MathDB

6

Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #6: Points of Intersection

Source:

4/29/2013
Find the sum of the x-coordinates of the distinct points of intersection of the plane curves given by x2=x+y+4x^2 = x + y + 4 and y2=y−15x+36y^2 = y - 15x + 36.
analytic geometry
2005 Calculus #6: Polar Coordinates and an Area

Source:

4/29/2013
The graph of r=2+cos⁡2θr=2+\cos2\theta and its reflection over the line y=xy=x bound five regions in the plane. Find the area of the region containing the origin.
calculusanalytic geometrygeometrygeometric transformationreflectionintegrationtrigonometry
2005 Geometry #6: Paper Triangle

Source:

5/16/2013
A triangular piece of paper of area 11 is folded along a line parallel to one of the sides and pressed flat. What is the minimum possible area of the resulting figure?
geometrytrapezoidquadraticssimilar triangles