Merced College; Don Power

 

INTERMEDIATE ALGEBRA STUDY GUIDE -- CH 5 and 6

 

5.1       Exponents:  Simplify:      

 

 

 

5.1       Scientific notation:  Divide and write the result in scientific notation:

         

 

5.3     Multiply polynomials:  Multiply (expand):

 

          a.  (3x-7)2

 

          b.  (6x-5)(8x2+x-2)

 

 

5.5     Factoring:  Factor completely:

         

          a.  3x2 − 13x + 10

          b.  6x3 + 39x2 + 45x

 

5.4     Special factoring:  Factor completely, if possible.  Hint you must remove all common factors first:

          a.  x2 - 2xy - 3ax + 6ay

          b.  16a4 + 54a

          c.  4x2 – 9

          d.  (x - y)2 - 16

          e.  x2 + 16

          f.  75r2 − 12t2

          g.  2x3 + 8x

 

 

5.6     Solve  x(x2 - 7x + 4) = 28

 

5.6     A small rocket is projected straight up from ground level with a velocity of 128 ft/sec.  Its height in feet after t seconds is given by h = -16t2 + 128t.

 

a.  Use this formula to find the height after 1, 2, 3, 4, 5, and 6 seconds.

b.  When will the rocket hit the ground? (Hint:  The height is 0 when it hits the ground;  substitute h = 0 and solve for t)

 

 

Chapter 6:  Expect to see all the following special factoring situations in questions throughout this chapter:

 

Common factor

Grouping

Sum of squares

Difference of squares

Sum/difference of cubes

                   Sign reversal

 

6.1     Identify the domain of a rational function  #1-20

                   Denom a constant   #1-2

                   Denom linear         #3-8

                   Denom sum of squares    #9-10

                   Denom factorable  #11-20

 

6.1     For the rational function f(x)= ____, find f(-3)

#21-26

 

6.1     Simplify the rational expression (reduce to lowest terms):

          #41-78

 

6.2     Multiply/divide rational expressions with monomials

                   #9-14, 37-42

 

6.2     Multiply/Divide rational expressions by converting division to multiplication, factoring, and reducing.

                   #19-36, 43-50

 

6.3     Add or Subtract fractions with different denominators: 

 

6.4     Add or subtract two rational expressions with different denominators

                   Factoring required

                   #43-70

 

6.5     Simplify complex fractions

          Level of difficulty #31-44

 

 

6.6     Divide by long division

                   By a binomial        #15-44

                   (you may need to allow for missing terms)

 

6.6     Divide by synthetic division       #57-66

                   By divisor of form x-a

                   (you may need to allow for missing terms)

 

 

6.6     Solve rational equations

          Single-term denominators #37-44, 46-48

          2-3 term denominators, factoring required:  #57-64

                   Results must be checked:  extraneous solutions are possible

 

6.7     Applications:  Select from

                   Distance-Rate-Time (possibly upstream-downstream) #33-34

                   Work-Rate #39-40

 

6.7     Variation: 

 

          Set up a variation equation:  #1-14

 

Find the constant of proportionality and write an equation that relates the variables:  #21-32

 

          Set up and solve a variation problem, #43-55, 60a, 60f.  Either:

          Direct variation, or

          Inverse variation, or

          Joint variation

                  

 

 

 

Return to:  Merced College; Don Power               Updated 10/10/07 by Don Power