# MATH 105 Sample Mastery Exam

1. Factor 4x2 - 9y2.
2. Expand (3x + 2)2.
3. Simplify (2x/y2)3.
4. Simplify (2x2 - x - 3)/(x2 - 1).
5. Solve the system
 2x + 3y = -5 x + y = -1
6. Solve 2x + 1/3 = x/2 - 1.
7. Solve |x - 1| ≤ 10
8. Simplify .
9. Find the equation of the graph given below. 10. Find the equation of the line parallel to 2x - y = 2 that passes through (1,4).
11. Find the zeros of f where f(x) = (x2 - 4)(2x + 8).
12. Use the graph of g(x) = x3 + x2 - 2x shown below to find the solution set of x3 + x2 > 2x. 13. Find the distance between (2,3) and (1,-6).
14. Solve 2/x + 3/x = 5/3.
15. Find the x-intercepts of the parabola y = x2 - 6x - 7.
16. Sketch the graph of x2 + y2 - 4x + 2y - 4 = 0.
17. Solve 2x2 + 6x - 3 = 0.
18. Find the domain of f(x) = (x + 4)/(2x - 6).
19. Given that f(x) = 2/x and g(s) = 3s - 5, compute f(g(t)).
20. Find the inverse f -1(x) where f(x) = x3 + 1.
21. Solve 32x + 1 = 1/3.
22. Which of the following statements are true
1. Every natural number is an integer.
2. Some integers are irrational numbers.
3. Some complex numbers are real.
23. Use the graph of y = x3 - 7x2 + 17x - 14 shown below to find the solution of x3 - 7x2 = 14 - 17x. 24. The graph of a function f(x) is shown below. Sketch the graph of h(x) = f(x + 1) - 4. 25. Sketch the graph of 26. The function C(x) = 10x2 + 40x + 90 gives the cost (in dollars) of producing x units of product. Find the cost for producing 4 units.
27. Find the vertical asymptotes of f(x) = 1/(x2 - 2x - 3).
28. Sketch the graph of f(x) = ex + 2.
29. Evaluate log2 16.
30. Express 5 log x - 6 log y + 3 log z as a single logarithm.
31. The fastest growing city in the United States between the years 1980 and 1990 was Moreno Valley, California. The population was approximately 30,000 in 1980 and 120,000 in 1990. Assuming exponential growth (i.e. the population P as a function of the time t in years is P = P0ekt), what will the population be in the year 1998?
32. Graph the system of inequalities y ≤ 1, xy/2.
33. A budding numismatist (coin collector) has a total of 15 silver dollars and quarters; the total face value of the silver dollars and the quarters is \$9.75. How many of each does he have?