A function

*f*has the property that*f*(3*x–*1) =*x*^{2}+*x*+ 1 for all real numbers*x*. What is*f*(5)?A function *f* has the property that *f*(3*x–*1) = *x*^{2} + *x* + 1 for all real numbers* x*. What is *f*(5)?

Suppose *d *is a digit. For how many values of *d* is 2.00*d*5 > 2.005?

Interactive version of problem and solution.

Interactive version of problem and solution.

On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5. What is his score?

Interactive version of problem and solution.

Interactive version of problem and solution.

Tom's age is* T* years, which is also the sum of the ages of his three children. His age* N* years ago was twice the sum of their ages then. What is *T/N* ?

The larger of two consecutive odd integers is three times the smaller. What is their sum?

Interactive version of problem and solution.

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

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 by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise?

Interactive version of problem and solution.

In order for Mateen to walk a kilometer(1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?

Triangle *ABC* has side lengths *AB* = 5, *BC* = 6, and *AC* = 7. Two bugs start simultaneously from *A*

and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point*D*. What is *BD*?

Interactive version of problem and solution.

and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point

Interactive version of problem and solution.

The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?

A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?

Which of the following numbers has the smallest primefactor?

(A) 55

(B) 57

(C) 58

(D) 59

(E) 61

Interactive version of problem and solution.

(A) 55

(B) 57

(C) 58

(D) 59

(E) 61

Interactive version of problem and solution.

Buy *Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi* from the MAA Bookstore

The 2007 AMC 10 will be scored by awarding 6 points for each correct response, 0 points for each incorrect response, and 1.5 points for each problem left unanswered. After looking over the 25 problems, Sarah has decided to attempt the first 22 and leave only the last 3 unanswered. How many of the first 22 problems must she solve correctly in order to score at least 100 points?

Interactive version of problem and solution.

At Frank's Fruit Market, 3 bananas cost as much as 2 apples, and 6 apples cost as much as 4 oranges. How many oranges cost as much as 18 bananas?

A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the *x*-intercepts of these two lines?

Interactive version of problem and solution.

Interactive version of problem and solution.

Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?

Interactive version of problem and solution.

Interactive version of problem and solution.

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