MathDB

2009 Algebra #9 - Minimum Value of Expression of Roots

Source:

1/2/2012

Let

f(x) =x^4+14x^3+52x^2+56x+16.

Let

z_1, z_2, z_3, z_4

be the four roots of

f

. Find the smallest possible value of

|z_az_b+z_cz_d|

where

\{a,b,c,d\}=\{1,2,3,4\}

.

2009 Calculus #9: Revolving Around a Line

Source:

6/23/2012

Let

\mathcal{R}

be the region in the plane bounded by the graphs of

y=x

and

y=x^2

. Compute the volume of the region formed by revolving

\mathcal{R}

around the line

y=x

.

calculusgeometry

2009 Combinatorics #9 - Filling out a 3x3 Grid

Source:

1/7/2012

The squares of a

3\times3

grid are filled with positive integers such that

1

is the label of the upper- leftmost square,

2009

is the label of the lower-rightmost square, and the label of each square divides the ne directly to the right of it and the one directly below it. How many such labelings are possible?

2009 Geometry #9: Angle Bisectors of a Triangle

Source:

6/23/2012

Let

ABC

be a triangle with

AB=16

and

AC=5

. Suppose that the bisectors of angle

\angle ABC

and

\angle BCA

meet at a point

P

in the triangle's interior. Given that

AP=4

, compute

BC

.

geometryincentertrigonometryangle bisector

9

Problems(4)