2009 AMC 10A Problems
Contents
[hide]- 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 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
One can holds ounces of soda. What is the minimum number of cans needed to provide a gallon (128 ounces) of soda?
Problem 2
Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes and quarters. Which of the following could not be the total value of the four coins, in cents?
Problem 3
Which of the following is equal to ?
Problem 4
Eric plans to compete in a triathalon. He can average miles per hour in the -mile swim and miles per hour in the -mile run. His goal is to finish the triathlon in hours. To accomplish his goal what must his average speed in miles per hour, be for the -mile bicycle ride?
Problem 5
What is the sum of the digits of the square of ?
Problem 6
A circle of radius is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?
Problem 7
A carton contains milk that is % fat, an amount that is % less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?
Problem 8
Three Generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a % discount as children. The two members of the oldest generation receive a discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs <dollar/>, is paying for everyone. How many dollars must he pay?
Problem 9
Positive integers , , and , with , form a geometric sequence with an integer ratio. What is ?
Problem 10
Problem 11
One dimension of a cube is increased by , another is decreased by , and the third is left unchanged. The volume of the new rectangular solid is less than that of the cube. What was the volume of the cube?
Problem 12
In quadrilateral , , , , , and is an integer. What is ?
Problem 13
Suppose that and . Which of the following is equal to for every pair of integers ?
Problem 14
Problem 15
The figures , , , and shown are the first in a sequence of figures. For , is constructed from by surrounding it with a square and placing one more diamond on each side of the new square than had on each side of its outside square. For example, figure has diamonds. How many diamonds are there in figure ?
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
For , let , where there are zeros between the and the . Let be the number of factors of in the prime factorization of . What is the maximum value of ?