Maybe this is why the US fails at math

Romanian mathematics, grade seven:

In triangle ABC, P is the midpoint of side BC. Let M be on AB and N be on BC such that MN is parallel to BC, and let Q be the intersection of MP and BN. The perpendicular from Q on AC intersects AC at R and the parallel from B to AC at T. Prove that a) TR is parallel to MR, and that b) angle MRQ is equal to angle PRQ.

7th grade math in the US:
What is a triangle?

"Diversity" in college admissions

In a typical freshman class of an Ivy League school,
(11% are international students and are not considered)

21% are 'underrepresented minorities' (Black, Latino, Native American, Pacific Islander, etc.)
10% are 'legacies' (parents associated with college or donated lots of money)
7% are athletic recruits
9% of remaining (5% of total) are from 'underrepresented states' (states that for some reason are less academically solid)
8% of remaining (5% of total) have suffered extreme hardships, are from extremely poor neighborhoods, or are first-generation college students

This means that only 41% of an incoming class will be admitted without these factors, which, despite having nothing to do with a student's academic ability, can greatly benefit the applicant's chances.

(These numbers are averages based on many 'freshman class profiles')

Things that will capture colleges' attention

Ranked from hardest to easiest to do.

1. International Tchaikovsky Competition, or some related musical event


2. Olympic games


3. Donation of over $10 million from your parents


4. International Science Olympiads


5. Writing a best seller book


6. Patenting an invention


7. Principal author for an article in the Journal of Biochemistry (or any other major scholarly periodical)


8. Nationally ranked athlete or musician


9. Intel or Siemens competition finalist


10. Higher-undergraduate or graduate level courses at a university (e.g. Abstract Algebra)


11. A glowing recommendation


12. Exchange student for a year or helping a major international cause (preferably having a major impact on self)


13. An essay that generates enormous emotions


14. More than 12 AP's with 5's


15. Valedictorian (especially in classes greater than 500 people)

If you can get any of the first few, you have a great "hook" in the admissions process, and given good scores, you'll be admitted. The final items are not as impressive, but still excellent for the high school level, so a few of those mixed in with a strong resume will create a highly favorable chance of acceptance.

Answers to the pervious quiz

There are no right or wrong answers for some of these; but you should be somewhere close. The most important part is the reasoning you used to arrive at your answer, which can involve a variety of methods.

1. 60,000,000,000,000 = 13 zeros


2. 466 - 209 = 466 - 200 - 9 = 257.


3. 105 - 75 is 30, so the halfway point is 15 from either number: 75 + 15 = 90.


4. We are looking for 5280/3. 17*3 = 51 and 18*3 is 54, and 52.8 is closer to 54 than to 51. So 5280/3 is about 1800 (1760 to be precise).


5. If the first day is Wednesday, then the 8th, 15th, 22nd, and 29th are also Wednesdays. Thus, the 7th, 14th, 21st, and 28th can be Tuesdays. The 35th cannot exist, so there can only be four Tuesdays.


6. I have no idea either. I don't have the music, but I would say it's about 25 keys a second, so 2250 keys over 90 seconds.


7. 300*.65 = 300*.6 + 300*.05 = 195.
   289 = 300 - 11, so 289*.65 = 195 - 11*.65 ≈ 195 - 7 = 188 since .65*10 = 6.5, so .65*11 will be a bit bigger than 6.5. 176 < 188, so it's not passing.


8. $.03 a sheet means about 33 sheets per dollar. That gives over 660 sheets with $20. If you want to be exact, consider that the assumption of 33 sheets/$1 comes up with one extra cent to spare after every dollar (33 sheets = $.99). Thus, with $20, there would be $.20 left, which can print 6 extra sheets. Thus, the exact number is 666 sheets.


9. 240000 miles is a bit less than 400000 km (1 mile = 1.6 km). Thus a round trip would be 800000 km, which would require 800000/300000 = 2.66 seconds. If I had to guess a more exact number, I would say 2.6 seconds since our 400000 km assumption was a little higher than actual.


10. There is no correct answer, unless you can go try it. I would try to reason it out like this:
    Assume a penny is 2 cm in diameter, and about .2 cm thick (actually it's about .14cm, so we're overestimating a bit). Thus its volume is .2π cm³, which is approximately .6 cm³ (using pi=3). 30 gallons ≈ 114 L (1 gallon is 3.78 L, or about 3.8L). 114L is 114000 mL = 114000 cm^3. 114000/.6 = 190000 pennies (114L was a very convenient estimate!).


11. That's 5 months minus four days, or 30*5 - 4 = 146. To be exact, it's 30+31+31+28+31-4= 147 days on a non-leap year.


12. 78/7 is about 11. From April 11 of this year to December of 2010 is 20.5 months, so the number of views is 11*20.5 = 11*20 + 11*.5 ≈ 225 million views!!!!


13. The sun is 93,000,000 miles away, so it would require more than 1,500,000 hours. 15/24 = 5/8 = .625, so 1,500,000 hours is 62,500 days. 625/365 < 640/360 = 16/9 = 1.78. Let's approximate as 1.75. Thus 62500/365 is around 175 years.


14. 30% tax is equal to keeping 70%, or .7*(gross income). Thus, with $75000 net income, that's 75000/.7 ≈ $104000 per year. He is paid every two weeks, or 1/26 of this amount, which is $4000 (I picked 104 since 104/26 = 4).


15. Decrease by 10% = .9x; raise by 10% = 1.1(.9x) = .99x. So there is a net decrease by 1% after every cycle. We can use the "rule of 72" backwards; after 72 years, it will halve. We go from $100 → $50 → $25 → $12.50 → $6.25 → $3.13 → 1.56 → $.78. So we half to cut it in half about 6.5 times (a very rough estimate). 6.5*72 = 468 times. (actually, the answer is 459, so not bad on our part!)


16. Let's assume the interest rate is 72%. The rule of 72 says it will double in 1 year, but obvious it will take longer than 1 year. Thus it underestimates the time required for higher interest rates.


17. This is completely open-ended.
    $600/month for rent means $7200 per year.
    $30/day for food → $900 per month → $10800 per year
    car and all insurances (excluding health): about $2500 a year
    clothing and other common expenses: $50 per week or $2500 a year.
    That's a total of $23000 a year.


18. 1 person will transmit it to 3 others, making 4 total infected. These four will spread it to 12 people, making a total of 16. Looks like powers of 4 !!! 4^3 = 64, 4^4 = 256, 4^5 = 1024 ≈ 1000, 4^6 = 4000, 4^10 = 1024000 ≈ 1000000, 4^14 = 256 million, which is close to 300 million (the population of the US), so it will take no more than 15 days to infect the entire country.


19. Every term after the second is the units digit of the product of the previous two entries. It starts repeating in cycles of 6: 6, 8, 8, 4, 2, 8, 6, 8, 8, 4, 2, 8, 6, .... The first two terms (2, 3) are not relevant in this pattern and will be eliminated, so the 1000th term in the whole sequence is just the 998th term in the repeating pattern. 998 - 166(6) = 2, so it will be the second term of the repeating sequence, or 8.


20. 22 < 2⁵, so 22²² < (2⁵)²² = 2¹¹⁰. Thus 2²²² is larger.

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Test your numerical literacy

How good are you with numbers? These questions, roughly in increasing order of difficulty, test your mathematical thinking and familiarity with numbers.
The answers are here.

NOTE: No calculators!!!

1. How many zeros are in 60 trillion?


2. 466-209=?


3. What number is halfway between 75 and 105?


4. To the nearest hundred, how many yards are in a mile (1 mile = 5280 feet)?


5. A month starts on Wednesday. What is the most number of Tuesdays it can have?


6. How many piano keys are pressed in this video?


7. Is 176/289 a passing score (passing is 65%)?


8. Printing a piece of paper costs $.03 per sheet. How many pages can I print (single-sided) with $20.00?


9. Light travels at 300000 km per hour. The moon is 240000 miles away. If we were to shine a light at the moon that bounces back, how long would it take to see it again from the time we begin shining it?


10. How many pennies can fit into a 30 gallon fish tank?


11. Estimate the number of days from November 15th, 2009 to April 11th, 2011.


12. In seven months so far, this video of Susan Boyle's audition on Britain's Got talent has received 78 million views. At this rate, how many views will it have by the end of next year?


13. How many years would it take for me to drive to the sun at 60 mph?


14. John works 50 hours a week, and gets $75000 a year after 30% income tax. If he is paid every two weeks, what should the gross income be on his paycheck?


15. A company discounts the price of a $100 item by 10% and then raises it by 10% again. How many times must this be repeated for the item to only cost $1?


16. The rule of 72 states that if money is invested at x%, then it will double in worth in 72/x years. For example, $100 at 3% interest will become $200 in approximately 72/3=24 years. For higher interest rates, does the rule overestimate or underestimate the time required?


17. What should the poverty rate be for a family of four?


18. One person has swine flu. Every day he spreads it to three other people. Assume that these other three people (along with the original person) each spread it to three more people the next day. If this keeps happening, how long would it take the entire US to be affected?


19. What is the 1000th term of this sequence: 2, 3, 6, 8, 8, 4, 2, 8, 6, 8, ... (hint: Fibonacci)


20. Which is greater, 2^222 or 22^22?

Answers will be posted Monday!