Individual Round
Grade 4
1. Evaluate the following expression: 4 " (7 ! 2) ! 8 ÷ 2
2. What is the remainder when you divide 449 by 23?
3. Twelve friends took all of their candy after Halloween and made it so each of them had the same
number of pieces. If one of the friends had 30 pieces of candy after that, how many pieces did the
twelve friends have all together?
4.
How many positive multiples of five are there that are less than 34?
5.
What is the area of the following triangle?
6.
A school raffle was held to raise money for a field trip to the zoo. If 7 students entered, 34 parents
entered, and 10 teachers entered the raffle, what is the probability that a student will be the winner
of the raffle? Express your answer as a reduced fraction.
7.
Martin Luther King Jr. lived from 1929 to 1968, Malcolm X lived from 1925 to 1965, and Jackie
Robinson lived from 1919 to 1972. For how many years were all three alive at the same time?
Assume that 1990 to 1992 would be considered two years.
8.
After finishing a tasty dinner, your mom is struggling to figure out what the tip should be. If the
total bill before the tip was $24.00 and she wants the tip to be 15% of the total, how much should
you tell her to give for the tip?
9.
One of the most common recommendations for the amount of water you should drink is 8 eightounce glasses each day. If you are awake for 16 hours each day and want to drink an equal amount
of water every hour, how many ounces of water per hour should you drink?
10. What is the volume of a cube whose side length is 10 units?
Individual Round
Grade 4
11. Tangrams are a set of shapes that are made by folding and cutting a whole square. If you have six
of the seven pieces, and know that the fraction of the whole they represent are
1 1 1 1 1
, , , , and
4 4 16 8 8
1
16 , what fraction of the whole does the final piece represent?
12. How many of the following twenty-six capital letters have at least one line of symmetry?
ACDFGHIJLMNOPQRSTUVWXYZ
13. Barbara answered 24 questions correctly on her first test, 26 correctly on her second test, and 40
correctly on her third test. What was the average number of questions she answered correctly?
14. How many squares of any size can be found in the following three-by-three square?
15. What is the probability of rolling a two on a fair, six-sided die, followed by getting heads when
flipping a fair two-sided coin? Express your answer as a reduced fraction.
16. If the circumference of a circle is equal to 44π, what is the radius of that same circle?
17. If four times a mystery number is equal to the mystery number plus 27, what is the mystery
number?
18. Below is a magic square, because each row, column, and diagonal sum to the same number,
defined as the “magic number”. If we were to increase each of the numbers in the square by three,
then double each of the numbers, what would the new magic number be?
Individual Round
Grade 4
19. If 96 is 120% of some number, what is 40% of that same number?
20. How many inches are there in 20.5 yards?
21. What is the median of the following list of fractions? Express your answer as a reduced
fraction.
3 7 2 3 1
, , , ,
4 8 9 14 2
22. What is the sum of the factors of 50?
23. Using the money that she earned over the course of the week, Nancy gave a third of it to the
church she goes to each week. A quarter of the remaining amount was then given to the local
animal shelter. After all of that charity, she was left with $60 which she used to buy herself a new
pair of shoes. How much money did she originally have?
24. If someone working at a grocery store earns $12 per hour, and earns 150% of their wage per hour
for any time above eight hours, how much money would a grocery cashier earn if he/she worked
from 8:30am to 10:00pm? Assume there were no unpaid breaks.
25. What is the sum of the reciprocals of 2.5 and 2? Express your answer as a decimal.
26. What value of x will satisfy the following equation?
3x ! 4 = 4x
27. What is the sum of the natural numbers between 100 and 200, inclusively?
28. When Pedro was ordering a ticket to see Avatar in theaters, he requested that his seat be in the
exact middle of the theater – an equal number of seats on either side of him in his row, and an
equal number of rows both in front and behind him. He received a ticket saying he was in “Row 7,
seat 10”. Assuming there are an equal number of seats in each row, how many seats are in that
theater?
29. If the diagonal in a square has a length of
40 , what is the area of the square?
30. How many perfect cubes are there that are less than 10,000?
Individual Round
Grade 5
1.
A school raffle was held to raise money for a field trip to the zoo. If 7 students entered, 34
parents entered, and 10 teachers entered the raffle, what is the probability that a student will be the
winner of the raffle? Express your answer as a reduced fraction.
2.
Martin Luther King Jr. lived from 1929 to 1968, Malcolm X lived from 1925 to 1965, and Jackie
Robinson lived from 1919 to 1972. For how many years were all three alive at the same time?
Assume that 1990 to 1992 would be considered two years.
3.
After finishing a tasty dinner, your mom is struggling to figure out what the tip should be. If the
total bill before the tip was $24.00 and she wants the tip to be 15% of the total, how much should
you tell her to give for the tip?
4.
One of the most common recommendations for the amount of water you should drink is 8 eightounce glasses each day. If you are awake for 16 hours each day and want to drink an equal
amount of water every hour, how many ounces of water per hour should you drink?
5.
What is the volume of a cube whose side length is 10 units?
6.
Tangrams are a set of shapes that are made by folding and cutting a whole square. If you have six
of the seven pieces, and know that the fraction of the whole they represent are
1 1 1 1 1
, , , , and
4 4 16 8 8
1
16 , what fraction of the whole does the final piece represent?
7.
How many of the following twenty-six capital letters have at least one line of symmetry?
ACDFGHIJLMNOPQRSTUVWXYZ
8.
Barbara answered 24 questions correctly on her first test, 26 correctly on her second test, and 40
correctly on her third test. What was the average number of questions she answered correctly?
9. How many squares of any size can be found in the following three-by-three square?
10. What is the probability of rolling a two on a fair, six-sided die, followed by getting heads when
flipping a fair two-sided coin? Express your answer as a reduced fraction.
Individual Round
Grade 5
11. If the circumference of a circle is equal to 44π, what is the radius of that same circle?
12. If four times a mystery number is equal to the mystery number plus 27, what is the mystery
number?
13. Below is a magic square, because each row, column, and diagonal sum to the same number,
defined as the “magic number”. If we were to increase each of the numbers in the square by three,
then double each of the numbers, what would the new magic number be?
14. If 96 is 120% of some number, what is 40% of that same number?
15. How many inches are there in 20.5 yards?
16. What is the median of the following list of fractions? Express your answer as a reduced
fraction.
3 7 2 3 1
, , , ,
4 8 9 14 2
17. What is the sum of the factors of 50?
18. Using the money that she earned over the course of the week, Nancy gave a third of it to the
church she goes to each week. A quarter of the remaining amount was then given to the local
animal shelter. After all of that charity, she was left with $60 which she used to buy herself a new
pair of shoes. How much money did she originally have?
19. If someone working at a grocery store earns $12 per hour, and earns 150% of their wage per hour
for any time above eight hours, how much money would a grocery cashier earn if he/she worked
from 8:30am to 10:00pm? Assume there were no unpaid breaks.
20. What is the sum of the reciprocals of 2.5 and 2? Express your answer as a decimal.
21. What value of x will satisfy the following equation?
3x ! 4 = 4x
Individual Round
Grade 5
22. What is the sum of the natural numbers between 100 and 200, inclusively?
23. When Pedro was ordering a ticket to see Avatar in theaters, he requested that his seat be in the
exact middle of the theater – an equal number of seats on either side of him in his row, and an
equal number of rows both in front and behind him. He received a ticket saying he was in “Row
7, seat 10”. Assuming there are an equal number of seats in each row, how many seats are in that
theater?
24. If the diagonal in a square has a length of
40 , what is the area of the square?
25. How many perfect cubes are there that are less than 10,000?
2010
26. What is the ones digit of 7 ?
27. Using a standard, 52-card deck of playing cards, what is the probability of choosing a three of
clubs followed by a two of hearts without replacement? Express your answer as a reduced
fraction.
28. On the way to work, Mary drove 30 miles at an average of 60 miles per hour. Because of traffic
though, on the way home, she drove the same 30 miles at an average of 20 miles per hour. What
was her overall average speed for the 40 miles she drove?
29. Below is an example of a day’s weather forecast from London. However, they often use Celsius .
On the particular day seen below, what is the positive difference between the high and low
5
temperature, in degrees Fahrenheit? Note that C = ( F " 32) ! .
9
Individual Round
Grade 5
30. What is the surface area of the triangular prism seen below?
Individual Round
Grade 6
1.
Tangrams are a set of shapes that are made by folding and cutting a whole square. If you have six
of the seven pieces, and know that the fraction of the whole they represent are
1 1 1 1 1
, , , , and
4 4 16 8 8
1
16 , what fraction of the whole does the final piece represent?
2.
How many of the following twenty-six capital letters have at least one line of symmetry?
ACDFGHIJLMNOPQRSTUVWXYZ
3.
Barbara answered 24 questions correctly on her first test, 26 correctly on her second test, and 40
correctly on her third test. What was the average number of questions she answered correctly?
4. How many squares of any size can be found in the following three-by-three square?
5. What is the probability of rolling a two on a fair, six-sided die, followed by getting heads when
flipping a fair two-sided coin? Express your answer as a reduced fraction.
6.
If the circumference of a circle is equal to 44π, what is the radius of that same circle?
7. If four times a mystery number is equal to the mystery number plus 27, what is the mystery
number?
8.
Below is a magic square, because each row, column, and diagonal sum to the same number,
defined as the “magic number”. If we were to increase each of the numbers in the square by three,
then double each of the numbers, what would the new magic number be?
Individual Round
Grade 6
9.
If 96 is 120% of some number, what is 40% of that same number?
10. How many inches are there in 20.5 yards?
11. What is the median of the following list of fractions? Express your answer as a reduced
fraction.
3 7 2 3 1
, , , ,
4 8 9 14 2
12. What is the sum of the factors of 50?
13. Using the money that she earned over the course of the week, Nancy gave a third of it to the
church she goes to each week. A quarter of the remaining amount was then given to the local
animal shelter. After all of that charity, she was left with $60 which she used to buy herself a new
pair of shoes. How much money did she originally have?
14. If someone working at a grocery store earns $12 per hour, and earns 150% of their wage per hour
for any time above eight hours, how much money would a grocery cashier earn if he/she worked
from 8:30am to 10:00pm? Assume there were no unpaid breaks.
15. What is the sum of the reciprocals of 2.5 and 2? Express your answer as a decimal.
16. What value of x will satisfy the following equation?
3x ! 4 = 4x
17. What is the sum of the natural numbers between 100 and 200, inclusively?
18. When Pedro was ordering a ticket to see Avatar in theaters, he requested that his seat be in the
exact middle of the theater – an equal number of seats on either side of him in his row, and an
equal number of rows both in front and behind him. He received a ticket saying he was in “Row 7,
seat 10”. Assuming there are an equal number of seats in each row, how many seats are in that
theater?
19. If the diagonal in a square has a length of
40 , what is the area of the square?
20. How many perfect cubes are there that are less than 10,000?
2010
21. What is the ones digit of 7 ?
22. Using a standard, 52-card deck of playing cards, what is the probability of choosing a three of
clubs followed by a two of hearts without replacement? Express your answer as a reduced
fraction.
Individual Round
Grade 6
23. On the way to work, Mary drove 30 miles at an average of 60 miles per hour. Because of traffic
though, on the way home, she drove the same 30 miles at an average of 20 miles per hour. What
was her overall average speed for the 40 miles she drove?
24. Below is an example of a day’s weather forecast from London. However, they often use Celsius .
On the particular day seen below, what is the positive difference between the high and low
5
temperature, in degrees Fahrenheit? Note that C = ( F " 32) ! .
9
25. What is the surface area of the triangular prism seen below?
26. What is the slope of a line which goes through the points with coordinates (6, -3) and (2, -5)?
Express your answer as a decimal.
27. How many unique ways can you arrange the letters in the word “FRACTAL”?
Individual Round
Grade 6
28. If two numbers, a and b, must be two prime numbers between 1 and 40 inclusively, what is the
a"b
largest possible value of
? Express your answer to the nearest integer.
a!b
29. If set A is the set of all prime numbers between 20 and 60, and set B is the set of numbers between
20 and 60 whose tens digit is greater than their ones digit, how many elements are in the union of
set A and B?
30. Suppose the probability of it raining on any given day in Washington is 70% and the probability of
it being warmer than 60 degrees is 35%. Assuming the two events are independent, what is the
probability that it will not rain and be colder than 60 degrees on any given day? Express your
answer as an exact decimal.
Individual Round
Grade 7
1. If the circumference of a circle is equal to 44π, what is the radius of that same circle?
2. If four times a mystery number is equal to the mystery number plus 27, what is the mystery
number?
3.
Below is a magic square, because each row, column, and diagonal sum to the same number,
defined as the “magic number”. If we were to increase each of the numbers in the square by three,
then double each of the numbers, what would the new magic number be?
4. If 96 is 120% of some number, what is 40% of that same number?
5. How many inches are there in 20.5 yards?
6. What is the median of the following list of fractions? Express your answer as a reduced
fraction.
3 7 2 3 1
, , , ,
4 8 9 14 2
7.
What is the sum of the factors of 50?
8.
Using the money that she earned over the course of the week, Nancy gave a third of it to the
church she goes to each week. A quarter of the remaining amount was then given to the local
animal shelter. After all of that charity, she was left with $60 which she used to buy herself a new
pair of shoes. How much money did she originally have?
9.
If someone working at a grocery store earns $12 per hour, and earns 150% of their wage per hour
for any time above eight hours, how much money would a grocery cashier earn if he/she worked
from 8:30am to 10:00pm? Assume there were no unpaid breaks.
10. What is the sum of the reciprocals of 2.5 and 2? Express your answer as a decimal.
11. What value of x will satisfy the following equation?
3x ! 4 = 4x
Individual Round
Grade 7
12. What is the sum of the natural numbers between 100 and 200, inclusively?
13. When Pedro was ordering a ticket to see Avatar in theaters, he requested that his seat be in the
exact middle of the theater – an equal number of seats on either side of him in his row, and an
equal number of rows both in front and behind him. He received a ticket saying he was in “Row
7, seat 10”. Assuming there are an equal number of seats in each row, how many seats are in that
theater?
14. If the diagonal in a square has a length of
40 , what is the area of the square?
15. How many perfect cubes are there that are less than 10,000?
2010
16. What is the ones digit of 7 ?
17. Using a standard, 52-card deck of playing cards, what is the probability of choosing a three of
clubs followed by a two of hearts without replacement? Express your answer as a reduced
fraction.
18. On the way to work, Mary drove 30 miles at an average of 60 miles per hour. Because of traffic
though, on the way home, she drove the same 30 miles at an average of 20 miles per hour. What
was her overall average speed for the 40 miles she drove?
19. Below is an example of a day’s weather forecast from London. However, they often use Celsius .
On the particular day seen below, what is the positive difference between the high and low
5
temperature, in degrees Fahrenheit? Note that C = ( F " 32) ! .
9
Individual Round
Grade 7
20. What is the surface area of the triangular prism seen below?
21. What is the slope of a line which goes through the points with coordinates (6, -3) and (2, -5)?
Express your answer as a decimal.
22. How many unique ways can you arrange the letters in the word “FRACTAL”?
23. If two numbers, a and b, must be two prime numbers between 1 and 40 inclusively, what is the
a"b
largest possible value of
? Express your answer to the nearest integer.
a!b
24. If set A is the set of all prime numbers between 20 and 60, and set B is the set of numbers between
20 and 60 whose tens digit is greater than their ones digit, how many elements are in the union of
set A and B?
25. Suppose the probability of it raining on any given day in Washington is 70% and the probability
of it being warmer than 60 degrees is 35%. Assuming the two events are independent, what is the
probability that it will not rain and be colder than 60 degrees on any given day? Express your
answer as an exact decimal.
26. If the ratio of x to y is 3:7, and 8 x + 3 y = 45 , what does x equal?
Individual Round
Grade 7
27. In a school of 200 students who are required to join at least one club, there are three main clubs
that students partake in: Book Club, Math Club, and Science Club. We know the following facts:
• 60 students are in Book Club, 140 students are in Math Club, and 100 students are in
Science Club
• 20 students are in all three clubs
• 30 students are in both the Science and Math Clubs but not the Book Club; 20 students
are in both the Book Club and Math Club but not the Science Club; and 10 students are
in both Book Club and Science Club, but not the Math Club.
How many students are only in Math Club?
28. If Joe is able to solve 30 math problems in six minutes, Moe is able to solve 28 math problems in
seven minutes, and Bo is able to solve 52 problems in 13 minutes, how many problems will they
be able to solve together in an hour?
29. What are the coordinates of the point where the lines y = 3 x ! 5 and y = x + 5 meet? Express
your answer in the form (a, b).
30. What is the sum of the number of edges, faces, and vertices on a cube?
Individual Round
Grade 8
1. What is the median of the following list of fractions? Express your answer as a reduced
fraction.
3 7 2 3 1
, , , ,
4 8 9 14 2
2.
What is the sum of the factors of 50?
3.
Using the money that she earned over the course of the week, Nancy gave a third of it to the
church she goes to each week. A quarter of the remaining amount was then given to the local
animal shelter. After all of that charity, she was left with $60 which she used to buy herself a new
pair of shoes. How much money did she originally have?
4.
If someone working at a grocery store earns $12 per hour, and earns 150% of their wage per hour
for any time above eight hours, how much money would a grocery cashier earn if he/she worked
from 8:30am to 10:00pm? Assume there were no unpaid breaks.
5. What is the sum of the reciprocals of 2.5 and 2? Express your answer as a decimal.
6. What value of x will satisfy the following equation?
3x ! 4 = 4x
7.
What is the sum of the natural numbers between 100 and 200, inclusively?
8.
When Pedro was ordering a ticket to see Avatar in theaters, he requested that his seat be in the
exact middle of the theater – an equal number of seats on either side of him in his row, and an
equal number of rows both in front and behind him. He received a ticket saying he was in “Row
7, seat 10”. Assuming there are an equal number of seats in each row, how many seats are in that
theater?
9. If the diagonal in a square has a length of
40 , what is the area of the square?
10. How many perfect cubes are there that are less than 10,000?
2010
11. What is the ones digit of 7 ?
12. Using a standard, 52-card deck of playing cards, what is the probability of choosing a three of
clubs followed by a two of hearts without replacement? Express your answer as a reduced
fraction.
13. On the way to work, Mary drove 30 miles at an average of 60 miles per hour. Because of traffic
though, on the way home, she drove the same 30 miles at an average of 20 miles per hour. What
was her overall average speed for the 40 miles she drove?
Individual Round
Grade 8
14. Below is an example of a day’s weather forecast from London. However, they often use Celsius .
On the particular day seen below, what is the positive difference between the high and low
5
temperature, in degrees Fahrenheit? Note that C = ( F " 32) ! .
9
15. What is the surface area of the triangular prism seen below?
16. What is the slope of a line which goes through the points with coordinates (6, -3) and (2, -5)?
Express your answer as a decimal.
17. How many unique ways can you arrange the letters in the word “FRACTAL”?
18. If two numbers, a and b, must be two prime numbers between 1 and 40 inclusively, what is the
a"b
largest possible value of
? Express your answer to the nearest integer.
a!b
Individual Round
Grade 8
19. If set A is the set of all prime numbers between 20 and 60, and set B is the set of numbers between
20 and 60 whose tens digit is greater than their ones digit, how many elements are in the union of
set A and B?
20. Suppose the probability of it raining on any given day in Washington is 70% and the probability
of it being warmer than 60 degrees is 35%. Assuming the two events are independent, what is the
probability that it will not rain and be colder than 60 degrees on any given day? Express your
answer as an exact decimal.
21. If the ratio of x to y is 3:7, and 8 x + 3 y = 45 , what does x equal?
22. In a school of 200 students who are required to join at least one club, there are three main clubs
that students partake in: Book Club, Math Club, and Science Club. We know the following facts:
• 60 students are in Book Club, 140 students are in Math Club, and 100 students are in
Science Club
• 20 students are in all three clubs
• 30 students are in both the Science and Math Clubs but not the Book Club; 20 students
are in both the Book Club and Math Club but not the Science Club; and 10 students are
in both Book Club and Science Club, but not the Math Club.
How many students are only in Math Club?
23. If Joe is able to solve 30 math problems in six minutes, Moe is able to solve 28 math problems in
seven minutes, and Bo is able to solve 52 problems in 13 minutes, how many problems will they
be able to solve together in an hour?
24. What are the coordinates of the point where the lines y = 3 x ! 5 and y = x + 5 meet? Express
your answer in the form (a, b).
25. What is the sum of the number of edges, faces, and vertices on a cube?
26. A group consisting of five pairs of students are trying to take a picture before their school dance.
If the only rule is that each person must be standing in the line next to the person they are going to
the dance with, how many unique ways could they stand for their picture?
27. Using the following equations, find the value of 20 x + 10 y .
3 x ! 9 y = 42
5 x + 10 y = !30
28. In a fun science experiment, you mixed 10 L of an 80% acidic solution with a 2L of an unknown
solution, and found that the result was a 70% solution. What percentage was the unknown
solution?
Individual Round
Grade 8
4
29. If you expand the expression (2x + 1)6 , what will the coefficient be for the x term?
30. In the dice game Yahtzee, the best roll you can get is called a Yahtzee (imagine that!) and is
achieved by rolling five of the same number with five fair, six-sided dice. If you are rolling all
five dice one time, what is the probability you will get a Yahtzee? Express your answer as a
reduced fraction.