Individual
5th Grade
Instructions: Problems 1 – 10 are multiple choice and count towards your team score. Bubble in the
letter on your answer sheet. Be sure to erase all mistakes completely.
1. Which of the following numbers is read aloud as “six hundred nine thousand, thirty-five”?
A. 609,035
B. 69,035
C. 609,305 D. 690,035 E. 60,935
2. Which of the following would be the cheapest to buy?
A. Four apples at $0.87 each
B. Eight kiwis at $0.47 each
C. Six oranges at $0.49 each
D. Three pears at $0.50 each
E. Ten carrots at $0.30 each
3. The volume of a community swimming pool would most likely be reported in which unit of
measurement?
A. kilograms
B. gallons
C. inches
D. teaspoons
E. meters
4. If you roll three fair six-sided dice, and the first two dice rolled land as a “1” and a “5”, what is the
probability the third die will land as a “3”?
A. 1/36
B. 1/6
C. 1/3
D. 1/2
E. 2/3
5. On his final math test, a student who answered 49 questions correctly scored 70%. If each
question is weighted equally, how many questions total were on the test?
A. 7
B. 34
C. 64
D. 70
E. 83
6. Which of the following shapes cannot have two pairs of parallel sides?
A. rhombus
B. parallelogram
C. rectangle
D. square
E. none of these
7. How many 2in ! 2in ! 2in cubes can fit into a 4in ! 4in ! 6in rectangular prism?
A. 2
B. 6
C. 8
D. 12
E. 48
8. Four out of the five choices below are equivalent to each other. Which one is not equivalent?
A. 82.5%
B. 0.0825
C. 33/40
D. 82.5:100 E. 825/1000
9. Which one of the following numbers is prime?
A. 111
B. 243
C. 251
D. 708
E. 921
10. Which of the following statistics is the greatest for the following list of data?
2, 4, 4, 4, 5, 6, 11, 14, 15
A. mean
B. median
C. half the range
D. mode
E. all are equal
www.blainesd.org/mathchamps/
Individual
5th Grade
Problems 11 – 30: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
11. Calculate the following expression: 6 + 3 " 2 ! 4 ÷ 2 .
12. How many lines of reflectional symmetry does a hexagon have?
13. In a poll of her classmates about their favorite school subjects, Marnie found that 15 students
chose mathematics, 10 chose history, and 10 chose art. If she decided to randomly select a
classmate, what is the probability that his/her favorite subject was mathematics? Express your
answer as a reduced fraction.
14. Christopher has 30 yards of material that he wants to give to his friends so that each friend can
create one lanyard. If it takes 6 feet of the material to create a lanyard, how many friends will he
be able to provide the materials for?
15. Shown below are two squares that have been joined together so that they share one side and thus
form a rectangle. If the perimeter of the rectangle is 36 inches, what is the area of the rectangle in
square inches?
16. What is the next number in the following sequence?
2, 6, 11, 17, 24, 32, 41, ...
17. Solve for x: 3 x + 2 = 38 .
18. The amount of drinking water that is consumed by the people of Bellingham is about 10 million
gallons per day. Assuming there are 80,000 people in Bellingham, how much water does the
average person consume in one week? Express your answer as a whole number of gallons.
19. The average SAT score of eleven students was 2,000. When Mary's score was added to the other
eleven scores, the average went up to 2,010. What is the positive difference between her score
and the initial average score?
www.blainesd.org/mathchamps/
Individual
5th Grade
20. MaryAnne gets a 10% increase in monthly salary each year. If her current monthly salary is
$1,000, what was her monthly salary two years ago? Express your answer to the nearest
dollar.
21. The lock on your diary allows you to set a three-digit combination. To make it harder on the rest
of your family though, you decide that each digit must be different. How many possible
combinations do you have to choose from?
22. Suppose that Michael Jordan, a famous basketball player, has just finished playing a game, and
scored 53 points. If he made 21 total shots, some of which were worth two points, and the rest of
which were worth three points, how many three-point shots did he make?
23. How many perfect squares between 1 and 600 are divisible by four?
24. In order to expand a rectangular building, a construction crew is going to increase each side length
of the floor by 20%. By what percentage will the area of the floor increase? Express your
answer to the nearest whole percent.
25. Call a triangle “cutesy” if it is an acute triangle and the degree measures of all three of its angles
are distinct whole numbers. What is the largest possible positive difference between the degree
measures of the largest and smallest angles in a “cutesy” triangle?
26. In a flight from Seattle to Los Angeles, a plane flew an average speed of 200 miles per hour.
Because of a tail wind, the plane was able to fly back to Seattle at an average speed of 250 miles
per hour. If the plane flew 1,000 miles each direction, what was the plane's average speed, in
miles per hour? Express your answer to the nearest integer.
27. If A is the set of all positive integers, and B is the set of all two-digit prime numbers less than 60,
how many elements are in the set A ∩ B?
28. In how many ways can the letters in the word “BUBBLE” be uniquely arranged?
29. If the complement of an angle is two-fifths of its supplement, what is the degree measure of the
angle?
30. A league of only four basketball teams decided that playing each other once would not make a
long enough season. So they decided that each team would play every other team four times.
How many games will the season last now?
www.blainesd.org/mathchamps/
Individual
6th Grade
Instructions: Problems 1 – 10 are multiple choice and count towards your team score. Bubble in the
letter on your answer sheet. Be sure to erase all mistakes completely.
1. Which of the following numbers is read aloud as “six hundred nine thousand, thirty-five”?
A. 609,035
B. 69,035
C. 609,305 D. 690,035 E. 60,935
2. Which of the following would be the cheapest to buy?
A. Four apples at $0.87 each
B. Eight kiwis at $0.47 each
C. Six oranges at $0.49 each
D. Three pears at $0.50 each
E. Ten carrots at $0.30 each
3. The volume of a community swimming pool would most likely be reported in which unit of
measurement?
A. kilograms B. gallons
C. inches
D. teaspoons
E. meters
4. If you roll three fair six-sided dice, and the first two dice rolled land as a “1” and a “5”, what is the
probability the third die will land as a “3”?
A. 1/36
B. 1/6
C. 1/3
D. 1/2
E. 2/3
5. On his final math test, a student who answered 49 questions correctly scored 70%. If each
question is weighted equally, how many questions total were on the test?
A. 7
B. 34
C. 64
D. 70
E. 83
6. Which of the following shapes cannot have two pairs of parallel sides?
A. rhombus
B. parallelogram
C. rectangle
D. square
E. none of these
7. How many 2in ! 2in ! 2in cubes can fit into a 4in ! 4in ! 6in rectangular prism?
A. 2
B. 6
C. 8
D. 12
E. 48
8. Four out of the five choices below are equivalent to each other. Which one is not equivalent?
A. 82.5%
B. 0.0825
C. 33/40
D. 82.5:100 E. 825/1000
9. Which one of the following numbers is prime?
A. 111
B. 243
C. 251
D. 708
E. 921
10. Which of the following statistics is the greatest for the following list of data?
2, 4, 4, 4, 5, 6, 11, 14, 15
A. mean
B. median
C. half the range
D. mode
E. all are equal
www.blainesd.org/mathchamps/
Individual
6th Grade
Problems 11 – 30: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
11. Calculate the following expression: 6 + 3 " 2 ! 4 ÷ 2 .
12. How many lines of reflectional symmetry does a hexagon have?
13. In a poll of her classmates about their favorite school subjects, Marnie found that 15 students
chose mathematics, 10 chose history, and 10 chose art. If she decided to randomly select a
classmate, what is the probability that his/her favorite subject was mathematics? Express your
answer as a reduced fraction.
14. Christopher has 30 yards of material that he wants to give to his friends so that each friend can
create one lanyard. If it takes 6 feet of the material to create a lanyard, how many friends will he
be able to provide the materials for?
15. Shown below are two squares that have been joined together so that they share one side and thus
form a rectangle. If the perimeter of the rectangle is 36 inches, what is the area of the rectangle in
square inches?
16. What is the next number in the following sequence?
2, 6, 11, 17, 24, 32, 41, ...
17. Solve for x: 3 x + 2 = 38 .
18. The amount of drinking water that is consumed by the people of Bellingham is about 10 million
gallons per day. Assuming there are 80,000 people in Bellingham, how much water does the
average person consume in one week? Express your answer as a whole number of gallons.
19. The average SAT score of eleven students was 2,000. When Mary's score was added to the other
eleven scores, the average went up to 2,010. What is the positive difference between her score
and the initial average score?
www.blainesd.org/mathchamps/
Individual
6th Grade
20. MaryAnne gets a 10% increase in monthly salary each year. If her current monthly salary is
$1,000, what was her monthly salary two years ago? Express your answer to the nearest
dollar.
21. The lock on your diary allows you to set a three-digit combination. To make it harder on the rest
of your family though, you decide that each digit must be different. How many possible
combinations do you have to choose from?
22. Suppose that Michael Jordan, a famous basketball player, has just finished playing a game, and
scored 53 points. If he made 21 total shots, some of which were worth two points, and the rest of
which were worth three points, how many three-point shots did he make?
23. How many perfect squares between 1 and 600 are divisible by four?
24. In order to expand a rectangular building, a construction crew is going to increase each side length
of the floor by 20%. By what percentage will the area of the floor increase? Express your
answer to the nearest whole percent.
25. Call a triangle “cutesy” if it is an acute triangle and the degree measures of all three of its angles
are distinct whole numbers. What is the largest possible positive difference between the degree
measures of the largest and smallest angles in a “cutesy” triangle?
26. In a flight from Seattle to Los Angeles, a plane flew an average speed of 200 miles per hour.
Because of a tail wind, the plane was able to fly back to Seattle at an average speed of 250 miles
per hour. If the plane flew 1,000 miles each direction, what was the plane's average speed, in
miles per hour? Express your answer to the nearest integer.
27. If A is the set of all positive integers, and B is the set of all two-digit prime numbers less than 60,
how many elements are in the set A ∩ B?
28. In how many ways can the letters in the word “BUBBLE” be uniquely arranged?
29. If the complement of an angle is two-fifths of its supplement, what is the degree measure of the
angle?
30. A league of only four basketball teams decided that playing each other once would not make a
long enough season. So they decided that each team would play every other team four times.
How many games will the season last now?
www.blainesd.org/mathchamps/
Individual
7th Grade
Instructions: Problems 1 – 10 are multiple choice and count towards your team score. Bubble in the
letter on your answer sheet. Be sure to erase all mistakes completely.
1. Which of the following shapes cannot have two pairs of parallel sides?
A. rhombus
B. parallelogram
C. rectangle
D. square
E. none of these
2. How many 2in ! 2in ! 2in cubes can fit into a 4in ! 4in ! 6in rectangular prism?
A. 2
B. 6
C. 8
D. 12
E. 48
3. Four out of the five choices below are equivalent to each other. Which one is not equivalent?
A. 82.5%
B. 0.0825
C. 33/40
D. 82.5:100 E. 825/1000
4. Which one of the following numbers is prime?
A. 111
B. 243
C. 251
D. 708
E. 921
5. Which of the following statistics is the greatest for the following list of data?
2, 4, 4, 4, 5, 6, 11, 14, 15
A. mean
B. median
C. half the range
D. mode
E. all are equal
6. Which of the following could be the lengths of the three sides of a right triangle?
A. 1, 2, 3
B. 5, 10, 11
C. 9, 12, 15
D. 2, 2, 4
E. 1, 3, 6
7. If the slope of a line that passes through the points with coordinates (2, -3) and (8, y) is 2/3, what
is y equal to?
A. -1
B. -2
C. 1
D. 2
E. 3
8. Which of the following is the correct scientific notation for the number 350,420,000?
A. 35.042 ! 107
B. 3.5042 ! 108
C. 3.5042 ! 109
D. 35.042 ! 108
9
E. 0.35042 ! 10
9. If a bag contains four blue chips, six red chips, and three orange chips, which of the following is
least likely to be drawn? Assume that each of the 13 chips is equally likely to be drawn.
A. Two blue chips without replacement
B. Two orange chips without replacement
C. Three red chips without replacement
D. Two red chips with replacement
E. Two blue chips with replacement
10. Which of the following has the greatest volume?
A. A cube with a side length of 3 inches
B. A sphere with a radius of 3 inches
C. A cylinder with a height and radius of 3 inches
D. Half of a sphere with a radius of 6 inches
E. Half of a cylinder with a height and radius of 6 inches
www.blainesd.org/mathchamps/
Individual
7th Grade
Problems 11 – 30: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
11. The lock on your diary allows you to set a three-digit combination. To make it harder on the rest
of your family though, you decide that each digit must be different. How many possible
combinations do you have to choose from?
12. Suppose that Michael Jordan, a famous basketball player, has just finished playing a game, and
scored 53 points. If he made 21 total shots, some of which were worth two points, and the rest of
which were worth three points, how many three-point shots did he make?
13. How many perfect squares between 1 and 600 are divisible by four?
14. In order to expand a rectangular building, a construction crew is going to increase each side length
of the floor by 20%. By what percentage will the area of the floor increase? Express your
answer to the nearest whole percent.
15. Call a triangle “cutesy” if it is an acute triangle and the degree measures of all three of its angles
are distinct whole numbers. What is the largest possible positive difference between the degree
measures of the largest and smallest angles in a “cutesy” triangle?
16. In a flight from Seattle to Los Angeles, a plane flew an average speed of 200 miles per hour.
Because of a tail wind, the plane was able to fly back to Seattle at an average speed of 250 miles
per hour. If the plane flew 1,000 miles each direction, what was the plane's average speed, in
miles per hour? Express your answer to the nearest integer.
17. If A is the set of all positive integers, and B is the set of all two-digit prime numbers less than 60,
how many elements are in the set A ∩ B?
18. In how many ways can the letters in the word “BUBBLE” be uniquely arranged?
19. If the complement of an angle is two-fifths of its supplement, what is the degree measure of the
angle?
20. A league of only four basketball teams decided that playing each other once would not make a
long enough season. So they decided that each team would play every other team four times.
How many games will the season last now?
21. What is the sum of the x and y coordinates of the point where the lines y = 2 x ! 3 and y + 22 = 3x
intersect?
www.blainesd.org/mathchamps/
Individual
7th Grade
22. If each interior angle in a regular polygon is 144 degrees, how many sides does the polygon have?
23. While reading a book on the history of mathematics, Zane found that, strangely enough, one of the
years was written in base-five notation. If the year given was 11022 5 , how would that year be
written in base 10?
24. What is the remainder when 3 2010 is divided by 5?
25. Eight friends in a club want to decide on a group of three students to be the “president”, “vicepresident” and “treasurer”, but then decide that coming up with a group of three people who will
be considered equal leaders of the club would require fewer decisions. How many fewer unique
arrangements are possible with that change?
26. If a spherical wooden marble originally had a radius of three inches, but had to be sanded down so
that the marble's radius shrunk by an inch, what was the positive difference in volume? Express
your answer to the nearest whole cubic inch.
27. Starting at the same spot, an ant walked 8 yards south to his anthill and an anteater walked 5 yards
east and then 20 yards south to his home. That evening, after both the ant and anteater were at
their respective homes, the anteater decided that he wanted to munch on ants for dinner. How far
away, in yards, is the anteater from the anthill?
28. Given the following system of equations, what is the value of x?
x+ y+z =8
2x ! y + z = 9
y + 4 z = 17
29. What is the smallest positive integer m that will make 40 ! m a perfect cube?
30. If a regular hexagon is inscribed inside a circle of radius 10 (as shown below), what is the area of
the hexagon? Express your answer to the nearest integer.
www.blainesd.org/mathchamps/
Individual
8th Grade
Instructions: Problems 1 – 10 are multiple choice and count towards your team score. Bubble in the
letter on your answer sheet. Be sure to erase all mistakes completely.
1. Which of the following shapes cannot have two pairs of parallel sides?
A. rhombus
B. parallelogram
C. rectangle
D. square
E. none of these
2. How many 2in ! 2in ! 2in cubes can fit into a 4in ! 4in ! 6in rectangular prism?
A. 2
B. 6
C. 8
D. 12
E. 48
3. Four out of the five choices below are equivalent to each other. Which one is not equivalent?
A. 82.5%
B. 0.0825
C. 33/40
D. 82.5:100 E. 825/1000
4. Which one of the following numbers is prime?
A. 111
B. 243
C. 251
D. 708
E. 921
5. Which of the following statistics is the greatest for the following list of data?
2, 4, 4, 4, 5, 6, 11, 14, 15
A. mean
B. median
C. half the range
D. mode
E. all are equal
6. Which of the following could be the lengths of the three sides of a right triangle?
A. 1, 2, 3
B. 5, 10, 11
C. 9, 12, 15
D. 2, 2, 4
E. 1, 3, 6
7. If the slope of a line that passes through the points with coordinates (2, -3) and (8, y) is 2/3, what
is y equal to?
A. -1
B. -2
C. 1
D. 2
E. 3
8. Which of the following is the correct scientific notation for the number 350,420,000?
A. 35.042 ! 107
B. 3.5042 ! 108
C. 3.5042 ! 109
D. 35.042 ! 108
9
E. 0.35042 ! 10
9. If a bag contains four blue chips, six red chips, and three orange chips, which of the following is
least likely to be drawn? Assume that each of the 13 chips is equally likely to be drawn.
A. Two blue chips without replacement
B. Two orange chips without replacement
C. Three red chips without replacement
D. Two red chips with replacement
E. Two blue chips with replacement
10. Which of the following has the greatest volume?
A. A cube with a side length of 3 inches
B. A sphere with a radius of 3 inches
C. A cylinder with a height and radius of 3 inches
D. Half of a sphere with a radius of 6 inches
E. Half of a cylinder with a height and radius of 6 inches
www.blainesd.org/mathchamps/
Individual
8th Grade
Problems 11 – 30: Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely.
You do not need to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If
3
your answer is a fraction like
, bubble in 316. For decimal answers like 3.14, bubble in 314.
16
11. The lock on your diary allows you to set a three-digit combination. To make it harder on the rest
of your family though, you decide that each digit must be different. How many possible
combinations do you have to choose from?
12. Suppose that Michael Jordan, a famous basketball player, has just finished playing a game, and
scored 53 points. If he made 21 total shots, some of which were worth two points, and the rest of
which were worth three points, how many three-point shots did he make?
13. How many perfect squares between 1 and 600 are divisible by four?
14. In order to expand a rectangular building, a construction crew is going to increase each side length
of the floor by 20%. By what percentage will the area of the floor increase? Express your
answer to the nearest whole percent.
15. Call a triangle “cutesy” if it is an acute triangle and the degree measures of all three of its angles
are distinct whole numbers. What is the largest possible positive difference between the degree
measures of the largest and smallest angles in a “cutesy” triangle?
16. In a flight from Seattle to Los Angeles, a plane flew an average speed of 200 miles per hour.
Because of a tail wind, the plane was able to fly back to Seattle at an average speed of 250 miles
per hour. If the plane flew 1,000 miles each direction, what was the plane's average speed, in
miles per hour? Express your answer to the nearest integer.
17. If A is the set of all positive integers, and B is the set of all two-digit prime numbers less than 60,
how many elements are in the set A ∩ B?
18. In how many ways can the letters in the word “BUBBLE” be uniquely arranged?
19. If the complement of an angle is two-fifths of its supplement, what is the degree measure of the
angle?
20. A league of only four basketball teams decided that playing each other once would not make a
long enough season. So they decided that each team would play every other team four times.
How many games will the season last now?
21. What is the sum of the x and y coordinates of the point where the lines y = 2 x ! 3 and y ! 22 = 3x
intersect?
www.blainesd.org/mathchamps/
Individual
8th Grade
22. If each interior angle in a regular polygon is 144 degrees, how many sides does the polygon have?
23. While reading a book on the history of mathematics, Zane found that, strangely enough, one of the
years was written in base-five notation. If the year given was 11022 5 , how would that year be
written in base 10?
24. What is the remainder when 3 2010 is divided by 5?
25. Eight friends in a club want to decide on a group of three students to be the “president”, “vicepresident” and “treasurer”, but then decide that coming up with a group of three people who will
be considered equal leaders of the club would require fewer decisions. How many fewer unique
arrangements are possible with that change?
26. If a spherical wooden marble originally had a radius of three inches, but had to be sanded down so
that the marble's radius shrunk by an inch, what was the positive difference in volume? Express
your answer to the nearest whole cubic inch.
27. Starting at the same spot, an ant walked 8 yards south to his anthill and an anteater walked 5 yards
east and then 20 yards south to his home. That evening, after both the ant and anteater were at
their respective homes, the anteater decided that he wanted to munch on ants for dinner. How far
away, in yards, is the anteater from the anthill?
28. Given the following system of equations, what is the value of x?
x+ y+z =8
2x ! y + z = 9
y + 4 z = 17
29. What is the smallest positive integer m that will make 40 ! m a perfect cube?
30. If a regular hexagon is inscribed inside a circle of radius 10 (as shown below), what is the area of
the hexagon? Express your answer to the nearest integer.
www.blainesd.org/mathchamps/