AMC12 Algebra 2

Question 1

If a+b=5 and ab=4, find a^3+b^3.

Accepted Answer

65

Answer

25

Answer

45

Answer

80

Question 2

The polynomial x^3-6x^2+11x-6 has roots r, s, t. Find r+s+t.

Accepted Answer

6

Answer

11

Answer

3

Answer

-6

Question 3

Solve 3^(2x) - 4*3^x + 3 = 0. What are the solutions?

Accepted Answer

x=0 or x=1

Answer

x=1 or x=2

Answer

x=-1 or x=0

Answer

x=0 or x=3

Question 4

If x + 1/x = 5, what is x^2 + 1/x^2?

Accepted Answer

23

Answer

25

Answer

27

Answer

21

Question 5

A function satisfies f(2x)=2f(x) and f(1)=3. Find f(8).

Accepted Answer

24

Answer

6

Answer

12

Answer

48

Question 6

For how many integers n is (n-1)/(n+1) also an integer?

Accepted Answer

4

Answer

2

Answer

1

Answer

3