Glenelg Math Team Jeopardy

Arithmetic

100

What is 1+2+3+4+5?

15

200

If the legs of a right triangle are of length 20 and 21, what is the length of the hypotenuse?

29

300

(1-1/2)(1-1/3)(1-1/4)...(1-1/2025)=?

1/2025

400

(2+1)(2²+1)(2⁴+1)...(2¹⁰²⁴+1)+1 can be expressed as 2^x. What is x?

2048

500

1*2*3+2*3*4+3*4*5+...+98*99*100=? 

(98*99*100*101)/4=24497550

Algebra

100

3x=6

What is x?

2

200

Mike collected an even number of insects in a jar - some beatles (all 6 legs), some spiders (all 8 legs). He counted 54 legs in all. How many spiders does he have?

3

300

If x+1/x=-2, what is x²+1/(x²)?

2

400

Alice starts at A running towards B, and Bob starts at B, running towards A. Assume they run at constant speeds. It takes time t for them to meet. If it takes 9 more minutes for Alice to make it to B and 16 more minutes for Bob to make it to A, what is t?

12 minutes

500

What is the remainder when x¹⁰⁰ is divided by x²-3x+2?

(2¹⁰⁰-1)x+(2-2¹⁰⁰)

Number Theory

100

How many primes are there up to 100?

25

200

3 distinct prime numbers sum to 16. What is their product?

66

300

0.123123123... is equal to what simplified fraction?

41/333

400

How many numbers are coprime (means GCD = 1) to 100?

40

500

What is the remainder when 10! is divided by 11?

10

Combo/Geo

100

How many sequences of heads and tails could I get with 4 coin flips?

16

200

How many ways are there to order the letters ABCDE?

120

300

What is the largest area of a rectangle that can be inscribed in a circle of radius 6?

72

400

A circle with center O and radius 10 has two lines that are tangent to it at A and B. These two lines intersect each other at point P. If angle AOB is equal to 120 degrees, what is the length of OP?

20

500

How many ways can we split 9 cookies between Alice, Bob, and Claire such that they each receive a positive number of cookies?

28

Bonus

500

Let a₁=1 and a₂=1. Let a_k=a_k-1+a_k-2 (Fibonacci sequence). Let b_k=a_2k/a_k. What is b₁₀?

123