AMATYC SML Training 10/8/2009

For more problems, please visit the AMATYC website at www.amatyc.org

For solutions to previous practice problems, see my website www.montgomerycollege.edu/~rpenn

1. If x² = x+3, then x³ =

a. x+6 b. 4x+3 c. 4x² +3 d. x² +3x + 3 e. x² + 27

2. Let f(x) = ax + b, with b<a both positive integers. If for positive integers p and q

f(p) = 18 and f(q)=39, what is the value of b?

3. A fixed point of a function f(x) is a real number r such that f(r)=r. How many of the following functions must have a fixed point?

Polynomial function of odd degree > 1 polynomial of even degree > 0

Trigonometric function y=AsinBx + D rational function y = (x-a) / (x-b)

A. 0 B. 1 C. 2 D. 3 E. 4

4. How many ordered pairs (x,y) of real numbers are solutions to the system

A. 0 B. 1 C. 2 D. 3 E. 4

5. Find the sum of the values of x for which is undefined:

A. 3 B. 4 C. 5 D. 6 E. 7

6. The sequence , , , , … is best described as which of the following?

A. geometric with common ratio log x B. geometric with common ratio x

C. arithmetic with common difference log x D. arithmetic with common difference x

E. neither geometric nor arithmetic

7. Find the number of points of intersection of the unit circle and the graph of the equation

A. 0 B. 1 C. 2 D. 3 E. 4

8. The sum of the absolute values of the solutions to can be written in the form , where c is a prime. Find a + b + c.

A. 12 B. 14 C. 16 D. 17 E. 19

9. Circle O has equation x² + y² = 16. If P is (1,0), Q is (-1,0) and R is any point on the circle O, what is the largest possible value of PR + QR

A. 8 B. C. D. 17/2 E.