Round 3

Geometry

100

 Find the area of a triangle with vertices at (0,0), (4,1), and (2,5).

9

200

 What is the equation of the line tangent to the circle x² + y² = 25 at the point (3, -4)?

3x - 4y = 25

300

A point P(3,8) is reflected across the line y = x. What are the new coordinates? 

(8,3)

Algebra

100

 Evaluate 2025² - 2024².

4049

200

Find the sum of the roots for the equation 3x² + 15x - 99 = 0.

-5

300

If x + 1/x = 3, find x³ + 1/x³.

18

Chemistry

100

How many angular nodes does a 3d orbital have? 

 

2

200

 You have 200 mL of 6M of HCl. How much water must you add to make it a 2M solution? 

400mL

300

How many moles of O₂ are needed to completely burn 1 mole of Butane (C₄H₁₀)?

6.5 or 13/2

World Geography

100

To travel through the Panama Canal from the Atlantic Ocean to the Pacific Ocean, in which compass direction do you primarily sail?

Southeast

200

What is the easternmost state in the United States?  

Alaska

300

 If you are standing at the Pacific entrance of the Panama Canal, which ocean is further east?

The Atlantic Ocean

English

100

How many different meanings can you create by moving the word "only" in the sentence: "She told him that she loved him"?

7

200

 Is it "Between you and I" or "Between you and me"?

Between you and me.

300

"I am going to lie down" or "I am going to lay down"?

"I am going to lie down"