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-minor 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)
(Don't scroll down past here so that the answers remain hidden.)
1. -3/7
2. x = 4 (Cramer's Rule involves the use of determinants. Do not count this as correct if determinants were not used.)
3. (x-7)²/9 + (y-5)²/1 = 1
4. The number of elements in A must be less than or equal to the number of elements in B.
5. 2/(x-2) - 2/(x+2)
6. 1/2
If your child can only get four out of six correct (66%), it would probably be a mistake to skip second year algebra.
Order Life of Fred: Advanced Algebra Expanded Edition. A hardback that covers all of second year algebra (and is a lot of fun).
It covers all of second-year high school algebra in 105 daily lessons. If any of advanced algebra is already known, doing two lessons in an hour would not be unusual.
This book is in stock and will be shipped to you immediately.
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