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Math Formulas

Has done the second year of high school algebra

There are many home schooling math curricula out there.

.......Some of them are so boring/repetitive that kids quickly forget anything they may have learned.

.......Some of them are mathematically light-weight.  The kids think that they have learned all of first-year algebra.  That is, until they hit their SATs or a college classroom.  At that point they find out that there are big gaps in their knowledge.

      Of the "heavyweights" in the homeschooling world, Saxon is usually considered the 800-pound gorilla, but it is sadly lacking in its content.  A couple of months ago I looked at his Alg 2 and compared it with Life of Fred: Advanced Algebra Expanded Edition. 
      I counted a dozen major topics that he leaves out that Life of Fred: Advanced Algebra Expanded Edition includes:
     1. Permutations
     2. Matrices
     3. Linear programming
     4. Series
     5. Sigma notation
     6. Sequences
     7. Combinations
     8. Pascal's triangle
     9. Math induction
     10. Partial fractions---needed in calculus
     11. Graphing in three dimensions
     12. Change-of-base rule for logarithms
All these topics should be in any full presentation of second-year high school algebra.


     With that in mind, let's see how much second-year algebra your child has learned. 

     Here are some representative questions to ask your child.  They are taken from Life of Fred: Advanced Algebra Expanded Edition.  Have them take out a piece of paper and play with these questions . . .



 1.  What is the slope of the line that is perpendicular to 
      y = (7/3)x - 5? (p. 205 in LOF:AA) 
2.  Using Cramer's Rule solve for x:
       x + y = 1
     3x = 2y + 18               (from p. 282)
3.  What is the equation of the ellipse whose vertices are 
(4, 5) and (10, 5) and which has a semi-major axis of length 1?  (p. 334)
4.  Let A and B be any two arbitrary sets.  Suppose we have a function f:A→B that is 1-1.  What can we say about the number of elements in A compared with the number of elements in B?   (p. 386)
5.  Resolve 8/(x²-4)  into partial fractions.     (p. 415)
6.  What is the sum of the infinite geometric progression
        1/3  +  1/9   +  1/27  +  1/81 +  . . .   ?   (p. 487)

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