MathDB

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Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #1: Absolute Value Equation

Source:

4/29/2013
How many real numbers xx are solutions to the following equation? ∣x−1∣=∣x−2∣+∣x−3∣ |x-1| = |x-2| + |x-3|
symmetry
2005 Calculus #1: Parallel Tangent Lines

Source:

4/29/2013
Let f(x)=x3+ax+b f(x) = x^3 + ax + b , with a≠b a \ne b , and suppose the tangent lines to the graph of ff at x=ax=a and x=bx=b are parallel. Find f(1)f(1).
calculusanalytic geometrygraphing linesslope
2005 Geometry #1: Cube Stuff

Source:

5/12/2013
The volume of a cube (in cubic inches) plus three times the total length of its edges (in inches) is equal to twice its surface area (in square inches). How many inches long is its long diagonal?
geometry3D geometry