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MATH-C Final Exam -- Study Guide

1. Subtract 4z from the product of 5 and (3−z)

2. Simplify

3. Multiply using FOIL:

4. Factor: a.

5. Solve: 90x³ + 60x² − 80x = 0

6. Solve A = a + (n − 1)d for n

7. Fred returns from a trip to Las Vegas with $427, which is 30% less money than he had at the beginning of the trip. How much money did he start with?

8. The longest side of a right triangle is 3 inches less than twice the shortest side. The third side measures 12 inches. Find the length of the shortest side.

9. Solve

10. Solve | 2(2x + 3) | − 5 = −1

11. Solve

12. Solve (2x − 1) (x + 3) = −6

13. Write the equation of the graph:

14. Find the slope and the y-intercept; write the equation:

15. Graph a. y = 3/5 x + 1

b. 3x − 2y = 12

c. 2x − 3y > −6

16. Determine the domain and range from the graph;

Does this represent a function? (Why?)

Is it one-to-one? (How do you know?)

17. Let f(x) = 4x −1 and g(x) = x² − 3x + 2

a. Find g(−4)

b. Write a formula for (f−g)(x)

18. The volume of a gas varies directly with the temperature (in degrees Kelvin). If a volume of 32 cubic meters corresponds to a temperature of 300^o K, what temperature is required to reduce the volume to 24 cubic meters? [Physics note: this problem assumes that the pressure is held constant]

19. The volume of a gas is inversely proportional to the pressure. If 18 cubic inches of gas is trapped inside a cylinder at a pressure of 15 pounds per square inch, what pressure must be applied to reduce the volume to 4 cubic inches? [Physics note: this problem assumes that the temperature is held constant]

20. Solve the systems of equations:

21. Solve the determinant equation

22. Write the determinant equation in slope-intercept form:

23. Calculate the determinant:

24. Solve for y using Cramer's rule:

25. How many liters of a 25% alcohol solution and how many liters of a 50% alcohol solution must be mixed to get 40 liters of a 30% alcohol solution?

26. A collection of nickels, dimes and quarters has a value of $9.60. If there are two more nickels than quarters, and one more dime than nickels, how many of each type of coin are in the collection?

27.

Graph the solution set:

28.

Write a system of inequalities

to describe the shaded region

29. State the domains:

30. Divide

31. Solve

32. A boat moves at 18 mph in still water. It travels 28 miles downstream in the same time it takes to travel 20 miles upstream. Find the speed of the current

33. A ski lift is 1320 feet long. If a ride on this lift takes 6 minutes, find the speed in miles per hour.

34. The current of a river is 3 mph. It takes a motorboat a total of 10 hours to travel 72 miles upstream and return [72 miles] downstream. What is the speed of the boat in still water?

35. Write with an appropriate radical symbol; then simplify:

36. Use properties of exponents to simplify:

37. Solve:

38. Combine the complex numbers: (3 + 2i) − (5 − 7i)

39. Simplify [divide]

40. Solve by the square root principle:

b. 2x² − 98 = 0

41. Solve by completing the square: x² − 8x + 13 = 0

42. Solve 2x − 3 = 3x² Suggestion: use the quadratic formula.

43. Solve

44. Give the x- and y-intercepts and the coordinates of the vertex; then graph:

y = −x² + 4x + 5

45. Solve, and graph the solution set: x² − 4x − 12 ≥ 0

46. Suppose you deposit $1500 in a savings account with an annual interest rate of 4.8.% compounded quarterly:

a. Write an equation that gives the amount of money in the account after t years.

b. Find the amount of money in the account after 7 years.

47. You are conducting an experiment with a radioactive substance. You start with 18.2 grams of the substance. The amount of the substance remaining after t minutes is described by the function A(t) = A_oe^−0.03t, where A_o is the initial amount and A(t) is the amount when time = t. How much of the substance remains after 20 minutes?