Ivy League colleges are highly selective. So admissions to these schools are similar to other highly selective colleges that do not belong to the Ivy League. 
The Ivy League is actually a sports league. All 8 Ivy League schools play each other in each of the sports each year. 
As far as admissions go, these schools (along with other highly selective schools) will receive so many applications from valedictorians and other top students that these very impressive applications become boring.
The best thing you can do, is make sure your academic record puts you squarely in the top 10% of students in your high school class, and then focus on showing initiative and making an impact in your community. 
There are many episodes of my podcast that would be helpful for this. 

First, your mindset. 
Always, always, always add the three magic words to any big goal you have. 
So if your dream is to study at Princeton, say "I want to get into Princeton, or something better." 
The three magic words will help you let go of desperation about any one school, by reminding you that you don't have enough awareness to know for sure which school is best for you, so you can work to get into your top choice, or something better.
Beyond that mindset, always make sure you have a range of great schools you are applying to. The question is not IF you will go to college, but where. 

You will need to demonstrate that you are capable of performing (and thriving) at an academically rigorous college. 
So, you need to take some difficult classes. 
The amount of difficult classes you need to take will depend on your high school landscape-- you need to be in the top 10% of your high school class academically.
Once you are there, you don't need to push to move higher up the ranks, instead focus on clarifying your core values and making a meaningful community impact. 

Beyond what I've already written as answers to other similar questions, remember that being memorable is more important that being impressive. 
30,000 schools in N. America means there will be tens of thousands of students who will be impressive within their own schools. 
You will want to branch out of your high school to make your impact. 
You also want to make sure your impact aligns with your core values so that you have the grit and resilience to stick with it when challenges arise. 
Making a community impact that aligns with your core values makes you a very unique and interesting applicant-- the kind that is much more likely to be admitted. 

This question comes straight out of the Impressiveness Trap. 
The activities you do and leadership roles you play are much less important the the level of impact you have on the communities you are a part of. 

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The best essays are exceptionally well-written. 
The personal statement and the supplemental essays are all important and should be carefully written. 
The personal statement is the way the teen provides a voice and the context that admissions officers will use to interpret the rest of the application.
So the keys to a great personal statement include:
1. make it personal (show personality)
2. make it insightful (show thoughtfulness)
3. make it meaningful (try to demonstrate your core values) 4. make it specific (don't summarize a year or more of that sport, choose one moment that opened up your mind or gave you greater empathy, a new perspective, or something like that)
5. make sure it is well written (this should represent the teen's best writing)
6. make it memorable (the best essays surprise the reader-- so perhaps it starts out being about the sport, but there is a surprise or twist in there and the conclusion is unexpected) One example of this is an essay from a football start. The essay began talking about being a start football player, and then in a surprise line after two paragraphs, the writer reveals that he hates contact.

I do for my own students, but unfortunately I don't have time to offer that service to others. 

Check the Common Data Set for your school of interest and make sure you scores are at or above the 75th percentile for that school. 
Retaking tests is a complicated question. I don't want to get too much into that here, but the rule of thumb is that once you are at the 75th percentile for that college, you shouldn't retake after that. 

Those exam scores are a good indication that you will be able to handle the rigor of a very competitive college. 
You should do your best to perform well in AP, IB, A-level, or other standardized tests. 

Follow the instructions from the various colleges you apply to. 
Generally, you will want to ask two teachers of core subjects who are willing and able to advocate for you and speak to your ability to perform well in the classroom. 

Follow the instructions from my podcast-- there is a lot there!

I just wrote an article for Business Insider about this. The article is not available publicly until tomorrow. I'll post the link when it is available!

Watch out for my article. You can also listen to this podcast: https://www.buzzsprout.com/1019335/14100856

Aid is given based on need, and not based on merit. 
The amount of aid is quite generous. 

Scholarships are available beginning very early on-- even in elementary school-- but most scholarships are available for seniors and college students. 
It is important to follow instructions strictly. 
Resourcefulness, excellent essay writing, and genuine community impact are some of the best ways to ensure you are competitive for scholarships. 

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Anim pariatur cliche reprehenderit, enim eiusmod high life accusamus terry richardson ad squid. 3 wolf moon officia aute, non cupidatat skateboard dolor brunch. Food truck quinoa nesciunt laborum eiusmod. Brunch 3 wolf moon tempor, sunt aliqua put a bird on it squid single-origin coffee nulla assumenda shoreditch et. Nihil anim keffiyeh helvetica, craft beer labore wes anderson cred nesciunt sapiente ea proident. Ad vegan excepteur butcher vice lomo. Leggings occaecat craft beer farm-to-table, raw denim aesthetic synth nesciunt you probably haven't heard of them accusamus labore sustainable VHS.

Folly the advice from the podcast.

Listen to the podcast.