2011 AMC8

Problem 1

Margie bought word/media/image1.gif apples at a cost of word/media/image2.gif cents per apple. She paid with a 5-dollar bill. How much change did Margie recieve?

word/media/image3.gif

Problem 2

Karl's rectangular vegetable garden is word/media/image4.gif feet by word/media/image5.gif feet, and Makenna's is word/media/image6.gif feet by word/media/image7.gif feet. Whose garden is larger in area?

word/media/image8.gif

word/media/image9.gif

word/media/image10.gif

word/media/image11.gif

word/media/image12.gif

Problem 3

Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?

word/media/image14.gif

Problem 4

Here is a list of the numbers of fish that Tyler caught in nine outings last summer:word/media/image15.gifWhich statement about the mean, median, and mode is true?

word/media/image16.gif

Problem 5

What time was it word/media/image17.gif minutes after midnight on January 1, 2011?

word/media/image18.gif

word/media/image19.gif

word/media/image20.gif

word/media/image21.gif

word/media/image22.gif

Problem 6

In a town of 351 adults, every adult owns a car, motorcycle, or both. If 331 adults own cars and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?

word/media/image23.gif

Problem 7

Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially bolded. What percent of the total area is partially bolded?

word/media/image25.gif

Problem 8

Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?

word/media/image26.gif

Problem 9

Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. What is Carmen's average speed for her entire ride in miles per hour?

word/media/image28.gif

Problem 10

The taxi fare in Gotham City is $2.40 for the first word/media/image29.gif mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?

word/media/image30.gif

Problem 11

The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?

word/media/image32.gif

Problem 12

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?

word/media/image33.gif

Problem 13

Two congruent squares, word/media/image34.gif and word/media/image35.gif, have side length word/media/image36.gif. They overlap to form the word/media/image36.gif by word/media/image6.gif rectangle word/media/image37.gif shown. What percent of the area of rectangle word/media/image37.gif is shaded?

word/media/image39.gif

Problem 14

There are word/media/image40.gif students at Colfax Middle School, where the ratio of boys to girls is word/media/image41.gif. There are word/media/image42.gif students at Winthrop Middle School, where the ratio of boys to girls is word/media/image43.gif. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?

word/media/image44.gif

Problem 15

How many digits are in the product word/media/image45.gif?

word/media/image46.gif

Problem 16

Let word/media/image47.gif be the area of the triangle with sides of length word/media/image48.gif, and word/media/image49.gif. Let word/media/image50.gif be the area of the triangle with sides of length word/media/image51.gif and word/media/image7.gif. What is the relationship between word/media/image47.gif and word/media/image50.gif?

word/media/image52.gif

Problem 17

Let word/media/image53.gif, word/media/image54.gif, word/media/image55.gif, and word/media/image56.gif be whole numbers. If word/media/image57.gif, then what does word/media/image58.gif equal?

word/media/image59.gif

Problem 18

A fair 6-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?

word/media/image60.gif

Problem 19

How many rectangles are in this figure?

word/media/image62.gif

Problem 20

Quadrilateral word/media/image34.gif is a trapezoid, word/media/image63.gif, word/media/image64.gif, word/media/image65.gif, and the altitude is word/media/image66.gif. What is the area of the trapeziod?

word/media/image68.gif

Problem 21

Students guess that Norb's age is word/media/image69.gif, and word/media/image70.gif. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb?

word/media/image71.gif

Problem 22

What is the tens digit of word/media/image72.gif?

word/media/image73.gif

Problem 23

How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?

word/media/image74.gif

Problem 24

In how many ways can 10001 be written as the sum of two primes?

word/media/image75.gif

Problem 25

A circle with radius word/media/image76.gif is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?

word/media/image78.gif