Find a Regression Equation           Solve Exponential and Logarithmic Equations

       (Questions 41-45)

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