Packet 13: Bonus 19
A method in which these quantities are “undetermined” can be used to find particular solutions of inhomogeneous differential equations. For 10 points each:
[10m] Name these quantities which multiply variables in polynomials. Vieta’s formulae relate these quantities to a polynomial’s roots.
ANSWER: coefficients [accept method of undetermined coefficients]
[10e] In a Maclaurin series, the coefficient of x to the n is equal to the nth derivative of f evaluated at 0, divided by this function of n. This function, denoted by an exclamation mark, is equal to the product of all the integers from 1 to n.
ANSWER: factorial [or bang]
[10h] With examples including Pell’s equation, if the coefficients and solutions of an equation are all integers, it is given this adjective, named after a 3rd century mathematician from Alexandria. This adjective also names a method of approximating real numbers by rationals.
ANSWER: Diophantine [accept Diophantine equation; accept Diophantine approximation; prompt on Diophantus of Alexandria]
<Editors, Other Science> | Packet M
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 2 | 31 | 20.32 | 100% | 81% | 23% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Amherst A | Dartmouth A | 10 | 10 | 10 | 30 | MEH |
| Boston College B | Boston University B | 10 | 10 | 0 | 20 | ME |
| Brandeis Bach | Tufts B | 0 | 10 | 0 | 10 | E |
| Brandeis Mozart | MIT A | 0 | 10 | 0 | 10 | E |
| Dartmouth B | Boston College A | 10 | 10 | 10 | 30 | MEH |
| Tufts A | Vermont B | 10 | 10 | 0 | 20 | ME |
| Vermont A | UConn A | 10 | 10 | 0 | 20 | ME |
| Williams A | Brown A | 10 | 10 | 10 | 30 | MEH |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| UK (North) | UK | Y | 1 | 20.00 | 100% | 100% | 0% |
| UK (South) | UK | Y | 1 | 30.00 | 100% | 100% | 100% |
| Eastern Canada (2) | US | Y | 1 | 20.00 | 100% | 100% | 0% |
| Upper Mid-Atlantic | US | Y | 9 | 17.78 | 100% | 67% | 11% |
| Midwest | US | Y | 1 | 30.00 | 100% | 100% | 100% |
| Northeast | US | Y | 8 | 21.25 | 100% | 75% | 38% |
| Pacific | US | Y | 8 | 21.25 | 100% | 100% | 13% |
| Southeast | US | Y | 1 | 10.00 | 100% | 0% | 0% |
| Upstate NY | US | Y | 1 | 20.00 | 100% | 100% | 0% |