A2A MAT115 Practice Test 2Topics - College Algebra Exam 2

  1. Be able to tell the difference between a linear, quadratic and cubic equation and know the techniques for solving each:
  2. Linear: One solution  isolate x
  3. Quadratic: One solution, 2 complex solutions, 2 real solutions.  Set polynomial to zero in descending order of power.
  4. Methods of solving:
  5. Factoring: Only in special cases two terms, three terms, four terms  2 real roots/solutions only  set factors = 0 independently
  6. Quadratic formula  Can be used on any quadratic equation 0, 1, 2 real or complex roots/solutions
  7. Completing the square  Can be used on any quadratic equation but not advisable if b/a not a whole number or simple fraction  0, 1, 2 real or complex roots/solutions
  8. Square root method  Only used when bx is missing  0, 1, 2 real or complex roots/solutions Examples: ax2 + c = 0 or (x + b)2 + c = 0
  9. Rational: Solutions depend on whether fraction terms simplify to a linear or quadratic equation. You must check your answers to make sure they are in the domain of the equation!!
  10. Solve by multiplying through the numerators by the LCD. Finish solving as linear or quadratic depending on how the numerators simplify.
  11. Third, fourth and fifth degree polynomials:  Can have as many solutions as the highest power.
  12. Solve byfactoring out the variable as a GCF and then solve as quadratic. Set GCF and any factors = 0 independently
  13. Radical: Solutions depend on whether radical terms simplify to a linear or quadratic equation

You must check your answers!!

  1. Solve by isolating the radical and squaring both sides of the equation.
  1. Use the discriminant only to determine the number and type of solutions for a quadratic equation
  2. Complete the square in the form of (x +A)2 + B = 0 (used for circles and solving quadratic equations)
  3. Use quadratic equations to solve area of rectangle, triangle, etc.
  4. Complex numbers:
  5. Complex number operations – Multiply, divide, addition and subtraction, rationalize the denominator
  6. Simplify ix as i, -i, 1, -1
  7. Simplify complex imaginary square roots with multiplication, division, addition and subtraction
  8. Given a shape, find the distance/length of the sides and determine if one or more corners are perpendicular. (See homework)
  9. Circles:
  10. Find the midpoint
  11. Find the equation of a circle given a radius and center or diameter (find the midpoint)
  12. Find the center and radius given an equation of a circle
  13. Two variable linear equations and graphing
  14. Find the equation of the line given:
  15. Two points,
  16. y-intercept and slope
  17. Picture of a graph,
  18. Parallel or perpendicular lines
  19. Vertical or horizontal line
  20. Model a contextual (word) problem with a linear applications