AMC12 Algebra 3

Question 1

If log(xy)=5 and log(x/y)=1, what is log x?

Accepted Answer

3

Answer

2

Answer

1

Answer

4

Question 2

How many real solutions does x^4 - 5x^2 + 4 = 0 have?

Accepted Answer

4

Answer

2

Answer

0

Answer

3

Question 3

If a and b are roots of 2x^2-3x+1=0, what is a/b + b/a?

Accepted Answer

5/2

Answer

3/2

Answer

1/2

Answer

7/2

Question 4

What is the range of f(x) = 3/(x^2+1)?

Accepted Answer

(0,3]

Answer

[1,3]

Answer

[0,3]

Answer

(0,3)

Question 5

If 2^(x+1) = 3^x, what is x?

Accepted Answer

log(2)/log(3/2)

Answer

log(3)/log(2)

Answer

log(2/3)

Answer

log(3/2)

Question 6

How many ordered pairs (x,y) of integers satisfy x^2+y^2=25?

Accepted Answer

12

Answer

8

Answer

4

Answer

16