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1、2017 AMC 10A Problems2017 AMC 10A (Answer Key)Printable version: Wiki | AoPS Resources PDF Instructions 1. This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. 2. You will receive 6 points for each correct answer, 2.
2、5 points for each problem left unanswered if the year is before 2006, 1.5 points for each problem left unanswered if the year is after 2006, and 0 points for each incorrect answer.3. No aids are permitted other than scratch paper, graph paper, ruler, compass, protractor and erasers (and calculators
3、that are accepted for use on the SAT if before 2006. No problems on the test will require the use of a calculator). 4. Figures are not necessarily drawn to scale.5. You will have 75 minutes working time to complete the test. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Contentsh
4、ide 1 Problem 1 2 Problem 2 3 Problem 3 4 Problem 4 5 Problem 5 6 Problem 6 7 Problem 7 8 Problem 8 9 Problem 9 10 Problem 10 11 Problem 11 12 Problem 12 13 Problem 13 14 Problem 14 15 Problem 15 16 Problem 16 17 Problem 17 18 Problem 18 19 Problem 19 20 Problem 20 21 Problem 21 22 Problem 22 23 Pro
5、blem 23 24 Problem 24 25 Problem 25 26 See alsoProblem 1What is the value of ? Solution Problem 2Pablo buys popsicles for his friends. The store sells single popsicles for each, -popsicle boxes for each, and -popsicle boxes for . What is the greatest number of popsicles that Pablo can buy with ? Sol
6、ution Problem 3Tamara has three rows of two -feet by -feet flower beds in her garden. The beds are separated and also surrounded by -foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet? Solution Problem 4Mia is “helping” her mom pick up toys that are s
7、trewn on the floor. Mias mom manages to put toys into the toy box every seconds, but each time immediately after those seconds have elapsed, Mia takes toys out of the box. How much time, in minutes, will it take Mia and her mom to put all toys into the box for the first time? Solution Problem 5The s
8、um of two nonzero real numbers is times their product. What is the sum of the reciprocals of the two numbers? Solution Problem 6Ms. Carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an A on the exam. Which of of these statements necessari
9、ly follows logically? Solution Problem 7Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following i
10、s closest to how much shorter Silvias trip was, compared to Jerrys trip? Solution Problem 8At a gathering of people, there are people who all know each other and people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur? Solu
11、tion Problem 9Minnie rides on a flat road at kilometers per hour (kph), downhill at kph, and uphill at kph. Penny rides on a flat road at kph, downhill at kph, and uphill at kph. Minnie goes from town to town , a distance of km all uphill, then from town to town , a distance of km all downhill, and
12、then back to town , a distance of km on the flat. Penny goes the other way around using the same route. How many more minutes does it take Minnie to complete the -km ride than it takes Penny? Solution Problem 10Joy has thin rods, one each of every integer length from cm through cm. She places the ro
13、ds with lengths cm, cm, and cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod? Solution Problem 11The region consisting of all points in three-dimensional
14、space within units of line segment has volume . What is the length ? Solution Problem 12Let be a set of points in the coordinate plane such that two of the three quantities and are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct d
15、escription for Solution Problem 13Define a sequence recursively by and the remainder when is divided by for all Thus the sequence starts What is Solution Problem 14Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Rogers allowance was dollars. The cost of his movie ticket was of the difference between and the cost of his soda, while the cost of his soda was of the difference between and the cost of his movie ticket. To the nearest whole percent, what fraction of did Roger pay for hi