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Northeastern
Section of the Mathematical Association of America 2009 Collegiate Mathematics Competition |
| HOME | RULES | PRACTICE
PROBLEMS
| REGISTRATION OLD COMPETITION QUESTIONS | OLD PRACTICE PROBLEMS || NES/MAA |
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| Date |
Problem |
Solution |
| Th, 10/8 |
For what value of $k$ does the equation $e^{2x}=k\sqrt{x}$ have exactly one solution? | Solution |
| M, 10/12 |
A student forgot the Product Rule for differentiation and made the mistake of thinking that $(fg)'=f'g'$. However, he was lucky and got the correct answer. The function $f$ that he used was $f(x)=e^{x^2}$ and the domain of his problem was $(\frac12, \infty)$. What was the function $g$? | Solution |
| W, 10/14 |
Show separately that the numbers 10201, 10101, and 100011 are composite in any base. | Solution |
| F, 10/16 |
Solve $\sqrt[3]{13x+37} - \sqrt[3]{13x-37}=\sqrt[3]{2}$. | Solution |
| M, 10/19 |
Let $A$ be a square matrix of rank 1 and trace 1. Prove that $A^2=A$. | Solution |
| Tu, 10/20 | We apologize for the technical difficulties the past few days! We hope that all the problems caused by my math display software upgrade have been resolved!! | |
| W, 10/21 |
The expression $a|b$ means that $a$ divides $b$. Suppose that $2^{m}|(3^{m}-1)$. Show that if $m\ne 1$, then $m$ is even. | Solution |
| M, 10/26 |
A 10-foot pole is dropped into a milling saw and randomly cut into three shorter poles. What is the probability that these three pieces will form a triangle? | Solution |
| M, 11/2 |
Without
performing multiplications, find the digits $a$ and $b$ in
23! = 2585201ab38884976640000.
|
Solution |
| W, 11/4 |
Given
f(x)=\frac{607}{607x+1} +
\frac{692}{692x+1}+\frac{-701}{-701x+1}.
determine, without using a computing device, whether or not
$f^{(12)}(0)=0$.
|
Solution |
| M, 11/9 |
A curve is
defined by the parametric equations
x=\int_1^t \frac{\cos u}{u}\,du \qquad y=\int_1^t \frac{\sin u}{u}\,du
Find the length of the arc of the curve from the origin to the nearest point where there is a vertical tangent line.
|
Solution |
| W, 11/11 | Find the largest possible area of a pentagon with five sides of length 1 and a right interior angle. | Check back on F, 11/13 |