MATH 0310 Review for Final Exam
1. For the graph:a. state the coordinates of
the y- intercept
b. state the slope
c. write the equation of the line
d. find the domain
e. find the range / /
1a ______
1b______
1c______
1d______
1e______
2. Find the slope of the line parallel to the line passing through and .
2______
3. State the slope of the line perpendicular to the line. 3______
A. B. C. D. E.
4. For the following graph of ,determine:
a.
b. the domain of
c. the range of / / 4a______
4b______
4c______
5. Find the domain for
6. Find a linear function whose graph has and-intercept. Then graph. 6______
7. A table of values is given. Write the equation of the line through the given points.7______
8. Find the equation of the line. Write equation of the line in slope- intercept form.
a. With slope equal to zero through (-3, 5) 8a______
b. With undefined slope through (-2, -5) 8b______
c. Horizontal through (-8, 2) 8c______d. Vertical through (9, 5) 8d______
e. Parallel to y = -4x +3 through (2, -3) 8e______
9. Determine whether each relation is a function. Answer yes or no. 9______
10. a. Graph / / b. Graph /11. In 1990, the life expectancy of females was 78.8 yr. In 2000, it was 79.8 yr.
Let E (t) represent the life expectancy of females and t the number of years since 1990.
a. Find a linear function that fits the data. 11a______
b. Use the function to estimate the life expectancy of females in 2010. 11b______
12. Find an equation of the line perpendicular to the line and containing the point.
Write the equation in the slope-intercept form.
12______
13. Factor completely:
a. 13a______
b. 13b______
c. 13c______
14. Simplify: a. 14a______
b. 14b______
15. Solve: 15______
16. A biker can travel 18 mph with no wind. The same rider can
bicycle 8 miles against the wind in the same time it takes to bicycle
12 miles with the wind. What is the speed of the wind? 16______
A. 9 mph B. 3.6 mph C. none of these D. 90 mph E. 9 mph
For problems 17 – 21, find the following, given that and
17. 17______
18 18______
19. 19______
20. domain of 20______
A. B. C. D. E.
21. domain of 21______
Solve the system of equations by graphing.
22./ / 22______
Solve the following systems of equations algebraically using the indicated methods.
23. (Substitution Method) 23______
24. (Elimination Method) 24______
Write the systems of equations. Then solve.
25. Retail orders. The St. Andrew’s Community Barbecue served 175 dinners. A child’s plate
Cost $3.50 and an adult plate cost $7.00. A total of $875 was collected. How many of each
type of plate were sold?
25 equations: ______25 solutions: ______
______
26. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be
mixed to get a 200-lb mixture that is 11.8% protein?
26 equations: ______26 solutions: ______
______
For problems 27 – 30, solve and graph the solution set on a number line. Then write the solution set in interval notation.
27. < 27______
28. or 28______
29. and 29______
30. -3 < 2x + 5 < 7 30______
31. Let. Find:
a. 31a______
b. 31b______
c. 31c______
d. State the domain of 31d______
32. Let
a. find 32a______
b. find the domain of 32b______
Simplify.
33. 33______
A. B. C. D. E.
34 34______
35. 35______
36. 36______
For problems 37 – 40, perform the indicated operations and simplify.
37. 37______
38. a. – 38a______
b. 38b______
39. a. Rewrite with rational exponents. 39a______
b. Rewrite in radical notation. 39b______
40. Rationalize each denominator:
a. 40a______
b. 40b______
c. 40c______
Solve #41 and #42.
41. = 41 ______
42. 42______
43. Find the distance between the points and. 43______
44. Find the midpoint of the line segment that joins the points
and. 44______
45. Find the equation of the circle in standard form if is the center and is a point on the circle. 45______
46. For +, state the center and radius of the circle. 46______
Solve #47 – #50.
47. 47______
48. 48______
49. 49______
50. 50______
A. B. C. D. E.
51. The function gives the distance in feet that a car going approximately 68 miles per hour will skid in seconds. Find the time it would take for the car to skid 180 feet. Round the answer to the nearest tenth. 51______
52 A ball is thrown upwards according to the following equation f (t) =. When will it
reach a height of 64 feet? 52______
53. Solve using a calculator. Round answer to three decimal places. 53______
54. Normally, it takes Professor Thompson 3 hours to grade a class of final exam essays. If his graduate assistant grades the essays, it takes her 5 hours. How long will it take them to grade the essays together? 54______
55. For find the:a. vertex
b. axis of symmetry
c. direction the parabola opens
d. intercept
e. intercepts
f. minimum or maximum value
g. Graph the function. / / 55a______
55b______
55c______
55d______
55e______
55f______
56. Graph the solution set of the system of inequalities.
/
57. Use a graphing calculator to solve. Use the window [- 4, 6, - 2, 6]. Round the answer to three
decimal places.
57______
58. Solve: 58.______
MATH 0310 Review *Answer Key*
1. a. (0, 1) d.b. = e.
c. =
2.
3. B / 10.b
4. a. 1 b. or
c. or
5. or / 11. a. () = 0.1 + 78.8
b. 80.8 years
12. y = 4x + 4
6.
/ 13 a.
b. 2(2x – 3)(2x + 3)
c. (3x – 4)(2x + 5)
14. a. b.
15. x = - 3
16. B
17.
7.
8. a. y = 5 b. x = -2
c. y = 2 d. x = 9
e. y= -4x + 5
9. Yes; No; Yes / 18. 5
19.
20. A.
10a.
/ 21. or
22.
23. No solution
24. (4, –5)
25.
100 children's plates; 75 adults’ plates
26.
80 lbs of soybean meal and 120 lbs of corn meal / 45. +
46. center = ;
27.
/ 47. - 6, 3
48. 3 ± 7
49. -2 ± 2
28. / 50. C
51. 9.2 seconds
52. t = 1 sec or t = 4 sec
29. no solution
30. (-4, 1)
/ 53. x = .232 or x = 1.434
54. hours
55. a. b.
31. a. 5 b.
c. d. or / c. downward d.
e.
f. maximum
32. a. b.
33. D
34.
35. 36.
37.
38. a. 8 – 10 b. 33 + 50 / g.
39. a. b.
40. a. b.
c.
41.
42.
43. 10
44. (–1, 4) / 56.
57. (1.530, 2.583)
58. [-1, 4]
Revised: March 2012 Page 10 Math 0310 Review for Final-MG-v04rev3.doc