LEARN BY DOING

All chapters begin with a "What you need to know" section, defining for the student where to begin a problem. It is easy to find the hint in the WYNTK section that can be used to solve a given problem. 

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What you need to know:  

• x^2 is defined as x*x (x multiplied by x). Also y^2 = y*y; z^3 = z*z*z, etc. 
• a(b+c) = ab + ac
• To solve for y = a/A + b/B, multiply both sides by AB
• Collect all the x's so that you end up with a simple “x =” type equation

If x/A + x/B + x/C = 1, then multiply both sides of the equation by ABC to get:

                      BCx + ACx + ABx = ABC, which can be reduced to: 

                        (BC+AC+AB)x = ABC, or x = ABC/(BC+AC+AB)

1. x^2 where x = 2                     
2. y^2- x^2 where x = 3 and y = 4
3. y^2/ x^2 where y = 2 and x = 1
4. x, where x^2= 9
5. x, where x^2+ y^2 = 25 and y = 3

At the end of each chapter, the "answers" are given. Not just the answer, of course, but the full explanation of how to go about solving the problem. Here are the answers to the above problems:

         Solve for:                                          Answers     Guide to Answers

1. x^2 where x = 2                                               4      22 = 2 x 2 = 4
2. y^2 - x^2 where x = 3 and y = 4                     7      42 - 32 = 16 - 9 = 7
3. y^2 / x^2 where y = 2 and x = 1                     4      22 / 12 = 4/1 = 
4. x, where x^2 = 9                                  +/- 3      Sqrt (9) = 3
5. x, where x^2 + y^2 = 25 and y = 3           +/- 4      x^2 + 3^2 = 25;  x = Sqrt (25-9) = 4

The essence of this approach is to do problems first and get the explanation as you are trying to work out the problem.