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The Contest Problem Book V: American High School Mathematics by George Berzsenyi, Stephen B. Maurer PDF

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By George Berzsenyi, Stephen B. Maurer

ISBN-10: 0883856409

ISBN-13: 9780883856406

This ebook should be of curiosity to an individual of any age who likes strong difficulties. Pre-calculus historical past is presumed. through the years maybe the preferred of the MAA challenge books were the highschool contest books, protecting the annual American highschool arithmetic Examinations (AHSME) that started in 1950, co-sponsored from the beginning via the MAA. ebook V additionally contains the 1st six years of the yankee Invitational arithmetic exam (AIME) which was once constructed as an intermediate step among the AHSME and america Mathematical Olympiad (USAMO). The AIME has a special resolution format--all solutions are integers among zero and 999. The editors of this quantity, George Berzsenyi and Stephen B. Maurer, have been respectively the chairs of the AIME and the AHSME. as well as an intensive index, they've got additional fabric to Contest challenge publication V no longer integrated in Contest Books I–IV, similar to: a entire world wide consultant to different challenge fabrics, extra suggestions to chose difficulties, and knowledge at the improvement and historical past of the AHSME, AIME, and USAMO checks.

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Extra resources for The Contest Problem Book V: American High School Mathematics Examinations

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20. Suppose 2 and y are inversely proportional and positive. If increases by p%, then y decreases by 2 21. In the configuration below, 8 is measured in radians, C is the center of the circle, BCD and ACE E are line segments, and A B is tangent to the circle at A. D B A A necessary and sufficient condition for the equality of the two shaded areas, given 0 < 8 < ~ / 2 ,is 22. Six distinct integers are picked at random from {1,2,3,. . ,10). What is the probability that, among those selected, the second smallest is 3?

Then the length of BC is (A) 3 (B) 3 + d (C)5 - 3 9 (D) 5 (E) none of the above 23. If -1 +i& -1 -i& and y= 2 ' 2 where i2 = -1, then which of the following is not correct? X = (A) z5+y5=-i (D)d1+ y" = -1 (B) z 7 + y 7 = - 1 (E)x13 + y13 = -1 (c) z 9 + y 9 = - 1 24. A non-zero digit is chosen in such a way that the probability of The probability that choosing digit d is logl,(d+l) - log,,d. the digit 2 is chosen is exactly 1/2 the probability that the digit chosen is in the set CONTESTPROBLEMBOOK V 18 25.

If the sequence {a,} is defined by then a100 equals (A) 9900 (B) 9902 (C) 9904 (D) 10100 (E) 10102 14. The product of all real roots of the equation x'Og1oZ = 10 is (A) 1 (B) -1 (C) 10 (D) lo-' (E) none of these 15. If sin22 sin32 = cos2x cos3x, then one value for x is (A) 18" (B) 30" (C) 36" (D) 45" (E) 60" 16. The function f(x) satisfies f(2+x) = f(2-x) for all real numbers x. If the equation f(x) = 0 has exactly four distinct real roots, then the sum of these roots is CONTEST PROBLEM BOOK V 10 A 17.

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The Contest Problem Book V: American High School Mathematics Examinations by George Berzsenyi, Stephen B. Maurer

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