Math Club End of Year Jeopardy Extravaganza

Algebra

67

If x=5, what is x?

5

167

Solve for x: 6x+67=73

1

267

If α, β, and γ are the three distinct roots of the equation x^3+2x^2-5x-6, what is α+β+γ?

-2

367

The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?

13

467

Brendan, Kaushal, and Artemii are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Brendon eats half of the cheese, then Kaushal eats half of the remaining half, then Artemii eats half of what remains, then back to Brendan, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Brendan eat in total?

4/7

Geometry

67

What shape has three sides

Triangle

167

Triangles ABC and PQR are similar. If Angle B = 90, AB = 12 and cos(P)=1/3, what is AC?

36

267

In Triangle ABC, AB=60, BC=36, AC=48. What is the area of ABC?

864

367

In triangle ABC, AB=7, AC=8, BC=9. Point D is on the circumscribed circle of the triangle such that AD bisects BAC. What is AD/CD?

(Hint: Use Ptolemy's Theorem)

5/3

467

Point E is the midpoint of side CD in square ABCD, and BE meets diagonal AC at F. The area of quadrilateral AFED is 45. What is the area of ABCD?

108

Calculus

67

What is the limit (n->infinity) of 1/n

0

167

If f(x)=67x^2 + 3e^2, what is f'(x)?

134x 

267

What is ∫1/(x²+4x+8) dx? 

(1/2)arctan((x+2)/2) + C

367

If we have parametric equations x = 3sin(t), y = t²

What is dy/dx in terms of t?

2t/3cos(t)

467

What is the infinite sum:

1+2/3+3/9+4/27+....?

9/4

Brainrot

67

What is 2⁶+2⁷

192

167

How many distinct, positive integer factors does 6741 have?

12

267

What is the units digit of 676767⁶⁷⁶⁷⁶⁷

3

367

Tanvi tosses a fair coin 7 times. What is the probability that at least 6 of the 7 coins show the same face?

1/8

467

The letters in the word "TTTUNGSAHUR" are rearranged. What is the probability that no two T's are adjacent to each other?

28/55

Math Club

67

What is the best club in Lake Washington High School?

Obvious

167

Who were the officers of math club this year?

Brendan, Johnny, Isabella

267

Who are the math club advisors?

Ms.Lu and Ms.Martinez (and honorarily, Mr. Tseng)

367

What is the room number of the room in which Math Club meetings are held? (If any team member goes out of the room during this question your entire team  is disqualified)

N272

467

How many tables are in the pod in front of the Math Club room? 

13