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1. A librarian is setting up tables in the media center. He can place 4 chairs around one table. If he pushes 2 tables together, he can place six chairs around the table. If 10 people need to sit around the table, how many tables should the librarian push together?
A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The nth triangle number is the number of dots in a triangle with n dots on a side. The sequence of triangular numbers for n = 1, 2, 3... is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
The sum of the n first triangular numbers is the nth tetrahedral number. Its formula is [n(n+1)(n+2)]/6. The sequence of numbers is: 1, 4, 10, 20, 35, 56, 84, 120, 165, ...
Apply the knowledge above to solve the following problem.
2. Josh wants to save $165.00 to buy a new iPod nano. He plans to save $1 the first month, $3 the second month, $6 the third month, and $10 the fourth month. If Josh continues this savings pattern, how many months will it take Josh to save $165.00?
A. 5 months
B. 7 months
C. 9 months
D. 13 months
3. Fiona took a rectangular piece of paper and folded it in half. Then, she folded it in half again. If the paper is folded in half three more times, how many sections will there be when Fiona completely unfolds it?
4. Mike used some shapes to balance the scale shown above. Based on the scale, which of the following is also true?
5. A rabbit, a squirrel, and a hamster eat more than two squirrels eat. A rabbit eats more than a hamster eats. According to the information just given, which of the following is true?
A. Two rabbits eat more than one squirrel eats.
B. One squirrel eats as much as two hamsters eat.
C. One rabbit eats more than one squirrel eats.
D. One rabbit eats less than one hamster eats.
6. Patrick and Susan both collect stamps. Susan has 5 times as many stamps as Patrick. If is used to represent the number of stamps that Patrick has, which expression describes the total number of stamps that Patrick and Susan have together?
7. In Mr. Wiggen’s class of 31 students, several were absent with a flu on Monday. On Tuesday, 2 more were absent. On Wednesday, 2 more were absent. This trend continued, until only 15 students were present on Friday. How many students had been absent on Monday?
8. Mrs. Fizzle wrote out the equation above. Then, she read out the following four word problems to her class. Which word problem uses the equation above to solve it?
A. Mariah ate two slices of pizza and drank three cups of water. If she spent $11, how much did one slice of pizza cost?
B. Shannon chopped three onions in order to make 11 servings of onion rings. How much onion was used for one serving?
C. Beth swam for three hours on Saturday and two hours on Sunday. If she swims two hours each day, how many more days will it take her to swim a total of 11 hours?
D. Hilary washed pickup trucks for $3 each and cars for $2 each. If she earned $11 in one morning, and washed only one car, how many pickup trucks did she wash?
9. The greatest common factor (GCF) of s and r is 1. The GCF of r and t is 4. Based on this information, which of the following must also be true?
A. r is even.
B. t is odd.
C. r + s is even.
D. s × t is odd.
10. Janet has 5 square yards of carpet to cover the floor of one closet in her house. The four closet sizes in Janet's house are listed below. For which closet is Janet's carpet not big enough?
A. 4 ft × 101/2 ft
B. 41/2 ft × 8 ft
C. 5 ft × 10 ft
D. 9 ft × 5 ft
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