Please print legibly. School / Team. Names. Directions: Answers must be left in one of the following forms:

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: 3/4) 3. Mixed number, fraction part simplified (example: 2 1/3) 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. If two different natural numbers have the same digits but in reverse order, each number is called the palimage of the other. For example, 738 and 837 are palimages of each other; so are 1234 and What two different numbers between 40 and 60 are palimages of each other? 1. and 2. Greta puts the numbers starting from 1 into four columns (A, B, C and D) using the pattern shown below. Into which column (A, B, C, or D) will Greta write the number 42? 2. A B C D In a local school, the ratio of the number of students who take part in sports to the number of students who do not is 3:5. 3. There are 408 students in the high school who take part in sports. How many students are there in the school? 4. Min has a collection of figures; all of them are either squares or triangles. She counts all the sides of the figures and gets a total of 19. What is the largest number of triangles Min could have? Yvette and Zoe live three miles away from school. One day, they decide to race home from school on their bikes. Yvette gives Zoe a two minute head start. If Zoe s average speed is 15 miles per hour, what is the average speed that Yvette must maintain to arrive home at the same time as Zoe? Tom s parents double his allowance every week, and the first week Tom receives 1 penny. What is Tom s allowance for the 15 th week? 6.

3 7. The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13 starts with two 1 s, and each term afterward is the sum of its two predecessors. What is the first number that ends with a 0 in this sequence? A rectangle has sides whose lengths are (whole numbers). The perimeter of the rectangle is 18 units. What is the largest possible value for the area of the rectangle? 8. sq. units 9. If a pair of pants costs $12.00 more than a shirt, and if two pairs of pants and three shirts costs $84.00, what is the cost of one shirt? 9. $ 10. Taylor and Emma are waiting in line to get on the school bus. Taylor is seventh in line. Emma is in the middle of the line. There are six students between Taylor and Emma. How many students are waiting in line? David has 4 cages of hamsters. The second cage has ½ as many hamsters as the first. The third cage has ½ as many hamsters as the second. The fourth cage has ½ as many hamsters as the third. What is the smallest number of hamsters David can have? 11.

4 12. Magic squares are mathematical puzzles that date back to 2200 B.C., when they were called lo-shu. In a magic square all the rows, columns, diagonals sum to the same number Fill in the following square using only the numbers from 0-15 (once each) so that the sum of rows, columns and diagonals is Same shapes are same numbers. Different shapes are different numbers. 13. = = 22 = + = 12 = - = The planet Polynum is inhabited by the Quadtris which have 4 legs and 3 heads, and the Pentabis, which have 5 legs and 2 heads. If 106 legs and 55 heads were counted at a recent gathering of both species, how many Quadtris were present? 14.

5 15. A local restaurant sells chicken nuggets in boxes of 6, 9, and 20. Determine which of the following quantities can be ordered. Number of desired nuggets: 15, 99, 19, 48, What number exceeds 23 by 4 more than twice the amount by which 15 exceeds -3? The pages of a book are numbered consecutively, beginning with 1. The digit 7 is printed 25 times in numbering the pages. What is the largest number of pages the book can have? Below is a series of growing shapes. Imagine that the building pattern continues. How many blocks will it take to build shape 7? How many blocks will it take to build shape 20? 18. Shape 7: blocks Shape 20: blocks 19. Find the weight of each block. 19. cylinder = lbs. cube = lbs. sphere = lbs. tall prism = lbs.

6 20. The coach of the tennis team was having problems selecting his team. He had to choose four players, two men and two women, from six who had tried out. Personal feelings were making it difficult for him. 1. Paul said, I ll play only if Sarah plays. 2. Sarah said, I won t play if Eric is on the team. 3. Eric said, I won t play if David or Linda is chosen. 4. David said, I ll play only if Amy plays. 5. Amy had no likes nor dislikes. 20. Who will the coach select?