By J. Douglas Faires, David Wells

For greater than 50 years, the Mathematical organization of the USA has been engaged within the building and management of hard contests for college kids in American and Canadian excessive faculties. the issues on those contests are built within the desire that every one highschool scholars attracted to arithmetic may have the chance to take part within the contests and should locate the event mathematically enriching. those contests are meant for college kids in any respect degrees, from the typical pupil at a regular university who enjoys arithmetic to the superior scholars on the so much specific tuition.

In the yr 2000, the Mathematical organization of the United States initiated the yank arithmetic Competitions 10 (AMC 10) for college kids as much as grade 10. the competition challenge e-book VIII is the 1st number of difficulties from that pageant overlaying the years 2001-2007. J. Douglas Faires and David Wells have been the joint administrators of the AMC 10 and AMC 12 in the course of that interval, and feature assembled this publication of difficulties and ideas.

There are 350 difficulties from the 1st 14 contests integrated during this assortment. an issue Index behind the publication classifies the issues into the subsequent significant topic components: Algebra and mathematics, Sequences and sequence, Triangle Geometry, Circle Geometry, Quadrilateral Geometry, Polygon Geometry, Counting Coordinate Geometry, strong Geometry, Discrete likelihood, information, quantity conception, and common sense. the most important topic parts are then damaged down into subcategories for ease of reference. the issues are cross-referenced once they signify a number of topic areas.

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A) 297 (B) 330 (C) 363 (D) 396 (E) 726 2. How many two-digit positive integers have at least one 7 as a digit? (A) 10 (B) 18 (C) 19 (D) 20 (E) 30 3. At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice? (A) 3 (B) 6 (C) 9 (D) 12 (E) 15 4. A standard six-sided die is rolled, and P is the product of the five numbers that are visible. What is the largest number that is certain to divide P ?

Andy’s lawn has twice as much area as Beth’s lawn and three times as much area as Carlos’ lawn. Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower. Suppose they all start to mow their lawns at the same time. Who will finish first? (A) Andy (B) Beth (C) Carlos (D) Andy and Carlos tie for first. (E) All three tie. ✐ ✐ ✐ ✐ ✐ ✐ “ContestBook10” — 2008/4/9 — 16:18 — page 20 — #36 ✐ 20 ✐ Problems 22. Let 4XOY be a right triangle with ∠XOY D 90ı . Let M and N be the midpoints of legs OX and OY , respectively.

Which of the following is closest to the number of miles between downtown St. Paul and downtown Minneapolis? (A) 13 (B) 14 (C) 15 (D) 16 (E) 17 ✐ ✐ ✐ ✐ ✐ ✐ “ContestBook10” — 2008/4/9 — 16:18 — page 37 — #53 ✐ 2004 AMC 10B Problems ✐ 37 9. A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle? (A) 200 C 25 (B) 100 C 75 (D) 100 C 100 (E) (C) 75 C 100 100 C 125 10. A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it.