Gearing up for Ivy League admission is one of the toughest challenge for high school students, whether they are homeschooled or not. Ivy admission requires excellence in all areas, exceeding requirements - and a healthy dose of luck.
Start the process by reading High School Subject Tests Simply Explained, so you understand the different subject tests available.
While some top-tier colleges will say they want 2-5 SAT Subject Tests, that's only what they REQUIRE. What they normally SEE is quite different. If you are thinking about an Ivy League school, it's important to carefully think through your strategy for high school tests. Your goal: provide all the test these universities require, plus all the test they normally see from other applicants, all without going totally bonkers with over-the-top test preparation. Sounds easy, doesn't it?
Ivy league college will usually request or require 2-5 SAT Subject tests. However, what most applicants actually give them is 2-5 AP Subject Tests, which are much more difficult test that measure much more difficult content.
You want to provide what they require AND provide what others normally submit, as well. Each university will have their own policy on whether or not you can substitutes and AP test for an SAT Test. So that makes things a little complicated. Remember, SAT Subject Tests are high school level, and AP tests are college level. In theory, then, if you can study enough to pass the AP, you should be able to pass the SAT Subject Test pretty easily.
For that reason, some families that are gearing up for selective colleges deride to take BOTH tests. Register for both, not at the same time (obviously). Prep for AP and take the test. Then prep for the much easier SAT Subject test, then take that test. Both test scores can be presented to colleges. This strategy is used by public school kids use because they aren't sure they will do well on the AP. You can withhold both scores until they see the scores when you get the results, and only submit excellent test results. I suggest that homeschool parents can do it differently. Give those sample tests at home so you KNOW how they will do on each subject test. Then you can safely submit scores without seeing them first, knowing your child will do well enough that the scores will all be some variation of "good."
Ivy league and highly selective colleges normally see much more than what they require from applicants. If they "require" 5 SAT Subject Tests then they normally see AT LEAST that many subject tests from applicants. Often, applicants submit those subject tests are AP exams, not just SAT subject tests.
Cover the core with subject tests for best results. Try to take one subject test in each major area of study: English, Math, History, Science, and Foreign Language. Taking just a math and science combo doesn't show the whole student.
It may be easier to take the Science and History first, if possible, because you can take them almost any year - after completing American History and after Chemistry, for example. But the math, English, and foreign language skills continue to build over time as long as you continue taking those subjects. For that reason, try to take those subject tests as soon as you finish your study of foreign language, or as late as possible.
Consider completing all the required subject tests by the end of junior year so a university can see the results as they make their initial analysis of the student, and they don't have to wait until the end of senior year to see some AP tests.
As much as possible, take the most advanced SAT Subject test in all subject areas, math and science and others, as soon as they can ace those tests at home, timed. Remember, those are high school level, so they may be able to do that pretty soon, before junior year.
Then start looking at the much more difficult AP tests. Taking the most advanced AP test in math is the best option - wait until they can pass that test at home with flying colors, getting a 5 at home, timed.
For more information, you might enjoy my short Coffee Break Book, Upper Echelon Education: How Homeschoolers Can Gain Admission to Elite Universities. It's going to take more than a short and sweet book to get the job done, but it's a great starting point. For your next step, consider The Comprehensive Record Solution, to help you create excellent homeschool record that demonstrate the academic preparation of your child. Then the College Launch Solution can provide the step-by-step guidance an reminders that will help you stay on task through the years.