Download wcmc.algebra final 2015

Whatcom County Math Championship – 2015
Algebra – 4th Grade
1. Evaluate the expression 62 – 5 + 4×(3+1).
2. What is the least common multiple of 36 and 90?
3. What value of x will make this equation true: 3x – 10 = 62.
4. Elsa can skate 18 miles in 3 hours; how many minutes would it take for her to skate 24
miles?
5. If 8, _____, ______, ______, 60 is an arithmetic sequence, what is the middle term?
6. If the sum of five consecutive numbers is 120, what is the middle number?
7. Ava finds that if she halves a certain number and adds 4 to the result, she gets the same
result as if she had doubled her original number and subtracted 4 from the result. What was
Ava’s number? Give your answer as a fraction in lowest terms.
8. The expression x ⊗ y means (a) take the first number and subtract the second number,
then (b) multiply that result by the second number, and finally (c) add the first number to the
result. What is 5 ⊗ 2?
9. What is the units digit of 22015?
10. What is the fraction halfway between
as a reduced fraction.
€
€
1
1
and on the number line? Write your answer
4
6
Whatcom County Math Championship – 2015
Algebra – 5th Grade
1. Elsa can skate 18 miles in 3 hours; how many minutes would it take for her to skate 24
miles?
2. If 8, _____, ______, ______, 60 is an arithmetic sequence, what is the middle term?
3. If the sum of five consecutive numbers is 120, what is the middle number?
4. Ava finds that if she halves a certain number and adds 4 to the result, she gets the same
result as if she had doubled her original number and subtracted 4 from the result. What was
Ava’s number? Give your answer as a fraction in lowest terms.
5. The expression x ⊗ y means (a) take the first number and subtract the second number,
then (b) multiply that result by the second number, and finally (c) add the first number to the
result. What is 5 ⊗ 2?
6. What is the units digit of 22015?
7. What is the fraction halfway between
a reduced fraction.
1
1
and on the number line? Write your answer as
4
6
8. The product of two numbers is 144 and their difference is 18. What is their sum?
€
€
9. If 30 < a < 60 and 120 < b < 270, what is the smallest value of the quotient b/a ?
10. What is the difference between the sum of the first 2015 even counting numbers and the
sum of the first 2015 odd counting numbers?
Whatcom County Math Championship – 2015
Algebra – 6th Grade
1. Ava finds that if she halves a certain number and adds 4 to the result, she gets the same
result as if she had doubled her original number and subtracted 4 from the result. What was
Ava’s number? Give your answer as a fraction in lowest terms.
2. The expression x ⊗ y means (a) take the first number and subtract the second number,
then (b) multiply that result by the second number, and finally (c) add the first number to the
result. What is 5 ⊗ 2?
3. What is the units digit of 22015?
4. What is the fraction halfway between
a reduced fraction.
1
1
and on the number line? Write your answer as
4
6
5. The product of two numbers is 144 and their difference is 18. What is their sum?
€
€
6. If 30 < a < 60 and 120 < b < 270, what is the smallest value of the quotient b/a ?
7. What is the difference between the sum of the first 2015 even counting numbers and the
sum of the first 2015 odd counting numbers?
8. Arrange the digits 1, 1, 2, 2, 3, 3 as a six digit number in which the 1s are separated by one
digit, the 2s are separated by 2 digits, and the 3s are separated by 3 digits. There are two
answers. What is the difference between those answers?
9. If 4, ____, _____, 72 is a geometric sequence, what is the third term? Round to the
nearest hundredth.
10. 8x = 27. What is 4x?
Whatcom County Math Championship – 2015
Algebra – 7th + 8th Grade
1. What is the fraction halfway between
a reduced fraction.
1
1
and on the number line? Write your answer as
4
6
2. The product of two numbers is 144 and their difference is 18. What is their sum?
€
€
3. If 30 < a < 60 and 120 < b < 270, what is the smallest value of the quotient b/a ?
4. What is the difference between the sum of the first 2015 even counting numbers and the
sum of the first 2015 odd counting numbers?
5. Arrange the digits 1, 1, 2, 2, 3, 3 as a six digit number in which the 1s are separated by one
digit, the 2s are separated by 2 digits, and the 3s are separated by 3 digits. There are two
answers. What is the difference between those answers?
6. If 4, ____, _____, 72 is a geometric sequence, what is the third term? Round to the
nearest hundredth.
7. 8x = 27. What is 4x?
8. The square of x is 48 larger than the square of y, and x is 4 larger than y. What is the
product xy?
9. The 9th term of the geometric sequence 24, 36, 54…will be a number in the form
What is n – m?
10. Let m = 22015 + 20152. What is the units digit of 2m + m2?
€
3n
.
2m