Algebra - Grade 5
Algebra - Grade 5
Algebra - Grade 5
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2002 Washington State Math Championship<br />
Unless a particular problem directs otherwise, give an exact answer or one rounded to the<br />
nearest thousandth.<br />
<strong>Algebra</strong> - <strong>Grade</strong> 5<br />
1. How many multiples of 7 are between 17 and 170?<br />
2. A case of tennis balls costs $55.44. There are 3 tennis balls in each can, and in each case the<br />
cans are arranged in 6 rows of 4 cans each. How much is each tennis ball worth?<br />
3. What is the next number in this sequence? 61, 50, 38, 25, 11, ___<br />
4. The sum of two numbers is -34; their product is 288. What is their difference?<br />
5. How many different squares are in the next figure?<br />
6. If P!Q = 2P " 3Q, what is the value of 1091!(39!(36!22)) ?<br />
7. A three-day truck rental from Haul Monitor costs $36.00 per day plus $0.15 per mile.<br />
Renting the same truck from Gotta Haul for 3 days costs $57.00 per day with unlimited<br />
mileage. After how many miles is it less expensive to rent from Gotta Haul?<br />
8. If 8 # 6 = 44, 7 # 6 = 34 , and 7 # 5 = 45, what is 8 # 5?<br />
9. When 4 numbers are added, three at a time, their sums are 20, 22, 26, and 31. What is the<br />
sum of all 4 numbers?<br />
10. What is the next number in this sequence? Express your answer as a reduced fraction.<br />
1<br />
3 , 2 5 , 3 7 , 5 9 , 8 ,1, __<br />
11
2002 Washington State Math Championship<br />
Unless a particular problem directs otherwise, give an exact answer or one rounded to the<br />
nearest thousandth.<br />
<strong>Algebra</strong> - <strong>Grade</strong> 6<br />
1. The sum of two numbers is -34; their product is 288. What is their difference?<br />
2. How many different squares are in the next figure?<br />
3. If P!Q = 2P " 3Q, what is the value of 1091!(39!(36!22)) ?<br />
4. A three-day truck rental from Haul Monitor costs $36.00 per day plus $0.15 per mile.<br />
Renting the same truck from Gotta Haul for 3 days costs $57.00 per day with unlimited<br />
mileage. After how many miles is it less expensive to rent from Gotta Haul?<br />
5. If 8 # 6 = 44, 7 # 6 = 34 , and 7 # 5 = 45, what is 8 # 5?<br />
6. When 4 numbers are added, three at a time, their sums are 20, 22, 26, and 31. What is the<br />
sum of all 4 numbers?<br />
7. What is the next number in this sequence? Express your answer as a reduced fraction.<br />
1<br />
3 , 2 5 , 3 7 , 5 9 , 8 ,1, __<br />
11
8. Harry is cleaning the laboratory aquarium. In cleaning the aquarium he needs to drain the<br />
water, remove and later replace a large rock, scrub the sides of the aquarium, and then fill it<br />
again. There are two drains which each drain the aquarium at the rate of 2 inches of depth per<br />
minute. There is a tap which fills it at the rate of 3 inches of depth per minute. According to<br />
the graph of the water depth in the aquarium and Harry’s time on the job, how many minutes<br />
is the large rock out of the aquarium?<br />
24<br />
20<br />
16<br />
Water<br />
Depth 12<br />
(inches)<br />
8<br />
4<br />
2 4 6 8 10 12 16 18 20 22<br />
Time since Harry began working (minutes)<br />
9. The modern marathon is a race which is 26 miles and 385 yards long. The original marathon<br />
was probably measured in stadia. One stadia is equal to 607 feet, and there are 5280 feet in a<br />
mile. To the nearest stadia, how long is a marathon?<br />
10. Light travels 186,282 miles per second. How many digits left of the decimal point would be<br />
needed to write the distance it travels in one year?
2002 Washington State Math Championship<br />
Unless a particular problem directs otherwise, give an exact answer or one rounded to the<br />
nearest thousandth.<br />
<strong>Algebra</strong> - <strong>Grade</strong> 7<br />
1. A three-day truck rental from Haul Monitor costs $36.00 per day plus $0.15 per mile.<br />
Renting the same truck from Gotta Haul for 3 days costs $57.00 per day with unlimited<br />
mileage. After how many miles is it less expensive to rent from Gotta Haul?<br />
2. If 8 ! 6 = 44, 7 ! 6 = 34 , and 7 ! 5 = 45, what is 8 ! 5?<br />
3. When 4 numbers are added, three at a time, their sums are 20, 22, 26, and 31. What is the<br />
sum of all 4 numbers?<br />
4. What is the next number in this sequence? Express your answer as a reduced fraction.<br />
1<br />
3 , 2 5 , 3 7 , 5 9 , 8 ,1, __<br />
11<br />
5. Harry is cleaning the laboratory aquarium. In cleaning the aquarium he needs to drain the<br />
water, remove and later replace a large rock, scrub the sides of the aquarium, and then fill it<br />
again. There are two drains which each drain the aquarium at the rate of 2 inches of depth per<br />
minute. There is a tap which fills it at the rate of 3 inches of depth per minute. According to<br />
the graph of the water depth in the aquarium and Harry’s time on the job, how many minutes<br />
is the large rock out of the aquarium?<br />
24<br />
20<br />
16<br />
Water<br />
Depth 12<br />
(inches)<br />
8<br />
4<br />
2 4 6 8 10 12 16 18 20 22<br />
Time since Harry began working (minutes)
6. The modern marathon is a race which is 26 miles and 385 yards long. The original marathon<br />
was probably measured in stadia. One stadia is equal to 607 feet, and there are 5280 feet in a<br />
mile. To the nearest stadia, how long is a marathon?<br />
7. Light travels 186,282 miles per second. How many digits left of the decimal point would be<br />
needed to write the distance it travels in one year?<br />
8. 2b or not 2b: If<br />
5(b ! 2)<br />
9<br />
! 6b<br />
11<br />
= 9 , then what is 2b?<br />
9. How many different squares are in the tenth figure?<br />
10. The first 4 designs are shown below. How many dots will there be in the tenth design?
2002 Washington State Math Championship<br />
Unless a particular problem directs otherwise, give an exact answer or one rounded to the<br />
nearest thousandth.<br />
<strong>Algebra</strong> - <strong>Grade</strong> 8<br />
1. What is the next number in this sequence? Express your answer as a reduced fraction.<br />
1<br />
3 , 2 5 , 3 7 , 5 9 , 8 ,1, __<br />
11<br />
2. Harry is cleaning the laboratory aquarium. In cleaning the aquarium he needs to drain the<br />
water, remove and later replace a large rock, scrub the sides of the aquarium, and then fill it<br />
again. There are two drains which each drain the aquarium at the rate of 2 inches of depth per<br />
minute. There is a tap which fills it at the rate of 3 inches of depth per minute. According to<br />
the graph of the water depth in the aquarium and Harry’s time on the job, how many minutes<br />
is the large rock out of the aquarium?<br />
24<br />
20<br />
16<br />
Water<br />
Depth 12<br />
(inches)<br />
8<br />
4<br />
2 4 6 8 10 12 16 18 20 22<br />
Time since Harry began working (minutes)<br />
3. The modern marathon is a race which is 26 miles and 385 yards long. The original marathon<br />
was probably measured in stadia. One stadia is equal to 607 feet, and there are 5280 feet in a<br />
mile. To the nearest stadia, how long is a marathon?<br />
4. Light travels 186,282 miles per second. How many digits left of the decimal point would be<br />
needed to write the distance it travels in one year?<br />
5. 2b or not 2b: If<br />
5(b ! 2)<br />
9<br />
! 6b<br />
11<br />
= 9 , then what is 2b?
6. How many different squares are in the tenth figure?<br />
7. The first 4 designs are shown below. How many dots will there be in the tenth design?<br />
8. The population of Clark County in 1990 was 238,095 and in 2000 was 345,238. The<br />
population of Spokane County in 1990 was 361,226 and in 2000 was 417,939. Assuming<br />
that both counties continue to grow at the linear rate according to census data, in April (census<br />
month) of what year will the population of Clark County first exceed that of Spokane<br />
County?<br />
9. The census data from the previous problem yields an annual growth rate of 3.8% for Clark<br />
County and an annual growth rate of 1.5% for Spokane County. If exponential growth is<br />
assumed using these rates and the 2000 census data is used as a base, in April (census<br />
month) of what year will the population of Clark County first exceed that of Spokane<br />
County?<br />
10. Given that<br />
3a + 2b + 7c = 336<br />
2a + 7b + 3c = 551<br />
7a + 3b + 2c = 421<br />
What is the value of a + b + c ?
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