A function f has the property that f(3x–1) = x2 + x + 1 for all real numbers x. What is f(5)?
Friday, May 29, 2009
Thursday, May 28, 2009
May 28, 2009
Suppose d is a digit. For how many values of d is 2.00d5 > 2.005?
Interactive version of problem and solution.
Interactive version of problem and solution.
Wednesday, May 27, 2009
May 27, 2009
Elisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now she can finish 12 laps in 24 minutes. By how many minutes has she improved her lap time?
Tuesday, May 26, 2009
May 26, 2009
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.
Friday, May 22, 2009
May 22, 2009
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 ?
Thursday, May 21, 2009
May 21, 2009
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
Wednesday, May 20, 2009
May 20, 2009
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.
Tuesday, May 19, 2009
May 19, 2009
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?
Friday, May 15, 2009
May 15, 2009
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 D. What is BD?
Interactive version of problem and solution.
Thursday, May 14, 2009
May 14, 2009
A square and an equilateral triangle have the same perimeter. Let A be the area of the circle circumscribed about the square and B be the area of the circle circumscribed about the triangle. Find A/B.
Wednesday, May 13, 2009
May 13, 2009
The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
Tuesday, May 12, 2009
May 12, 2009
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?
Monday, May 11, 2009
May 11, 2009
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
Friday, May 8, 2009
May 8, 2009
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.
Thursday, May 7, 2009
May 7, 2009
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?
Wednesday, May 6, 2009
May 6, 2009
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.
Monday, May 4, 2009
May 4, 2008
Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?
Friday, May 1, 2009
May 1, 2009
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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