Math Club Jeopardy

Arithmetic

100

If a @ b = a² - b² and a # b = (a - b)², then what is the value of (5 @ 3) # 6?

100

200

What is the value of 100 - 101 + 102 - 103 + ... + 200 - 201?

51

300

What is the square root of 1³ + 2³ + 3³ + ... + 9³?

45

400

What is the value of 1² + 2² + 3² + ... + 10²?

385

500

If the value of (3+2)(3²+2²)(3⁴+2⁴)(3⁸+2⁸) = a^b - c^b, what is the value of a + b + c?

21

Equation

100

If 7x + 12 = 5x - 78, what is the value of x?

-45

200

Find the product of x and y if 5x + 3y = -7 and x + 3y = 9. Express your answer as a common fraction.

52/3

300

There are a total of 67 animals in a zoo of only birds and donkeys. All the birds have two legs except for a disabled one-leg bird, and all donkeys have four legs except two disabled two-leg donkeys. If there are a total of 201 legs, what fraction of disabled donkeys are there? Express your answer as a common fraction.

1/18

400

Find the value of x+2y+3z if 3x-2y+11z = 12 and -x + 2y - 4z = -3.

6

500

What is the value of x+y+z if:

2x + 5y + 2z = -38

3x - 2y + 4z = 17

-6x + y - 7z = -12

-7

Sequences

100

The 19th term of an arithmetic sequence is 234 and the common difference is 8. What is the value of the first term?

90

200

In a geometric sequence, the first term is 27 and the common difference is 2/3. What is the smallest integer of the sequence?

8

300

What is the sum of the arithmetic sequence 4 + 11 + 18 + 25 + ... + 354?

9129

400

What is the sum of the infinite sequence 1/2 + 1/16 + 1/128 + 1/1024 + ...?

4/7

500

Suppose that {a_n} is an arithmetic sequence with a₁ + a₂ + a₃ + ... + a₁₀₀ = 100 and a₁₀₁ + a₁₀₂ + a₁₀₃ + ... + a₂₀₀ = 200. What is the value of a₂ - a₁?

0.01

Number Theory

100

What is the units digit of 5^123456789?

5

200

What is the remainder when 2025² is divided by 8?

1

300

Convert the number 1234₅ to base 10.

194

400

For any positive integer M, the notation M denotes the product of the integers 1 through M. What is the largest integer n for which 5ⁿ is a factor of the sum 98! + 99! + 100! ?

26

500

If a four-digit number 2X9Y = 2^X ⋅ 9^Y, then what is the value of the product of X and Y?

10

Mystery (double pts)

100

How many ways are there to choose 8 balls from 12 identical balls?

1

200

If 10 ⋅ 10! + 9 ⋅ 9! + 8 ⋅ 8! + ... + 2 ⋅ 2! + 1 ⋅ 1! can be written as a! - b, what is the sum of a and b?

12

300

What is the sum of roots (solutions) to the equation |x² - 12x + 34| = 2?

18

400

What is the largest area of a circle that can be inscribed in a right triangle with side lengths 7, 24, and 25?

 3π

500

What is the sum of all the values of three-digit N such that N is divisible by 11 and N/11 is equal to the sum of the squares of the digits of N?

1353