A
B
C
D
E
F
G
Diﬃculty:
Hard
CCSS-M:
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords.
18

In 1991 the population of a town was a perfect square. Tenyears later, after an increase of 150 people, the population was9 more than a perfect square. Now, in 2011, with an increaseof another 150 people, the population is once again a perfectsquare. Which of the following is closest to the percent growthof the town’s population during this twenty-year period?
(A)42(B)47(C)52(D)57(E)62
2011 AMC 10A, Problem #19—“What are the populations of the town in 1911, 2001 and 2011?”
2. The percent growth from 1991 to 2011 was784-484484≈62%.Diﬃculty:HardCCSS-M:N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.
19

Two points on the circumference of a circle of radiusrareselected independently and at random.From each point achord of lengthris drawn in a clockwise direction. What isthe probability that the two chords intersect?
2011 AMC 10A, Problem #20—“Start with the points at special positions, for example, one radiusapart.”
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. I
20

Two counterfeit coins of equal weight are mixed with 8identical genuine coins. The weight of each of the counterfeitcoins is different from the weight of each of the genuine coins.A pair of coins is selected at random without replacementfrom the 10 coins. A second pair is selected at random withoutreplacement from the remaining 8 coins. The combined weightof the first pair is equal to the combined weight of the secondpair.What is the probability that all 4 selected coins aregenuine?
(A)711(B)913(C)1115(D)1519(E)15