Math 115 Final Exam Review

1. Solve the equation: 2x - 4(5x + 1) = 3x + 17. (Answer: x = -1).

2. Solve for g :

3. Simplify each exponential expression.

4. Let f(x) = x² - 2x + 3:Find:

5. Find the domain of the function.

6. Find the slope of the line through the points A(-2,3) and B(7,-3).

7. Write the equation of a line, in standard form, passing through the
point A(4,-7) and parallel to the line whose equation is 3x+y-9 = 0: (Ans.
3x + y = 5).

8. Solve the system of equations.
3x + 2y = -8
2x + 5y = 2 (Ans. (-4,2))

9. When a plane flies with the wind, it can travel 2160 miles in 3 hours.
When the plane flies in the opposite direction, against the wind, it takes 4
hours to y the same distance. Find the speed of the plane in still air and
the speed of the wind. (Ans. 630 mph and 90 mph)

10. The perimeter of a rectangular table tennis top is 28 feet. The
difference between 4 times the length and 3 times the width is 21 feet. Find
the dimensions. (Ans. 9 ft by 5 ft).

11. Solve the system of equations.
x + 2y - z = 5
2x - y + 3z = 0
2y + z = 1.
(Ans. (2,1,-1))

12. Solve the inequality and graph the solution set on the number line.
3(2x - 1) - 2(x - 4) ≥ 7 + 2(3 + 4x).
(Ans. (-∞,-2])

13. Solve for x : 2l x - 3l - 7 = 10. (Ans. x = -5.5 and 11.5)

14. Solve for x : l2x + 5l - 7 < -6. (Ans. -3 < x < -2)

15. Graph the inequality 3x - 4y > 12

16. Find the maximum value of z = 2x + 3y under the constraints:
x ≥ 0, y ≥ 0
x + y ≤ 8
3x + 2y ≥ 6.
(Ans. Maximum z = 24)

17. Multiply and simplify [(x+3)+5y][(x+3)-5y]. (Ans. x²+6x+9-25y²)

18. Factor completely.

19. Multiply and simplify:

20. Subtract and simplify:

21. Simplify the complex fraction :

22. Divide using Synthetic Division: (3x⁴ - 2x² - 10x - 20) (x - 2)
(Ans. 3x³ + 6x² + 10x + 10)

23. Solve the rational equation and check your answer:

24. Add: (7 + 2i) + (5 - 10i). (Ans. 12 - 8i)

25. Multiply: (7 + 8i)(7 - 8i). (Ans. 113)

26. Divide:

27. Multiply and simplify:

28. Rationalize the denominator:

29. Evaluate:

30. Perform the indicated operations and simplify:

31. Solve the equation and check your answer.

32. Solve by using the square root property: (x - 3)² = 20. (Ans.

33. Solve by completing the square: x² - 6x + 7 = 0.

34. Solve by the quadratic formula: x²-2x+19 = 0

35. Graph:

36. Solve the equation: x⁴ - 6x² + 8 = 0:

37. Solve each inequality and graph the solution set on the number line.

38. Graph

39. Simplify:

40. Solve the equation:

41. Find the distance between the two points A(-2,-6) and B(3,-4):
(Ans. )

42. Find the midpoint of the line segment with endpoints A(-2,-1) and
B(-8, 6). (Ans. )

43. Give the center, radius, and graph of the circle (x+1)²+(y-4)² = 25:
(Ans. Center (-1, 4) and R = 5)

44. Complete the square and give center and radius of the circle: x² +
y² + 8x - 2y - 8 = 0
(Ans. Center (-4, 1), R = 5)

45. Graph:

46. Graph :

47. (4 each) Evaluate: