MathDB

11

Part of 2006 AMC 10

Problems(2)

Graph of equation

Source: AMC 12 2006A, Problem 11

2/5/2006
Which of the following describes the graph of the equation (x \plus{} y)^2 \equal{} x^2 \plus{} y^2?
<spanclass=′latex−bold′>(A)</span> the empty set<spanclass=′latex−bold′>(B)</span> one point<spanclass=′latex−bold′>(C)</span> two lines <span class='latex-bold'>(A)</span>\text{ the empty set}\qquad <span class='latex-bold'>(B)</span>\text{ one point}\qquad <span class='latex-bold'>(C)</span>\text{ two lines}
<spanclass=′latex−bold′>(D)</span> a circle<spanclass=′latex−bold′>(E)</span> the entire plane<span class='latex-bold'>(D)</span>\text{ a circle}\qquad <span class='latex-bold'>(E)</span>\text{ the entire plane}
AMC
Factorial sums

Source: AMC 10 2006B, Problem 11

2/17/2006
What is the tens digit in the sum 7! \plus{} 8! \plus{} 9! \plus{} \cdots \plus{} 2006!? <spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>9 <span class='latex-bold'>(A) </span> 1 \qquad <span class='latex-bold'>(B) </span> 3 \qquad <span class='latex-bold'>(C) </span> 4 \qquad <span class='latex-bold'>(D) </span> 6 \qquad <span class='latex-bold'>(E) </span> 9
factorialAMC