Download Whatcom County Math Championship – 2016 Individual – 4th Grade

Whatcom County Math Championship – 2016
Individual – 4th Grade
1. If 6
2
is written as a mixed fraction, what is the difference between the numerator and the denominator?
3
2. Write 0.92 as a reduced fraction.
€
3. What is the average of the first 5 even numbers?
4. If 9 more than four times a number is 61, what is the number?
5. What is 28?
6. What is the next term in this sequence: 108, 72, 48, ____?
7. What is the sum of the first 8 square numbers?
8. When it is 11:00, what is the angle measure between the minute hand and the hour hand?
9. How many prime numbers are there between 1 and 30?
10. As Elsa counts backwards from 212 to –40 by 3s, she takes one step; 209 would be the first step. On what
step will she count the number 32?
11. How many ways are there to arrange the letters in the word BRICK?
12. Rene can make 4 crepes in 12 minutes. How many crepes can he make in an hour and a half?
13. If Philip draws a card from a regular 52 – card deck, what is the probability that he will get a 3? Write your
answer as a reduced fraction.
14. Point M is the midpoint of line segment AB, B is at (20, 4), M is at (18, –2) and A is at (p, q). What is p+q?
15. If the angles in a triangle are x, x and 3x, what is the measure of the biggest angle?
16. A water lily doubles itself every day. If it takes 6 days for a 4 foot by 5 foot pond to be covered by lilies
from the first batch of 120 lilies, on what day was the pond half – full?
17. If Dasha rolls two six – sided dice and adds the results, what is the probability that she will roll a 9 or more?
Write your answer as a reduced fraction.
18. How many triangles of all sizes are there in this picture:
19. What is
6
minus its reciprocal? Write your answer as a reduced fraction.
5
20. What value of x will make this true: (5 – 1)(5 – 2)(5 – 3)(5 – 4)(5 – x) = 0?
21.€ Using only nickels, dimes and quarters, how many ways can you make 95 cents?
22. What percent of 48 is 60?
23. What is the remainder when you divided 2016 by 23?
24. If you count backwards from 2016 by 0.6 each time, what is the first whole one digit number you say?
25. The area of a square is twice its perimeter. What is the side length of the square?
26. What is the largest whole number perimeter you can make with a rectangle that has an area of 48?
27. How many prime numbers are there between 150 and 200?
28. Six consecutive odd numbers add up to 2016. What is the largest of these numbers?
29. What is 1+
2
4
3+
5+6
? Write your answer as a reduced fraction.
30. Find x, the length of BD.
A€
6 x
B
D
8
10
C
Whatcom County Math Championship – 2016
Individual – 5th Grade
1. What is the next term in this sequence: 108, 72, 48, ____?
2. What is the sum of the first 8 square numbers?
3. When it is 11:00, what is the angle measure between the minute hand and the hour hand?
4. How many prime numbers are there between 1 and 30?
5. As Elsa counts backwards from 212 to –40 by 3s, she takes one step; 209 would be the first step. On what
step will she count the number 32?
6. How many ways are there to arrange the letters in the word BRICK?
7. Rene can make 4 crepes in 12 minutes. How many crepes can he make in an hour and a half?
8. If Philip draws a card from a regular 52 – card deck, what is the probability that he will get a 3? Write your
answer as a reduced fraction.
9. Point M is the midpoint of line segment AB, B is at (20, 4), M is at (18, –2) and A is at (p, q). What is p+q?
10. If the angles in a triangle are x, x and 3x, what is the measure of the biggest angle?
11. A water lily doubles itself every day. If it takes 6 days for a 4 foot by 5 foot pond to be covered by lilies
from the first batch of 120 lilies, on what day was the pond half – full?
12. If Dasha rolls two six – sided dice and adds the results, what is the probability that she will roll a 9 or more?
Write your answer as a reduced fraction.
13. How many triangles of all sizes are there in this picture:
14. What is
6
minus its reciprocal? Write your answer as a reduced fraction.
5
15. What value of x will make this true: (5 – 1)(5 – 2)(5 – 3)(5 – 4)(5 – x) = 0?
16.€ Using only nickels, dimes and quarters, how many ways can you make 95 cents?
17. What percent of 48 is 60?
18. What is the remainder when you divided 2016 by 23?
19. If you count backwards from 2016 by 0.6 each time, what is the first whole one digit number you say?
20. The area of a square is twice its perimeter. What is the side length of the square?
21. What is the largest whole number perimeter you can make with a rectangle that has an area of 48?
22. How many prime numbers are there between 150 and 200?
23. Six consecutive odd numbers add up to 2016. What is the largest of these numbers?
24. What is 1+
2
4
3+
5+6
? Write your answer as a reduced fraction.
25. Find x, the length of BD.
A€
6 x
B
D
10
C
8
26. If 1.42 is written as a reduced fraction, what is the difference between the numerator and denominator?
27. The two triangles below are similar; what is x + y?
18
12
15
x
6
y
28. 234 base 5 is equal to 36 in what base?
29. 435 is the sum of the first ____ terms of the sequence 1, 2, 3, 4, 5…
30. How many whole number values of n will make this statement true: 1,000 < 2n < 10,000.
Whatcom County Math Championship – 2016
Individual – 6th Grade
1. How many ways are there to arrange the letters in the word BRICK?
2. Rene can make 4 crepes in 12 minutes. How many crepes can he make in an hour and a half?
3. If Philip draws a card from a regular 52 – card deck, what is the probability that he will get a 3? Write your
answer as a reduced fraction.
4. Point M is the midpoint of line segment AB, B is at (20, 4), M is at (18, –2) and A is at (p, q). What is p+q?
5. If the angles in a triangle are x, x and 3x, what is the measure of the biggest angle?
6. A water lily doubles itself every day. If it takes 6 days for a 4 foot by 5 foot pond to be covered by lilies from
the first batch of 120 lilies, on what day was the pond half – full?
7. If Dasha rolls two six – sided dice and adds the results, what is the probability that she will roll a 9 or more?
Write your answer as a reduced fraction.
8. How many triangles of all sizes are there in this picture:
9. What is
6
minus its reciprocal? Write your answer as a reduced fraction.
5
10. What value of x will make this true: (5 – 1)(5 – 2)(5 – 3)(5 – 4)(5 – x) = 0?
€ Using only nickels, dimes and quarters, how many ways can you make 95 cents?
11.
12. What percent of 48 is 60?
13. What is the remainder when you divided 2016 by 23?
14. If you count backwards from 2016 by 0.6 each time, what is the first whole one digit number you say?
15. The area of a square is twice its perimeter. What is the side length of the square?
16. What is the largest whole number perimeter you can make with a rectangle that has an area of 48?
17. How many prime numbers are there between 150 and 200?
18. Six consecutive odd numbers add up to 2016. What is the largest of these numbers?
19. What is 1+
2
4
3+
5+6
? Write your answer as a reduced fraction.
20. Find x, the length of BD.
A€
6 x
B
D
10
C
8
21. If 1.42 is written as a reduced fraction, what is the difference between the numerator and denominator?
22. The two triangles below are similar; what is x + y?
18
12
15
x
6
y
23. 234 base 5 is equal to 36 in what base?
24. 435 is the sum of the first ____ terms of the sequence 1, 2, 3, 4, 5…
25. How many whole number values of n will make this statement true: 1,000 < 2n < 10,000.
26. What fraction of the large rectangle is shaded? Write your answer as a reduced fraction.
27. For whole numbers m and n, define m ⊕ n as
nearest hundredth.
m −n
. What is 8 ⊕ (4 ⊕ 6)? Round your answer to the
m+n
28. A cube has a volume of 512, what is the longest distance from one vertex to another? Round your answer
€
to the nearest hundredth.
29. If anis a geometric sequence, and a1 = 108 and a3 = 48, what is a4?
x2
x
30. If
+
= 7, what is x?
x +1 x +1
€
Whatcom County Math Championship – 2016
Individual – 7th + 8th Grade
1. A water lily doubles itself every day. If it takes 6 days for a 4 foot by 5 foot pond to be covered by lilies from
the first batch of 120 lilies, on what day was the pond half – full?
2. If Dasha rolls two six – sided dice and adds the results, what is the probability that she will roll a 9 or more?
Write your answer as a reduced fraction.
3. How many triangles of all sizes are there in this picture:
4. What is
6
minus its reciprocal? Write your answer as a reduced fraction.
5
5. What value of x will make this true: (5 – 1)(5 – 2)(5 – 3)(5 – 4)(5 – x) = 0?
6.€ Using only nickels, dimes and quarters, how many ways can you make 95 cents?
7. What percent of 48 is 60?
8. What is the remainder when you divided 2016 by 23?
9. If you count backwards from 2016 by 0.6 each time, what is the first whole one digit number you say?
10. The area of a square is twice its perimeter. What is the side length of the square?
11. What is the largest whole number perimeter you can make with a rectangle that has an area of 48?
12. How many prime numbers are there between 150 and 200?
13. Six consecutive odd numbers add up to 2016. What is the largest of these numbers?
14. What is 1+
2
4
3+
5+6
? Write your answer as a reduced fraction.
15. Find x, the length of BD.
A€
6 x
B
D
8
10
C
16. If 1.42 is written as a reduced fraction, what is the difference between the numerator and denominator?
17. The two triangles below are similar; what is x + y?
18
12
15
x
6
y
18. 234 base 5 is equal to 36 in what base?
19. 435 is the sum of the first ____ terms of the sequence 1, 2, 3, 4, 5…
20. How many whole number values of n will make this statement true: 1,000 < 2n < 10,000.
21. What fraction of the large rectangle is shaded? Write your answer as a reduced fraction.
22. For whole numbers m and n, define m ⊕ n as
nearest hundredth.
m −n
. What is 8 ⊕ (4 ⊕ 6)? Round your answer to the
m+n
23. A cube has a volume of 512, what is the longest distance from one vertex to another? Round your answer
€
to the nearest hundredth.
24. If anis a geometric sequence, and a1 = 108 and a3 = 48, what is a4?
x2
x
25. If
+
= 7, what is x?
x +1 x +1
26. A pentagon has exterior angles of x, 2x, 3x, 4x and 5x. What is the smallest interior angle of this pentagon?
€ 27. There are five whole numbers between 1 and 100 that have 12 factors. What is the median of these
numbers?
28. If Philip draws a card from a regular 52–card deck and rolls a fair six–sided die, what is the probability that
his card number will be higher than his die number? Count Jacks as 11, Queens as 12, Kings as 13, Aces as 1.
Write your answer as a reduced fraction.
29. If the lines y = 3x – 5 and 2x + 3y = 18 meet at (a, b), what is a + b?
30. For any positive integer n, define \n/ as the sum of all the positive divisors of n, with the exception of n
itself. For example, \6/ is 1 + 2 + 3 = 6 and \20/ is 1 + 2 + 4 + 5 + 10 = 22. What is the first number n for
which \n/ > 50?