2011 AMC 12A Problems

Problem 1

A cell phone plan costs dollars each month, plus cents per text message sent, plus cents for each minute used over hours. In January Michelle sent text messages and talked for hours. How much did she have to pay?

Solution

Problem 2

There are coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

Solution

Problem 3

A small bottle of shampoo can hold milliliters of shampoo, whereas a large bottle can hold milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?

Solution

Problem 4

At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of , , and minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

Solution

Problem 5

Last summer $30%$ (Error compiling LaTeX. Unknown error_msg) of the birds living on Town Lake were geese, $25%$ (Error compiling LaTeX. Unknown error_msg) were swans, $10%$ (Error compiling LaTeX. Unknown error_msg) were herons, and $35%$ (Error compiling LaTeX. Unknown error_msg) were ducks. What percent of the birds that were not swans were geese?

Solution

Problem 6

Solution The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was points. How many free throws did they make?

Problem 7

A majority of the students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than . The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was . What was the cost of a pencil in cents?

Solution

Problem 8

In the eight term sequence , , , , , , , , the value of is and the sum of any three consecutive terms is . What is ?

Solution

Problem 9

At a twins and triplest convention, there were sets of twins and sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many handshakes took place?

Solution

Problem 10

A pair of standard -sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference?

Solution

Problem 11

Solution

Circles and each have radius 1. Circles and share one point of tangency. Circle has a point of tangency with the midpoint of $\overbar{AB}.$ (Error compiling LaTeX. Unknown error_msg) What is the area inside circle but outside circle and circle

$\textbf{(A)}\ 3 - \frac{\pi}{2} \qquad \textbf{(B)}\ \frac{\pi}{2} \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ \frac{3\pi}{4} \qquad \textbf{(E)}\ 1+\frac{\pi}{2}}$ (Error compiling LaTeX. Unknown error_msg)

Problem 12

Solution A power boat and a raft both left dock on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock How many hours did it take the power raft to go from to

A - 3 B - 3.5 C- 4 D - 4.5 E - 5

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution