Math 45

Sample 4th Midterm

Dr. Wilson

1. Let y = 3x2 + 4x - 5

Find the y-intercept, x-intercepts, the coordinates of the vertex, and sketch the graph.

Solve 3x2 + 4x - 5 > 0 for x.

2. Solve for x

3. Graph   y = 1.1x

4. Change to logarithmic form  ex = a

5. Change to exponential form  t = log x

6. Expand

7. Express as a single log:   3logb x - logb y + 4 logb z

8. Solve for  x:   3x = 4x - 1

9. Solve for  x:   log4 (x + 3) - log4 (x - 1) = 1

10. Suppose that the population of a city is 10,000 in 1970 and 50,000 in 1990. Assume further that the population is given by the formula

A = Pert

where   P   is the population in the year 1970,   t is the number of years since 1970, and   r   is a suitable constant.

11. The half life of a radioactive substance is 2.3 years. Scientists figure that it will be safe to handle it if there is only 10% of the radioactivity left. How long would one have to wait until it was deemed safe?

12. Write out Pascal's triangle to the 7th row.

13. Remove parentheses and simplify   (x + y)6.

14. Compute   23C7.

15. Compute the square root of 40.

16. Compute   e2.

17. Compute   ln 2.

18. Let   f(x) = 3x + 4,   g(x) = x2 - 3.   What is

(f + g)(x)
(f - g)(x)
(fg)(x)
(f/g)(x)
(fog)(x)
(fog)(x)

19. Let   f(x) = 3x + 4.   Find   f -1(x).   Graph both   f   and   f -1   in the same coordinate system.