# 2006 AMC 10B SOLUTIONS PDF

Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. For more than 50 years, the Mathematical Association of America has been engaged in the construction and administration of challenging contests for students in American and Canadian high schools. The problems for these contests are constructed in the hope that all high school students interested in mathematics will have the opportunity to participate in the contests and will find the experience mathematically enriching. These contests are intended for students at all levels, from the average student at a typical school who enjoys mathematics to the very best students at the most special school.

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Sandwiches at Joe's Fast Food cost purchase 5 sandwiches and 8 sodas? Problem 1. How many dollars will it cost to. What is. Problem 2. The ratio of Mary's age to Alice's age is. Problem 3. Alice is. How many years old is Mary? Problem 4. A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display? Problem 5. Doug and Dave shared a pizza with 8 equally-sized slices.

Doug wanted a plain pizza, but Dave wanted anchovies on half of the pizza. The cost of a plain pizza was 8 dollars, and there was an additional cost of 2 dollars for putting anchovies on one half.

Dave ate all of the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each then paid for what he had eaten. How many more dollars did Dave pay than Doug? What non-zero real value for.

Problem 6. Problem 7. A parabola with equation. Problem 8. Problem 9. How many sets of two or more consecutive positive integers have a sum of 15? For how many real values of. Problem Which of the following describes the graph of the equation.

Rolly wishes to secure his dog with an 8-foot rope to a square shed that is 16 feet on each side. His preliminary drawings are shown.

Which of these arrangements give the dog the greater area to roam, and by how many square feet? A player pays. In this case the player wins if the second number matches the first and loses otherwise. How much should the player win if the game is fair? In a fair game. A die is rolled. If the number on the die is odd, the game is lost. If the. A number of linked rings, each 1 cm thick, are hanging on a peg. The top ring has an outside diameter of 20 cm. The outside diameter of each of the outer rings is 1 cm less than that of the ring above it.

The bottom ring has an outside diameter of 3 cm. What is the distance, in cm, from the top of the top ring to the bottom of the bottom ring? Odell and Kershaw run for 30 minutes on a circular track. How many times after the start do they pass each other?

A circle of radius 1 is tangent to a circle of radius 2. The sides of. What is the area of. What is the area of quadrilateral. In addition,. A license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other.

How many distinct license plates are possible? How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression?

Six distinct positive integers are randomly chosen between 1 and , inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5? How many four-digit positive integers have at least one digit that is a 2 or a 3? When one farmer owes the other money, he pays the debt in pigs or goats, with "change" received in the form of goats or pigs as necessary. What is the amount of the smallest positive debt that can be resolved in this way?

Circles with centers. A common internal tangent intersects the. Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron? A bug starts at one vertex of a cube and moves along the edges of the cube according to the following rule.

At each vertex the bug will choose to travel along one of the three edges emanating from that vertex. Each edge has equal probability of being chosen, and all choices are independent. What is the probability that after seven moves the bug will have visited every vertex exactly once? For real numbers. A football game was played between two teams, the Cougars and the Panthers.

The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score? The smaller circle is painted red, and the.

What is the ratio of the blue-. What is the smallest possible area of the square? A region is bounded by semicircular arcs constructed on the side of a square whose sides measure. What is the perimeter of this region? Which of the folowing is equivalent to. A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle? Francesca uses grams of lemon juice, grams of sugar, and grams of water to make lemonade.

There are 25 calories in grams of lemon juice and calories in grams of sugar. Water contains no calories. How many calories are in grams of her lemonade?

In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is What is the greatest possible perimeter of the triangle? Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces.

What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee? What is the area of rhombus. Leap Day, February 29, , occured on a Sunday.

On what day of the week will Leap Day, February 29, , occur? Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same?

What is the area of the shaded region in the figure, which is.

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## 2018 AMC 10B Answer Key答案解析

Sandwiches at Joe's Fast Food cost purchase 5 sandwiches and 8 sodas? Problem 1. How many dollars will it cost to. What is. Problem 2. The ratio of Mary's age to Alice's age is.

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## 2006 AMC 10A & 10B Answers

The selection process takes place over the course of roughly four stages. The United States Math Team of is the only team ever to achieve a perfect score all six members earned perfect marks , and is colloquially known as the "dream team". The "members of the Committee on the American Mathematics Competitions CAMC are dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. The CAMC believes that one way to meet this goal is to identify, recognize and reward excellence in mathematics through a series of national contests called the American Mathematics Competitions". There are certain rewards for doing well on the AMC tests.

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## American Mathematics Competitions

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