Math 060/ College of the Canyons/ Fall 2009

Final Exam Information:

The final exam is a 2-hour timed exam. There will be no calculators or notes allowed.

There will be approximately 40 questions, including 5 word problems.

Review your chapter exams as well as the sample problems on the following pages.

Formulas provided on the final: 3 3 2 2( )( )a b a b a ab b 3 3 2 2( )( )a b a b a ab b

Memorize the following: (create flash cards)

Slope formula: 2 1

2 1

y ym

x x

Point-Slope form for the equation of a line: 1 1( )y y m x x

Slope-Intercept form for the equation of a line: y mx b

Where m is the slope and (0, )b represents the coordinates of the y-intercept.

All the rules for exponents. See the green box on page 426 of the Blitzer text.

2 2

2 2 2

2 2 2

( )( )

2 ( )

2 ( )

1

a b a b a b

a ab b a b

a ab b a b

a b

b a

Quadratic formula when solving quadratic equations: 2 4

2

b b acx

a

Uniform Motion: R T D or D

TR

Work: 1time together time together

individual time individual time where 1 represents one whole job completed.

Mixture: (Percent) (Quantity) = Amount

Break-even point: Revenue = Cost

Reciprocal of x: 1

x

Area of a rectangle: A LW

Pythagorean’s Formula: 2 2 2a b c

Sample Problems for the Math 060 Final Exam, Fall 2009.

Simplify

1. 2(3 7)x

2.

2

3

2

2x

x

3. x

x

x

x

23

2419

32

2 2

4. 672

12176

6

122

2

2

2

xx

xx

xx

xx

5.

xy

yx

11

1122

6. 3 240

7. 21

7 (rationalize the denominator)

8. 2 48 3 27 12

9. 2 2500 8 45 180x x x

10. 3 2

3

28 14 21 49

7

y y y

y

11. 3 4 3

2

x x

x

Factor completely. Recall: 3 3 2 2( )( )a b a b a ab b and 3 3 2 2( )( )a b a b a ab b

12. 10832 xx

13. 4411 2x

14. 205 2x

15. 6427 3x

16. 106318 2 xx

17. xxx 604 23

18. 483 4x

19. 168 24 xx

20. 307020 2 xx

Slopes and Equations of Lines

21. Given the equation 5 3 15x y :

a. Complete the ordered pairs. (3, ) and ( ,5) .

b. Write the coordinates of the x-intercept. ( , )

c. Write the coordinates of the y-intercept. ( , )

d. Find the slope.

e. Graph the equation on the grid provided.

22. Find the slope of the line that passes through ( 1, 2) and ( 3, 4) .

For #23-25, write your lines in slope-intercept form.

23. Write the equation of the line that passes through the points ( 2, 3) and (2, 5) .

24. Write the equation of the line that passes through ( 4,6) and is parallel to the line whose

slope = 9 .

25. Write the equation of the line that passes through ( 5,2) and is perpendicular to the line

943 yx .

Solve the following systems of equations. Write answers as an ordered-pair (x,y). If there are

infinitely many solutions or no solution, state so. Be familiar with the different techniques to

solve a system, such as graphing (5.1), the addition/elimination method (5.2), and the

substitution method (5.3). One question will require you to graph. The other two questions will

provide you with the option of the substitution technique or the addition/elimination technique.

26. 475

32

yx

yx

27. 75

1329

yx

yx

28. 363

242

yx

yx

29. 2 3

5 2 10

x y

x y

Solve the equations.

30. 36

5

2

33

2

3xx

31. 0714 2 xx

32. 08149 2x

33. Solve for h: 1

2A bh

34. 0323 2 xx

35. 25 18x x

36. 4

33

4

42

x

x

x

xx

37. 2

12 3 5

4 2 2r r r

38. Solve by the quadratic formula or completing the square: 0482 xx

Graphing lines, functions, and inequalities

39. Graph 2443 yx

40. Graph 5

2

3

4xy

41. Graph ( ) 2 1f x x

42. Graph the line that passes through ( 2,1) and has slope = 3

4.

43. Find the following function values, and then graph 2( ) 2 3f x x x .

a. ( 1)f

b. (1)f

c. (3)f

d. Graph.

44. Solve for x and graph the solution set. 2 3 8x .

Applications

45. At 9:45 A.M., a bus left Point Reyes, California, traveling north at 40 miles per hour.

Two hours later, a second bus left Point Reyes traveling south at 35 miles per hour. At

what time will the buses be 230 miles apart?

46. Two cars travel the same route, both leaving from the same point. The slower car

averages 40 miles per hour, and the faster car averages 50 miles per hour. If the faster car

leaves 2 hours after the slower car, in how many hours will the faster car overtake the

slower car.

47. With the current, you can row 24 miles in 3 hours. Against the same current, you can row

only 3

2 of the distance in 4 hours. Find your rowing speed in still water and the speed of

the current.

48. It took a boat 20 minutes longer to go 6 miles up a river than it did for the return trip with

the current. If the current moves at 2 mph, find the rate of the speed of the boat in still

water.

x 6 -4 0 4 -6 -2 6 2 -6

Applications continued.

49. How many liters of a 50% alcohol solution must be added with 80 liters of a 20% alcohol

solution to make a 40% alcohol solution?

50. How many milliliters of alcohol must be added to 100 ml of a 7% iodine solution to make

a 2% iodine solution?

51. A child’s piggy bank contains nickels, dimes and quarters. There are four times as many

nickels as dimes and ten fewer quarters than nickels. The total value of all the coins is

$5.30. Find the number of each type of coin.

52. The length of a rectangular garden is 5 feet greater than the width. The area of the

rectangle is 300 square feet. Find the length and the width.

53. The hypotenuse of a right triangle is 4 meters long. One leg is 1 meter longer than the

other. Find the lengths of the legs.

54. A pool can be filled by one pipe in 3 hours and by a second pipe in 6 hours. How long

will it take using both pipes to fill the pool?

55. A company that manufactures desks has fixed costs of $80,000 weekly. Each desk costs

$50 to manufacture. If the desks are sold at $250 each, write equations for the company’s

weekly costs and weekly revenue for x desks that are manufactured and sold. Then find

the weekly break-even point for the company.

56. When three times the reciprocal of a number is subtracted from twice the number, the

result is 1. Find the number(s).