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:
3. Linear programming
5. Sigma notation
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)