Universidad de Puerto Rico Recinto Universitario de Mayag¨ uez
Universidad de Puerto Rico
´ OLIMPIADAS MATEMATICAS DE PUERTO RICO 2012-2013 FIRST PHASE ANSWER FORM Student’s information: Last name:
First name:
Grade: 3rd 4th 5th
6th 7th 8th
Home phone: (
)
Student’s e-mail:
9th 10th 11th -
Gender: F
M
Teacher’s e-mail:
School’s name: School’s city:
School: Private
a 1 2 3 4 5 6 7 8 9 10
Instructions: Mark your answers with an x b c d e a b c 11 12 13 14 15 16 17 18 19 20
Public
d
e
Responses must be sent electronically through the web page www.ompr.pr before may 8, 2012 or trough mail to the address below: Dr. Luis F. C´ aceres-Duque Departamento de Ciencias Matem´ aticas Call Box 9000 Mayag¨ uez, PR 00681-9000
Olimpiadas Matem´aticas de Puerto Rico
3rd, 4th and 5th grades
´ Universidad de Puerto Rico OLIMPIADAS MATEMATICAS Universidad de Puerto Rico Recinto Universitario de DE PUERTO RICO Mayag¨uez Primera fase 2012-2013
3rd, 4th and 5th grades 3-point problems 1. What number is covered by the flower?
a. 2
b. 3
c. 4
d. 5
e. 6
2. Father hangs the laundry outside on a clothesline. He wants to use as few pins as possible. With 3 towels he needs to use 4 pins. How many pins does he need to hang 9 towels?
a. 8
b. 10
c. 12
d. 13
e. 18
3. Melissa and Juan were playing darts. Each one threw three darts (see the picture). Who won and how many more points did the winner score? a. Melissa scored 3 more points. b. Juan scored 4 more points. c. Melissa scored 2 more points. d. Juan scored 2 more points. e. Melissa scored 4 more points.
1
Olimpiadas Matem´aticas de Puerto Rico
3rd, 4th and 5th grades
4. There are coins on the board. We want to have 2 coins in each column and in each row. How many coins need to be removed?
a. 0
b. 1
c. 2
d. 3
e. 4
5. A regular pattern on a wall was created with 2 kinds of tiles: grey and with stripes (see the picture). Some tiles have fallen off the wall. How many grey tiles fell off?
a. 13
b. 8
c. 7
d. 6
e. 5
6. At a school party Carlos, Daniel and H´ector each received a bag with 10 candies. Each of the boys ate just 1 candy and gave 1 candy to the teacher. How many candies did they have left altogether?
a. 8
b. 10
c. 24
d. 27
e. 30
7. In a box there are three boxes, each one of which contains three smaller boxes. How many boxes are there in total? a. 9
b. 10
c. 12
2
d. 13
e. 15
Olimpiadas Matem´aticas de Puerto Rico
3rd, 4th and 5th grades
4-point problems 8. Grandmother made 11 cookies. She decorated 5 cookies with raisins and then 7 cookies with nuts. At least how many cookies were decorated with both raisins and nuts? a. 1
b. 2
c. 5
d. 7
e. 12
9. In four of the following five pictures the white area is equal to the grey area. In which picture are the white area and the grey area different?
a.
b.
c.
d.
e.
10. In a Sudoku the numbers 1, 2, 3 and 4 can occur only once in each column and in each row. In the mathematical Sudoku below Patricia must first write the results and then complete the Sudoku. Which number will Patricia put in the gray cell?
a. 1
b. 2
c. 3
d. 4
e. 1 o´ 2
11. In the animal school 3 kittens, 4 ducklings, 2 goslings and several lambs are taking lessons. Teacher Owl found out that all of her pupils have 44 legs altogether. How many lambs are there in the animal school? a. 6
b. 5
c. 4
d. 3
e. 2
12. A parallelepiped is made of three pieces (see the drawing). Each of the pieces consists of 4 cubes and is of one color. What does the white piece look like?
a.
b.
c.
d. 3
e.
Olimpiadas Matem´aticas de Puerto Rico
3rd, 4th and 5th grades
13. The year 2012 is a leap year, which means there are 29 days in February. Today, on the 15th March 2012, my grandfather’s ducklings are 20 days old. When did they hatch from their eggs? a. on the 22nd of February
c. on the 24th of February
b. on the 23rd of February
d. on the 25th of February
e. on the 26th of February
14. A flea wants to climb a staircase with many steps. She makes only two different jumps: 3 steps up or 4 steps down. Beginning at the ground level, at least how many jumps will she have to make in order to take a rest on the 22nd step?
a. 7
b. 9
c. 10
d. 12
e. 15
5-point problems 15. Gregor forms two numbers with the digits 1, 2, 3, 4, 5 and 6. Both numbers have three digits, each digit is used only once. He adds these two numbers. What is the greatest sum Gregor can get? a. 975
b. 999
c. 1083
d. 1173
e. 1221
16. Miguel chose some number, multiplied it by itself, added 1, multiplied the result by 10, added 3, multiplied the result by 4 and obtained 2012. What number did Miguel choose? a. 11
b. 9
c. 7
d. 8
e. 5
17. Among Nicole’s classmates there are twice as many more girls than boys. Which of the following numbers can be equal to the number of all the children in this class? a. 20
b. 22
c. 25
4
d. 29
e. 30
Olimpiadas Matem´aticas de Puerto Rico
3rd, 4th and 5th grades
18. The upper coin is rotated without sliding around the fixed lower coin to a position shown on the picture. Which are the resulting relative positions of the kangaroos?
a.
c.
b.
d. e. Depends on the rotation speed.
19. Three balloons cost 12 cents more than one balloon. How much does one balloon cost? a. 4
b. 6
c. 8
d. 10
e. 12
20. A rectangular paper sheet is 192 mm × 84 mm. Cutting such a sheet along just one line you get a square; then you do the same with the remaining part of the sheet and so on. What is the length of the side of the smallest square one gets with this procedure? a. 1 mm
b. 4 mm
c. 6 mm
d. 10 mm
e. 12 mm
Responses must be sent electronically through the web page www.ompr.pr before may 8, 2012 or trough mail to the address below: Dr. Luis F. C´aceres-Duque Departamento de Ciencias Matem´aticas Call Box 9000 ¨ PR 00681-9000 Mayaguez, 5