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Revised: June 2008 Page 1 Math 0310 Review for Final-v02

MATH 0310 Review for Final Exam 

1. For the graph:

a. state the coordinates of they- intercept

b. state the slope

c. write the equation of theline

d. find the domain

e. find the range

x

y

 

1a _______________________ 

1b________________________

1c________________________

1d________________________

1e________________________

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 2 5 8 x y . 3.________________ 

A.2

5B.

5

2C.

2

5D.

5

2E.

8

5 

4. For the following graph of  f  ,

determine:

a. 1 f   

b. the domain of  f   

c. the range of  f   

x

y

 

4a_________________

4b_________________

4c_________________ 

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Revised: June 2008 Page 2 Math 0310 Review for Final-v02

5. Find a linear function whose graph has 3m and y -intercept 0,2 . Then graph.

x

y

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_________________

x

y

 

x

y

 

x

y

 

8. a. Graph 3 x  

x

y

 

b. Graph 2 y  

x

y

 

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Revised: June 2008 Page 3 Math 0310 Review for Final-v02

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 34 y x and containing the point 2, 4 .

Write the equation in the slope-intercept form.10_________________ 

For problems 11  – 15, find the following, given that 63 x x f  and 12 x xg  

11.  x f g 11________________ 

12. 2g f  12________________ 

13.   f g x 13________________ 

14. domain of  xg 14________________ 

A. , B. 1,1 C. 1, D. 0 E. ,1  

15. domain of  x f 

g

15________________ 

Solve the system of equations by graphing.

16.2

3

2

632

 x y

 y x

 

x

y

 

16________________ 

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Revised: June 2008 Page 4 Math 0310 Review for Final-v02

Solve the following systems of equations.

17.5102

125

 y x

 x y17________________ 

18.1353

134

 y x

 y x18________________ 

19. 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 ofplate were sold?

19. equations: _______________

19. solutions: _______________

20. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should bemixed to get a 200-lb mixture that is 11.8% protein?

20. equations: ______________ 

20. solutions: ______________ 

For the following exercises, solve and graph the solution set on a number line. Then write thesolution set in interval notation.

21. 45 y > 9 21_________________ 

22. 7 2 x < 4 22________________ 

23. 153 x or 1 4 x 23________________ 

24. 153 x and 1 4 x 24________________ 

25. Let ( ) 5 2  f x x. Find:

a.  f  ( –10) 25a_______________ 

b.  f  (0) 25b_______________ 

c.  f  (3) 25c_______________ 

d. State the domain of  f  25d_______________ 

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Revised: June 2008 Page 5 Math 0310 Review for Final-v02

26. Let 3  x x f   

a. find 8 f  26a_______________ 

b. find the domain of  x f  26b_______________ 

Simplify.

27. 3 8627 y x 27________________ 

A. 2 2 239  x y y   B.2 2

3 x y   C.3 5

3 x y   D.2 2 233  x y y   E.

3 43 x y  

28.9

410

 x28________________ 

29. 18 29________________ 

Perform the indicated operation and simplify.

30  x x x x 50287 30________________ 

31. a. i49  –  i61 31a________________ 

b. i49 i61 31b________________ 

32. a. Rewrite 6 5 x

 with rational exponents. 32a________________ 

b. Rewrite 2

1

 x in radical notation. 32b________________ 

33. Rationalize each denominator:

a.3

 x33a________________ 

b.

23

433b________________ 

c.i3

733c________________ 

Solve.

34.  x = 1115 x 34 ________________ 

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Revised: June 2008 Page 6 Math 0310 Review for Final-v02

35. 4133  x 35________________ 

36. Find the distance between the points 5,7 and 3,1 . 36_________________ 

37. Find the midpoint of the line segment that joins the points 5,7 and 3,1 .

37.______________ 

38. Find the equation of the circle in standard form if 5,7 is the center and 3,1 is a point on

the circle. 38_______________ 

39. For2

2 x + 962

 y , state the center and radius of the circle. 39_______________ 

Solve.

40. 01832

 x x 40_______________

41. 493 2 x 41_______________

42. 442  x x 42_______________

43. 05222

 x x 43______________ 

A. 1 3i   B. 2, 1   C.1 3

2 2i   D. 1 11 i   E. 1 11  

44. 065 24  x x 44______________ 

45. Solve 2( ) 3 5 1  f x x x using a calculator. Round to three decimal places. 45______________ 

46. 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?

46_______________ 

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Revised: June 2008 Page 7 Math 0310 Review for Final-v02

47. For 2 2 3  f x x x find the:

a. vertex

b. axis of symmetry

c. direction the parabola opens

d.  y intercept

e.  x intercepts

f. minimum or maximum value

g. Graph the function.

x

y

 

47a._____________ 

47b______________ 

47c______________ 

47d______________ 

47e______________ 

47f.______________ 

48. Solve: 2 4 3 0 x x 48______________

49. Graph the linear inequality .1243 y x  

x

y

 

50. Graph the solution set of the system of inequalities.

623

1

 y x

 x y 

x

y

 

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Revised: June 2008 Page 8 Math 0310 Review for Final-v02

MATH 0310 Review**Answer Key**

1. a.(0, 1) 8b.

b. m =3

1 

c.  y = 13

1 x  

d.. ,  

e. ,  

2. 3m  9. a.  E ( t ) = 0.1 t  + 78.8

b. 80.8 years 

3. B5

2m  

10. 44 x y  

11 732  x x x f g  

4. a. 1 12. 5

b. 4 x x or 4, 13.  f g x = 332

 x  

c. 1 y y or 1, )  14. A ,  

5. ( ) 3 2  f x x  15. 2 x x or (-∞, 2)U (2, ∞) 

16. 632, y x y x  

17. No solution

18. (4, –5)

6. 5 2 y x  

7. Yes; No; Yes 

19.87575.3

175

 AC 

 AC  

100 children's plates; 75 adults’ plates 

8a.

20.)200(118.09.16.

200

 y x

 y x 

80 lbs of soybean meal120 lbs of corn meal

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Revised: June 2008 Page 9 Math 0310 Review for Final-v02

21.

( – , –1)

22.

5,6)  

23.

( , 5 5, )  

24. no solution 

34. 5 x  

35.21

 x  

36. 10

37. ( –1, 4)

25a. 5

b. 5  

c. i  

d. 25 x x or (-∞, 5/2] 

38.2

5 x + 10072

 y  

39. center = 6,2 ; 3r   

26a. 2  

b. ,  

40.  x -6, 3

41.  x 3 ± 7 i  

27. D 3 2223 y y x  

28.3

2 5 x 

29. 23 i  

42.  x -2 ± 2 2  

43. C  x   1 32 2

i  

44.  x   6 , 6 , ,i i  

30. 4 2 x x  

31a. 8 – 10 i  

b. 33 + 50 i  

45.  x   .232, 1.434  

46. 10 feet

32a. 65

 x  

b.  x  

33a.3

3 x 

b.7

2412c.

21 7

10 10i  

)-1

)6-5

5-5

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Revised: June 2008 Page 10 Math 0310 Review for Final-v02

47a. 1.4 47g.

b. 1 x  

c. downward

d. 0,3  

e. 1,0 3,0and   

f. maximum 4  

x

y

 

48.

 x (- , -3] [-1, )  

49.

x

y

 

50.

x

y

 

-1-3