Copyright 2016 Art of Problem Solving Mindy made three purchases for dollars, dollars, and dollars. What was her total, to the nearest dollar? The three prices round to , , and , which has a sum of 2006 AMC 8 (Problems Answer Key Resources ( Preceded by First Question Followed by Problem 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America (http:/www.maa.org)s American Mathematics Competitions (http:/amc.maa.org). Retrieved from “ title=2006_AMC_8_Problems/Problem_1&oldid=55964“ 2006 AMC 8 Problems/Problem 1 Problem Solution See Also Copyright 2016 Art of Problem Solving On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesnt answer the last 5. What is his score? As the AMC 8 only rewards 1 point for each correct answer, everything is irrelevant except the number Billy answered correctly, . 2006 AMC 8 (Problems Answer Key Resources ( Preceded by Problem 1 Followed by Problem 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America (http:/www.maa.org)s American Mathematics Competitions (http:/amc.maa.org). Retrieved from “ title=2006_AMC_8_Problems/Problem_2&oldid=55965“ 2006 AMC 8 Problems/Problem 2 Problem Solution See Also Copyright 2016 Art of Problem Solving 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? When Elisa started, she finished a lap in minutes. Now, she finishes a lap is minutes. The difference is . 2006 AMC 8 (Problems Answer Key Resources ( Preceded by Problem 2 Followed by Problem 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America (http:/www.maa.org)s American Mathematics Competitions (http:/amc.maa.org). Retrieved from “ title=2006_AMC_8_Problems/Problem_3&oldid=55966“ 2006 AMC 8 Problems/Problem 3 Problem Solution See Also Copyright 2016 Art of Problem Solving Initially, a spinner points west. Chenille moves it clockwise revolutions and then counterclockwise revolutions. In what direction does the spinner point after the two moves? If the spinner goes clockwise revolutions and then counterclockwise revolutions, it ultimately goes counterclockwise which brings the spinner pointing . 2006 AMC 8 (Problems Answer Key Resources ( Preceded by Problem 3 Followed by Problem 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America (http:/www.maa.org)s American Mathematics Competitions (http:/amc.maa.org). Retrieved from “ title=2006_AMC_8_Problems/Problem_4&oldid=55967“ 2006 AMC 8 Problems/Problem 4 Problem Solution See Also 1 Problem 2 Solution 2.1 Solution 1 2.2 Solution 2 3 See Also Points and are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square? Drawing segments and , the number of triangles outside square is the same as the number of triangles inside the square. Thus areas must be equal so the area of is half the area of the larger square which is . If the side length of the larger square is , the side length of the smaller square is . Therefore the area of the smaller square is , half of the larger squares area, . Thus, the area of the smaller square in the picture is . 2006 AMC 8 Problems/Problem 5 Contents Problem Solution Solution 1 Solution 2 See Also Copyright 2016 Art of Problem Solving The letter T is formed by placing two inch rectangles next to each other, as shown. What is the perimeter of the T, in inches? If the two rectangles were seperate, the perimeter would be . It easy to see that their connection erases 2 from each of the rectangles, so the final perimeter is . 2006 AMC 8 (Problems Answer Key Resources ( Preceded by Problem 5 Followed by Problem 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 All AJHSME/AMC 8 Problems and Solutions The problems on this page are copyrighted by the Mathematical Association of America (http:/www.maa.org)s American Mathematics Competitions (http:/amc.maa.org). Retrieved from “ title=2006_AMC_8_Problems/Problem_6&oldid=55969“ 2006 AMC 8 Problems/Problem 6 Problem Solution See Also Copyright 2016 Art of Problem Solving Circle has a radius of