2002 amc 10 b problems pdf

Annual american mathematics contest 10 amc 10 contest a. Myexamcloud amc 10 practice tests helps you to get great score in real exam. Based on artificial intelligence ai, machine learning, and deep learning, we devised a data mining and predictive analytics tool for math problem similarity searching. The mathematical association of america american mathematics. The probability that he gets at least as many heads as tails is a 5 16 b 3 8 c 1 2 d 5 8 e 11 16 22. The case x 4 shows that x is not necessarily a multiple of 3 and that none of the other statements must be true. The ratio 22001 32003 62002 is a 1 6 b 1 3 c 1 2 d 2 3 e 3 2 2. The order of the numbers in the second row is to be reversed.

The sum of these four primes is a even b divisible by 3 c divisible by 5 d divisible by 7 e prime for how many integers n is the square of an integer. Students who perform well on the amc 10 or amc 12 competitions are invited. Solution problem 2 paul owes paula 35 cents and has a pocket full of 5cent coins, 10cent coins, and 25cent coins that he. Start with book viii for amc 10 prep and book ix for amc 12 prep. How many different numbers could represent the total points scored by the player. This is a twentyfivequestion, multiple choice test. Amc 10 2002 14 both roots of the quadratic equation x 2. We provided 35 sets of past real amc 12 tests 20002017 with answer keys and also developed 20 sets of amc 12 mock test with detailed solutions to help students prepare for the amc 12 contest. Selection file type icon file name description size revision time user. The problems and solutions for this amc 10 were prepared by the maas committee on the amc 10 and amc 12 under the direction of amc 10 subcommittee chair. The cone has diameter 10 and altitude 12, and the axes of the cylinder and cone coincide. The best way to prepare for the amc 10 is to do lots of practice problems either on your own or with a small group and then check your solutions with an answer key. Problem 1 at a movie theater, the manager announces that a free ticket will be given to the rst person in line whose birthday is the same as someone in line who has already bought a ticket. The aime is a 15 question exam which takes 3 hours in which each answer is an integer number from 0999.

Points a, b, c, and d lie on a line, in that order, with ab cd and bc 12. If an arc of 45 on circle a has the same length as an arc of 30 on circle b, then the ratio of the area of circle a to the area of circle b is a 4 9 b 2 3 c 5 6 d 3 2 e 9 4 8. Similarly in her tenth game, she scored fewer than 10 points and her pointspergame average for the 10 games was also. Wednesday, february 27, 2002 contest b the mathematical association of america american mathematics competitions presented by the akamai foundation amc 12 53rd annual american mathematics contest 12 1. Sawyers class were asked to do a taste test of five kinds of candy. The positive integers a b a b and a l b are all prime numbers. Thus, a student who answers 23 questions correctly and 2 questions.

Archive of amcseries contests for the amc 8, amc 10, amc 12, and aime. Problem solving uisng vietas theorem sample problems 2 example 10. E we have 22001 u00b7 32003 62002 22001 u00b732003 2u00b7 3 2002 22001 u00b7 32003 22002 u00b7 32002 3 2. Douglas faires, department of mathematics youngstown state university, youngstown, oh.

Amc 10 practice tests and ebooks online books are available online at myexamcloud exam simulator training platform. For this reason, we provided all 35 sets of previous official amc 10 contests 20002017 with answer keys and also developed 20 sets of amc. Using this powerful tool, we examined the types, styles, frequencies, characteristics, and traits of questions in all past amc 12 exams, and. The difference between the aime and the amc 10 and amc 12 is that all the problems in the latter can be solved by precalculus methods. Find 2 2 1 1 if and are two roots of the equation x2 x 3 0. Mock amc series contests for the amc 8, amc 10, amc 12, and aime. Our online amc 10 problem series course has been instrumental preparation for thousands of top amc 10 scorers over the past decade. Solutions 2008 9thamc 10 a 2 solutions 2008 amc 10 a 3 is an integer, x must be even. Which of the cones below can be formed from a 252 sector of a circle of radius 10 by aligning the two straight sides. Jan 30, 2020 print page 191, pdf page 212 practice under testing conditions. These mock contests are similar in difficulty to the real contests, and include randomly selected problems from the real contests. Amc 10 student practice questions continued points a and c lie on a circle centered at o, each of ba and bc are tangent to the circle, and.

Keep a log and set incremental goals start with book viii for amc 10 prep and book ix for amc 12 prep. The number 2564 6425 is the square of a positive integer n. Amc 10 2000 problems amc 10 2001 problems amc 10 2002a problems amc 10 2002b problems amc 10 2003a. The publication, reproduction or communication of the problems or solutions of this test during the period when students are eligible to participate seriously jeopardizes the integrity of the results. The arithmetic mean of the nine numbers in the set. Adding the two equations and dividing by gives, so. A 8 3 b 30 11 c 3 d 25 8 e 7 2 v 24 w 18 x y 25 z 21 22. The percent of the plane that is enclosed by the pentagons is closest to. A circle and two distinct lines are drawn on a sheet of paper. Each handout covers topics beyond those learned in school and normally consists of 2 pages.

The plane is tiled by congruent squares and congruent pentagons as indicated. Suppose a, b, and c are three numbers for which 1001c. In decimal representation, the sum of the digits ofn is a 7 b 14 c 21 d 28 e 35 15. The rest contain each individual problem and its solution. Mary typed a sixdigit number, but the two 1s she typed didnt show. Douglas faires, department of mathematics youngstown state university, youngstown, oh 445550001 email. Coin a is ipped three times and coin b is ipped four times. When is appended to a list of integers, the mean is increased by.

The answers to the problems are to be marked on the amc 10. American mathematics competitions amc 10, 20002007 contests. You may practice more than once, and each attempt features new problems. With a lot of algebra, the solution is found to be.

E we have 22001 u00b7 32003 62002 22001 u00b732003 2u00b7 32002 22001 u00b7 32003 22002 u00b7 32002 3 2. The first link contains the full set of test problems. The number of possible values of k is a 0 b 1 c 2 d 3 e more than four. A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. Thearithmeticmeanofthe ninenumbersin theset 9,99,999,9999. The sum of these four primes is a even b divisible by 3 c divisible by 5 d divisible by 7. The second link contains the answers to each problem. Discuss problematic questions with other mathletes. The american mathematics competitions amc are the first of a series of competitions in. Recent changes random page help what links here special pages. Practice math contests zoom international math league. What is the sticker price of the computer, in dollars. The mean weight of the rocks in a is 40 pounds, the mean weight of the rocks in b is 50 pounds, the mean weight of the rocks in the combined piles a and b is 43 pounds, and the mean weight of the rocks in the combined piles a and c is 44 pounds. If you have either of these feelings, then you are not alone.

Denote the height of a pane by 5x and the width by 2x. All problems from past amc 12 20002017 form our big data system. Tuesday, february 12, 2002 contest a the mathematical association of america american mathematics competitions presented by the akamai foundation amc 12 53rd annual american mathematics contest 12 1. Prepare with one of the best amc 10 study course developed by subject experts. Dissemination at any time via copier, telephone, email, internet or media of any type is a violation of the competition rules. Let be the sum of the integers and be the number of elements in the list. The number 2564 a 6425 is the square of a positive integer n. Read mathematical problem solving for competitions from book vi. For this reason, we provided all 35 sets of previous official amc 10 contests 20002017 with answer keys and also developed 20 sets of amc 10 mock test with detailed solutions to help you prepare for this premier contest. In her ninth game, she scored fewer than 10 points and her pointspergame average for the nine games was an integer. Amc 10 p 2002 2 mathematical association of america. What is the largest possible number of points of intersection of these figures. Mock amcseries contests for the amc 8, amc 10, amc 12, and aime.

Problem solving uisng vietas theorem sample problems. Since the internal tangent is shorter than the external tangent, pq intersects ab at a point d that divides ab into parts proportional to the radii. Archive of amc series contests for the amc 8, amc 10, amc 12, and aime. Wednesday, february 27, 2002 contest b the mathematical association of america american mathematics competitions presented by the akamai foundation amc 10 3rd annual american mathematics contest 10 1. If a, b,c,d are positive real numbers such that a, b,c,d form an increasing arith metic sequence and a, b,d form a geometric sequence, then a d is a 1 12 b 1 6 c 1 4 d 1 3 e 1 2 10. The problems and solutions for this amc 10 were prepared by the maas. When is appended to the enlarged list, the mean of the enlarged list is decreased by. Competition math circles handouts are made by its officers. Which of the following statements must be true about x. In decimal representation, the sum of the digits of n is a 7 b 14 c 21 d 28 e 35 15. The ratio 248 482 equals a 1 4 b 1 2 c 1 d 2 e 8 2.