1985 AIME Problems

Problem 1

Let , and for let. Calculate the product .

Solution

Problem 2

When a right triangle is rotated about one leg, the volume of the cone produced is . When the triangle is rotation about the other leg, the volume of the cone produced is . What is the length (in cm) of the hypotenuse of the triangle?

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

---

• USA AIME 1985