### Math 1010 (Intermediate Algebra) - Final Review

The final review for a Math 1010 course.  If you can complete this review you should be able to do well in any test.  For the solution procedure and answers click on the problem's number.  Enjoy!

1)  (1.1)  Solve for x.

2)  (3.2)  You want to make a 10 pound mixture of almonds and peanuts that is worth \$4.60 per pound.  The almonds are worth \$5 per pound and the peanuts are worth \$3 per pound.  How many pounds of almonds and peanuts should you use?

3)  (1.3)  Solve for b.

4)  (2.6)  Solve for x.

5)  (2.6)  Solve the following inequality for x.  Write your answer in interval notation.

6)  (2.1-2.3)  Graph the following relation.  Determine the domain and range.  Is it a function?

7)  (2.2)  Let f(x) = -5x + 2.  Find the following:

8)  (2.2)  Let f(x) = x^2 - 4x + 2.  Find f(-3)

9)  Determine whether the relation represents a function.

10)  (2.1-2.3)  Graph the following function.  Determine the domain and range.

11)  (1.6)  Write an equation of the line that passes through the following points.  (Write your answer in slope-intercept form.)

12)  (1.7)  Write an equation of the line that passes through the points (1,5) and is parallel to 3x-y=2.  (Write your answer in slope-intercept form.)

13)  (3.1)  Solve the following system of equations using elimination.

14)  (3.2)  A plane can fly 2000 miles with a tailwind in 4 hours.  It can make the return trip against the same wind in 5 hours.  Find the speed of the plane in still air and the speed of the wind.

15)  (3.3)  Solve the following system of equations.

16)  (3.6)  Graph the following system of linear inequalities.

18)  (4.1-4.2)  Simplify.

19)  (4.2)  Divide using synthetic division.

20)  (4.5)  Factor completely.

21)  (4.6)  Factor completely.

22)  (4.8)  Solve for x.

23)  (4.8)  A cannonball is fired from a cliff.  The height s of the cannonball (in feet) as a function of time (in seconds) can be modeled by the function:

24)  (5.1)  State the domain of the rational expression.

25)  (5.1)  Perform the indicated operation and simplify.

26)  (5.2)  Perform the indicated operation and simplify.

27)  (5.3)  Perform the indicated operation and simplify.

28)  (5.3)  Simplify.

29)  (5.4)  Solve for x.

31)  (5.6)  Robin can run twice as fast as she walks.  If she runs for 12 miles and walks for 8 miles, the total time to complete the trip is 5 hours.  Find her average speed walking and her average speed running.

32)  (5.6)  Suppose that a kitchen sink can be filled in 4 minutes with the faucet turned on.  If the sink is full it takes 12 minutes to drain the sink when the drain is left open.  If the sink's drain is left open and the faucet is turned on, how long will it take to fill the sink?

33)  (6.2)  Evaluate the following:

34)  (6.3)  Simplify.

35)  (6.4)  Simplify.  (Assume all variables are non-negative.)

36)  (6.3)  Simplify.

37)  (6.4)  Simplify.  (Assume all variables are non-negative.)

38)  (6.5)  Simplify by rationalizing the denominator.

39)  (6.5)  Simplify by rationalizing the denominator.

40)  (6.6)  Graph the following function.  Determine the domain and range.

41)  (6.7)  Solve for x.

42)  (6.7)  Solve for x.

43)  (6.8)  Divide.  Write your answer in standard form, a + bi.

44)  (6.8)  Simplify.

45)  (7.1)  Solve for x.

46)  (7.1)  Solve for x by completing the square.

47)  (7.2)  Solve for x using the quadratic formula.

48)  (7.2)  A small television measures 12 inches diagonally.  The length is 2 inches more than the height.  What are the dimensions of the television?  (Round your answer to 1 decimal place.)

49)  (7.3)  Solve for x.

50)  (7.3)  Solve for x.

51)  (7.4)  Graph the following function.  Determine the domain and range.

52)  (7.5)  Graph the following function.  Determine the vertex of the parabola.  Determine whether the function has a maximum or minimum value.  Determine the x and y intercepts.

53)  (7.6)  Solve for x.  Graph the solution set.

54)  (8.1)  Let f(x) = x^2 - x + 1 and g(x) = x + 2.  Find the following:

55)  (8.1)  Determine which of the following (from previous problems are one-to-one functions).

56)  (8.1)  Find the inverse of the following one-to-one function.

57)  (8.2)  Graph the following function.  Determine the domain and range.

58)  (8.2)  Solve for x.

59)  (8.3)  Evaluate the following:

60)  (8.3)  Graph the following function.  Determine the domain and range.

61)  (8.3)  Solve for x.

62)  (8.4)  Write the following expression as a single logarithm.

63)  (8.5)  Assume that the equation P(t) = 296(1.011)^(t-2005) models the population P of the United States (in millions of people) in the rear t.  In what year will the population of the United States reach 351 million people?  Round your answer to the nearest year.)

64)  (9.1)  Find the distance between the following points:

65)  (9.1)  Find the midpoint of the line segment between the following points:

66)  (9.2, 2.2)  Write an equation (in standard form) of the circle whose radius is 6 and center is (-2, 4).  Graph the circle.  Is it a function?

67)  (9.2)  Determine the radius and the center of the circle defined by the following equation.