AMC10美国数学竞赛真题 xx年Word格式.docx

1、 . What is Problem 2 A number is more than the product of its reciprocal and its additive inverse. In which interval does the number lie? Problem 3 The sum of two numbers is . Suppose is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

2、 Problem 4 What is the maximum number for the possible points of intersection of a circle and a triangle? Problem 5 How many of the twelve pentominoes pictured below have at least one line of symmetry? Problem 6 Let and denote the product and the sum, respectively, of the digits of . Suppose is a ?

3、the integer . For example, two-digit number such that . What is the units digit of Problem 7 When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number? Problem 8 Wanda

4、, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how man

5、y school days from today will they next be together tutoring in the lab? Problem 9 The state income tax where Kristin lives is levied at the rate of of annual income plus of any amount above of the first . Kristin of her noticed that the state income tax she paid amounted to annual income. What was

6、her annual income? Problem 10 If , , and are positive with , , and , then Problem 11 Consider the dark square in an array of unit squares, part of which is shown. The ?rst ring of squares around this center square contains unit squares. The second ring contains unit squares. If we continue this proc

7、ess, the number of unit squares in the ring is Problem 12 Suppose that is the product of three consecutive integers and that by . Which of the following is not necessarily a divisor of ? is divisible Problem 13 A telephone number has the form , where each letter represents a different digit. The dig

8、its in each part of the numbers are in decreasing order; that is, , , and . Furthermore, , , and are consecutive even digits; , , , and are consecutive odd digits; and . Find . Problem 14 A charity sells benefit tickets for a total of . Some tickets sell for full price （a whole dollar amount）, and t

9、he rest sells for half price. How much money is raised by the full-price tickets? Problem 15 A street has parallel curbs feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is feet and each stripe is feet long. Find the d

10、istance, in feet, between the stripes? Problem 16 The mean of three numbers is more than the least of the numbers and less than the greatest. The median of the three numbers is . What is their sum? Problem 17 Which of the cones listed below can be formed from a radius by aligning the two straight si

11、des? sector of a circle of Problem 18 The plane is tiled by congruent squares and congruent pentagons as indicated. The percent of the plane that is enclosed by the pentagons is closest to Problem 19 Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and p

12、owdered. How many different selections are possible? Problem 20 A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length . What is the length of each side of the octagon? Problem 21 A right circular cylinder with its diameter equal

13、to its height is inscribed in a right circular cone. The cone has diameter and altitude , and the axes of the cylinder and cone coincide. Find the radius of the cylinder. Problem 22 In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbe

14、rs are represented by , , , , and . Find . Problem 23 A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white? Problem 24 In trapezoid , , are perpendicular to , and . What is , with Problem 25 How many positive integers not exceeding ? are multiples of or but not