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 = 1.1^x

4. Change to logarithmic form e^x = a

5. Change to exponential form t = log x

6. Expand

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

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

9. 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

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

• a) Find the value of r which will explain this data.
• b) Use this value of r to predict the population in year 2000
• c) In what year will the population reach 100,000?

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

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

12. Compute ₂₃C₇

13. Compute the square root of 40.

14. Compute e²

15. Compute ln 2