AMC 10A 试题及答案解析Word文档格式.docx

1、= the amount Pam spent = the amount Susan spent Pam pays 10 more dollars than Susan 2、Define and . What is ?3、An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. It is filled with water to a height of 40 cm. A brick with a rectangular base that measures 40 cm

2、by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise?The volume of the brick is . Thus the water volume rose . 4、The larger of two consecutive odd integers is three times the smaller. What is their sum?Let the two consecutive odd integers be , . Then

3、, so and their sum is .5、A school store sells 7 pencils and 8 notebooks for . It also sells 5 pencils and 3 notebooks for . How much do 16 pencils and 10 notebooks cost?We let cost of pencils in cents, number of notebooks in cents. Then Subtracting these equations yields . Backwards solving gives .

4、Thus the answer is . 6、At Euclid High School, the number of students taking the AMC10 was 60 in 2002, 66 in 2003, 70 in 2004, 76 in 2005, 78 and 2006, and is 85 in 2007. Between what two consecutive years was there the largest percentage increase?We compute the percentage increases:1. 2. 3. 4. 5. Th

5、e answer is . In fact, the answer follows directly from examining the differences between each year. The largest differences are , and it is easy to see that due to the decreased starting number of students in 2002 that that will be our answer. 7、Last year Mr. John Q. Public received an inheritance.

6、 He paid 20% in federal taxes on the inheritance, and paid 10% of what he has left in state taxes. He paid a total of for both taxes. How many dollars was the inheritance?After paying his taxes, he has of the inheritance left. Since is of the inheritance, the whole inheritance is .8、Triangles and ar

7、e isosceles with and . Point D is inside . , and . What is the degree measure of ?We angle chase, and find out that:9、Real numbers and satisfy the equations and . What is ?And Substitution gives , and solving for yields . Thus . 10、The Dunbar family consists of a mother, a father, and some children.

8、 The average age of the members of the family is , the father is years old, and the average age of the mother and children is . How many children are in the family?Let be the number of children. Then the total ages of the family is , and the total number of people in the family is . So 11、The number

9、s from to are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum?The sum of the numbers on the top face of a cube is equal to the sum of the numbers on the bottom face of the cube; these numbers represent all of the ve

10、rtices of the cube. Thus the answer is .12、Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourists are possible?Ea

11、ch tourist has to pick in between the guides, so for tourists there are possible groupings. However, since each guide must take at least one tourist, we subtract the cases where a guide has no tourist. Thus the answer is . 13、Yan is somewhere between his home and the stadium. To get to the stadium h

12、e can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yans distance from his home to his distance from the stadium?Let the distance from Yans in

13、itial position to the stadium be and the distance from Yans initial position to home be . We are trying to find , and we have the following identity given by the problem:Thus and the answer is 14、A triangle with side lengths in the ratio is inscribed in a circle of radius . What is the area of the t

14、riangle?Since 3-4-5 is a Pythagorean triple, the triangle is a right triangle. Since the hypotenuse is a diameter of the circumcircle, the hypotenuse is . Then the other legs are and . The area is 15、Four circles of radius are each tangent to two sides of a square and externally tangent to a circle of radius , as shown. What is the area of the square?The diagonal has length . Therefore the sides have length , and the area is Alternate Solution Exten