Download Algebra - Grade 5

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