MathDB

12

Part of 2015 AMC 10

Problems(2)

Graph

Source: 2015 10A #12

2/4/2015
Points (π,a)(\sqrt{\pi}, a) and (π,b)(\sqrt{\pi}, b) are distinct points on the graph of y2+x4=2x2y+1y^2+x^4=2x^2y+1. What is ∣a−b∣|a-b|?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>π2<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>1+π<spanclass=′latex−bold′>(E)</span>1+π <span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>\dfrac{\pi}{2}\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\sqrt{1+\pi}\qquad<span class='latex-bold'>(E) </span>1+\sqrt{\pi}
quadraticsalgebrapolynomialVietaquadratic formulaabsolute valueAMC
Points of a Line within a Circle

Source: 2015 amc 10b #12

2/26/2015
For how many integers xx is the point (x,−x)(x,-x) inside or on the circle of radius 1010 centered at (5,5)(5,5)? <spanclass=′latex−bold′>(A)</span>11<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>14<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span> 11 \qquad<span class='latex-bold'>(B) </span> 12 \qquad<span class='latex-bold'>(C) </span> 13 \qquad<span class='latex-bold'>(D) </span> 14 \qquad<span class='latex-bold'>(E) </span> 15
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