MATH 0310 Review for Final Exam
Total Page：16
File Type：pdf, Size：1020Kb
MATH 0310 Review for Final Exam
1. For the graph: y a. state the coordinates of the 1a ______y- intercept x 1b______
b. state the slope 1c______c. write the equation of the
line 1d______
d. find the domain 1e______
e. find the range
2. Find the slope of the line parallel to the line passing through (3,- 1) and (4,2) . 2.______
3. State the slope of the line perpendicular to the line 2x- 5 y = 8. 3.______
2 5 2 5 8 A. - B. - C. D. E. - 5 2 5 2 5
4. For the following graph of f , y determine: 4a______a. f 1 x b. the domain of f 4b______ c. the range of f 4c______
Revised: May 2010 Page 1 0949715cc17a2251f9ff0544cbe73692.doc 5. Find a linear function whose graph has m = 3 and y -intercept (0,2) . Then graph. y
x
5______
6. A table of values is given. Write the equation of the line through the given points.6______
x y 2 8 1 3 0 2 1 7 2 12
7. Determine whether each relation is a function. Answer yes or no. 7______y y y
x x x 8. a. Graph x 3 y y 2 y b. Graph
x x
Revised: May 2010 Page 2 0949715cc17a2251f9ff0544cbe73692.doc 9. 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. 9a______
b. Use the function to estimate the life expectancy of females in 2010. 9b______
10. Find an equation of the line perpendicular to the line x 4y 3 and containing the point (-2, - 4) . Write the equation in the slope-intercept form. 10______
2 2x - 1 11. Subtract: - 11______x+1 x2 - 1 1- 2x -3 1- 2x A. B. C. x2 -1 (x- 1)( x + 1) x( x - 1)
-1 4x - 1 D. E. (x- 1)( x + 1) (x+ 1)( x - 1)
x 18 3 12. Solve: = - 12.______x+4x2 +2 x - 8 x - 2
13. 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? 13.______
A. 9 mph B. 3.6 mph C. none of these
D. 90 mph E. 9 mph
Revised: May 2010 Page 3 0949715cc17a2251f9ff0544cbe73692.doc For problems 14 – 18, find the following, given that f x 3x 6 and gx x 2 1 14. g f x 14______
15. f g2 15______
16. (f g )( x ) 16.______
17. domain of gx 17______
A. (-ゥ, ) B. (-1,1) C. (-1, ) D. {0} E. (- ,1)
g 18. domain of x 18______ f
Solve the system of equations by graphing . y
2x 3y 6 19______19.. 2 y x 2 3 x
Solve the following systems of equations. 5y 12 x 20. 20______2x 10y 5
4x 3y 1 21. 21______3x 5y 13
22. Write the systems of equations. Then solve. 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? 22. equations: ______
22. solutions: ______
Revised: May 2010 Page 4 0949715cc17a2251f9ff0544cbe73692.doc 23. 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?
23. equations: ______
23. solutions: ______
For the following exercises, solve and graph the solution set on a number line. Then write the solution set in interval notation.
24. -7�x 2 < 4 24______
25. 3x 15 or x -1 4 25______
26. 3x 15 and x -1 4 26______
27. Let f( x )= 5 - 2 x . Find:
a. f (–10) 27a______
b. f (0) 27b______
c. f (3) 27c______
d. State the domain of f 27d______
28. Let f x 3 x
a. find f 8 28a______
b. find the domain of f x 28b______
Simplify.
29. 3 27x 6 y 8 29______
A. -9x2 y 2 3 y 2 B. -3x2 y 2 C. -3x3 y 5 D. -3x2 y 2 3 y 2 E. -3x3 y 4
4x10 30 30______9
31. 18 31______
Revised: May 2010 Page 5 0949715cc17a2251f9ff0544cbe73692.doc Perform the indicated operation and simplify.
32 7x 8x 2x 50x 32______
33. a. 9 4i– 1 6i 33a______b. 9 4i 1 6i 33b______34. a. Rewrite 6 x 5 with rational exponents. 34a______1 b. Rewrite x 2 in radical notation. 34b______
35. Rationalize each denominator: x a. 35a______3
4 b. 35b______3 2
7 c. 35c______3 i
Solve #36 and 37.
36. x = 5x 11 1 36 ______
37. 3 3x 1 4 37______
38. Find the distance between the points (-5,7) and (3,1) . 38______
39. Find the midpoint of the line segment that joins the points (-5,7) and (3,1) . 39______
40. Find the equation of the circle in standard form if (-5,7) is the center and(3,1) is a point on the circle. 40______
41. For x 22 +y 62 9 , state the center and radius of the circle. 41______
Revised: May 2010 Page 6 0949715cc17a2251f9ff0544cbe73692.doc Solve 42 -- 46.
42. x 2 3x 18 0 42______
43. x 32 49 43______
44. x 2 4x 4 44______
45. 2x 2 2x 5 0 45______
1 3 A. 1 � 3i B. 2, - 1 C. i D. 1 � 11 i E. 1 � 11 2 2
46. x 4 5x 2 6 0 46______
47. Solve f( x )= 3 x2 - 5 x + 1 using a calculator. Round to three decimal places. 47______
48. The area of a rectangular football field is 90 feet. If the length exceeds the width by one foot, what is the length of the field? 48______
2 y 49. For f( x) = - x +2 x + 3 find the: 49a.______a. vertex 49b______b. axis of symmetry x
49c______c. direction the parabola opens
49d______d. y - intercept 49e______e. x - intercepts
49f.______f. minimum or maximum value
g. Graph the function.
50. Graph the solution set of the system of inequalities. y
y x 1 3x 2y 6 x
Revised: May 2010 Page 7 0949715cc17a2251f9ff0544cbe73692.doc 8b.
1. a. (0, 1) d. (-ゥ, ) 1 MATH b. m = e. (-ゥ, ) 3 0310 1 Review c. y = x 1 3 **Answer Key* 9. a. ( t ) = 0.1t + 78.8 2. m = 3 E b. 80.8 years 5 10. y 4x 4 3. B m = - 2 11 D 4. a. 1 12. x = -3 b.{x x � 4} or [-4, ) 13. B c.{y y 1} or [1, ) 14. g f x x 2 3x 7 5. f( x )= 3 x + 2 15. 5
16. 3x3- 6 x 2 + 3 x - 6 17. A (-ゥ, )
6. y=5 x + 2 18. x x 2 or (-∞, 2)U (2, ∞) 7. Yes; No; Yes
8a.
19. x, y2x 3y 6 20. No solution 21 (4, –5)
C A 175 5 22. 34a. 3.5C 7A 875 x 6 100 children's plates; 75 adults’ plates b. x
3x x y 200 35a. 23. 3 .16x .09y .118(200) 12 4 2 21 7 80 lbs of soybean meal b. c. + i Revised: 120 May lbs 2010of corn meal Page 8 7 10 10 0949715cc17a2251f9ff0544cbe73692.doc
) -5-5 65