Score. Please print legibly. School / Team Names. Directions: Answers must be left in one of the following forms: 1. Integer (example: 7)

Transcription

1 Score Please print legibly School / Team Names Directions: Answers must be left in one of the following forms: 1. Integer (example: 7)! 2. Reduced fraction (example:! )! 3. Mixed number, fraction part simplified (example: 2! ) 4. Radical form, if not possible to simplify to a whole number (example: 7 ) 5. Money: rounded to the nearest cent (example: $10.15) 6. As otherwise specified in the problem

2 1. Michael participates at a free throw basketball contest. For each successful throw he makes, he gets 8 points and for each miss he is penalized 5 points. After 26 throws he has 0 points. How many successful throws did he make? 1. throws 2. In the figure below, a large square is made up of 16 smaller squares. How many different squares of varying sizes can one find in the figure? 2. squares 3. In January, Rick and Fran drove 680 miles on I- 55 from St. Louis to New Orleans. Along the way, in order, they passed Cape Girardeau MO, Memphis TN, and Jackson MS. It is 115 miles from St. Louis to Cape Girardeau; 380 miles from Cape Girardeau to Jackson; and 395 miles from Memphis to New Orleans. How far is it from Cape Girardeau to Memphis? 3. miles 4. Twenty- two rods of equal length are needed to build this 2 by 4 array of 8 small squares. How many rods would be needed to construct a 2 by 1000 array of 2000 small squares? 4. rods

3 5. A two- digit number AB is called good if A 2 + B 2 = 65. List all the different possibilities for AB Solve for x What is the positive difference between the area of a square with perimeter 120m and the area of a rectangle with perimeter 120m, if the length of the rectangle is three times its width? 7. m 2 8. About 2500 years ago, the Greek mathematician Archimedes studied the Geometry of a game called Stomachion. The game consisted of 14 polygonal pieces that fit together to form a 12 by 12 square grid (see the diagram). The 14 pieces do not overlap and every vertex of each shape lies exactly on a lattice point of this grid. In square units, what is the area of triangle ABC? 8. sq. units

4 9. Given x y =!!!!!!!! find 7 4. Express your answer as a fraction How many zeroes are at the end of the product of 25 billion times 80 trillion? 10. zeroes 11. Using only 1, 2, 3, and 4, complete this 4x4 Ken- Ken Puzzle. What is the sum of the four numbers in the boxes labeled A, B, C, and D? Amy and Bryan walk toward each other from A to B. Amy walks at 220 feet per minute and Bryan takes 15 minutes to walk a mile. The distance between A and B is 11 miles. If they start walking to each other at the same time, how long will it take for them to meet? (Hint: 1 mile = 5280 feet) (Round to the nearest minute) 12.

5 13. The Strong Goldbach conjecture states that any even number greater than 7 can be written as the sum of two different prime numbers. In how many ways can 60 be written as the sum of two different prime numbers? Josh put $10 into savings on January 1, $20 on February 1, $30 on March 1, and so on. Each month he saved $10 more than the previous month. Kim put $1 into savings on January 1, $2 on February 1, $4 on March 1, and so on. Each month she put twice as much as the previous month into her savings. At the end of one year, how much more had Kim saved than Josh? 14. $ 15. On this calendar for March 2013, nine numbers have been shaded. Circle any three of those nine numbers so that exactly one number from each row and exactly one number from each column have been circled. What is the largest possible product of any three numbers you could circle? Complete this 5 by 5 grid so that the numbers 1, 2, 3, 4, and 5 occur in every row and in every column. In addition, the eight greater than and less than symbols indicate which of the two adjacent numbers is larger or smaller. What is the sequence of numbers in the second row (from the top)? 16.,,,,

6 17. If a square has two of its vertices at (2, 2) and (2, 2), how many such squares are possible? 17. squares 18. The average of the ages of the mother, the father, and their three children is 21, while the average of the children is 11. How old is the father if he is 4 years older than the mother? 18. years old 19. A standard six- sided die with faces labeled 1 through 6 is rolled. One face is face- down on a table. Let P equal the product of the other five numbers. What is the largest number that must be a factor of P? In the sequence 1, 2, 5, 10, 17, 26, 37, 50., find the 50 th number of the sequence. 20.