MATH 1453 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #1 - SPRING 2007 - DR. DAVID BRIDGE

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

Mark the statement as true or false.

1) Every rational number is an integer.

2) Some rational numbers are irrational.

3) Some rational numbers are integers.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Add or subtract as indicated.

4) (2n5 - 5n2 - 18) - (13n2 + 7n5 + 8)

A) -5n5 - 18n2 - 10 B) -5n5 + 2n2 - 10 C) -5n5 - 18n2 - 26 D) -49n7

5) (8n5 - 5n4 + 2n) + (6n5 - 2n4 - 4n)

A) 14n - 7n5 - 2n4 B) 14n5 - 7n4 - 2n C) 8n5 + 6n4 - 9n D) 5n10

6) (4n7 + 12n6 - 8n) - (9n7 + 8n6 - 13n)

A) -5n7 + 21n6 - 21n B) 4n14 C) -5n7 + 4n6 - 21n D) -5n7 + 4n6 + 5n

Find the product.

7) (x - 2)(-4x - 1)

A) -4x2 + 2x + 7 B) -4x2 + 7x + 2 C) -4x2 + 7x + 7 D) -4x2 + 5x + 2

8) (-4x + 2)(-3x - 7)

A) 12x2 + 22x + 22 B) -7x2 + 22x + 22 C) 12x2 + 22x - 14 D) -7x2 + 22x - 14

9) (7y - 4)(49y2 + 28y + 16)

A) 343y3 + 64 B) 343y3 + 112y2 - 64

C) 343y3 - 64 D) 49y3 + 64

10) -4x(12x2 + 11x + 6)

A) -48x3 - 68x2 B) -48x3 - 44x2 - 24x

C) -48x3 + 11x2 - 24x D) -48x3 - 44x2 + 6x

Solve the problem.

11) The polynomial 0.0041x4 + 0.0051x3 + 0.0055x2 + 0.13x + 1.95 gives the predicted sales volume of a company,

in millions of items, where x is the number of years from now. Determine the predicted sales 19 years from now.

A) 504.31 million B) 750.86 million C) 548.32 million D) 575.7 million

12) Total profit is defined as total revenue minus total cost. R(x) and C(x) are the revenue and cost from the sale of x

televisions. If R(x) = 280x - 0.7x2 and C(x) = 4000 + 0.7x2 , find the profit from the sale of 100 televisions.

A) $24,000 B) $10,000 C) $18,000 D) $32,000

Factor out the greatest common factor.

13) 14m9 + 18m5 + 8m3

A) m3(14m6 + 18m2 + 8) B) No common factor

C) 2m3(7m6 + 9m2 + 4) D) 2(7m9 + 9m5 + 4m3)

14) 25m2 - 18r3

A) m2(25 - 18m) B) 2(12m2 + 9r3)

C) No common factor D) 3(8m2 - 6r3)

Factor completely.

15) x2 - x - 20

A) (x + 1)(x - 20) B) (x + 5)(x - 4) C) Prime D) (x + 4)(x - 5)

16) x2 + 6x - 72

A) (x - 12)(x + 6) B) Cannot be factored

C) (x - 12)(x + 1) D) (x + 12)(x - 6)

17) x2 - x - 35

A) (x + 5)(x - 7) B) (x - 5)(x + 7)

C) Cannot be factored D) (x - 35)(x + 1)

18) 3x2 - 3x - 18

A) 3(x - 2)(x + 3) B) 3(x + 2)(x - 3)

C) (3x + 6)(x - 3) D) Cannot be factored

19) x2 + 20x + 100

A) (x + 10)(x - 10) B) Prime C) (x - 10)2 D) (x + 10)2

Use factoring to solve the equation.

20) (x + 8)(x - 16) = 0

A) 8, -16 B) -16, 8 C) 16, 8 D) -8, 16

21) x2 - 4x + 4 = 49

A) 7, -7 B) -5, -9 C) 51 D) 9, -5

22) r2 + 8r + 16 = 14

A) -4 + 14, -4 - 14 B) 10

C) 4 + 14, 4 - 14 D) 14, 14

23) x2 + 4x - 45 = 0

A) -9, 1 B) 9, -5 C) -9, 5 D) 9, 5

Solve by the square-root property.

24) (x - 4)2 = 49

A) 53 B) -3, -11 C) 7, -7 D) 11, -3

25) (x + 2)2 = 44

A) -2 + 2 11, -2 - 2 11 B) -2 + 2 22, -2 - 2 22

C) 2 11 - 2, 2 11 + 2 D) 2 11, -2 11

26) (x + 16)2 - 2 = 0

A) 16 ± 2 B) -14, 18 C) -16 ± 2 D) -4 ± 2

Use the quadratic formula to solve the equation. Give both exact and approximate answers.

27) 4m2 + 8m + 1 = 0

A)-2 ± 3

2; -0.134, -1.866 B)

-2 ± 5

2; 0.118, -2.118

C)-2 ± 3

8; -0.033, -0.467 D)

-8 ± 3

2; -3.134, -4.866

28) 7n2 = -12n - 2

A)-6 ± 22

7; -0.187, -1.527 B)

-12 ± 22

7; -1.044, -2.384

C)-6 ± 22

14; -0.094, -0.764 D)

-6 ± 2

7; -0.655, -1.059

29) x2 - x = -30

A) -5, -6 B) 1, 30

C) 5, 6 D) No real number solutions

Use the discriminant to determine the number of real solutions of the equation.

30) s2 - 3s + 2 = 0

A) No real solutions B) 2 C) 1

31) t2 + 12t + 36 = 0

A) 2 B) 1 C) No real solutions

32) v2 + 5v + 3 = 0

A) 1 B) No real solutions C) 2

33) 5 + 3z2 = -5z

A) No real solutions B) 2 C) 1

Solve the problem.

34) A rectangular garden has dimensions of 22 feet by 15 feet. A gravel path of equal width is to be built around the

garden. How wide can the path be if there is enough gravel for 258 square feet?

A) 4 ft B) 5.5 ft C) 3 ft D) 5 ft

Graph the linear equation.

35) -6y = x - 4

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

36) -x = 6y - 4

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

37) 2y - 8x = 2

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

38) 4x + y = 0

A)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

B)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

C)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

D)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

Give the x-intercepts and y-intercepts of the graph.

39)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: 3; y-intercept: -5 B) x-intercept: -5; y-intercept: 3

C) x-intercept: 5; y-intercept: -3 D) x-intercept: -3; y-intercept: 5

40)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) x-intercept: -5; y-intercept: -3 B) x-intercept: 5; y-intercept: 3

C) x-intercept: -3; y-intercept: -5 D) x-intercept: 3; y-intercept: 5

Find the x-intercepts and y-intercepts of the graph of the equation.

41) 2x + y = 10

A) x-intercept: 9; y-intercept: -8 B) x-intercept: -8; y-intercept: 9

C) x-intercept: 5; y-intercept: 10 D) x-intercept: 10; y-intercept: 5

42) -2x + y = 8

A) x-intercept: 6; y-intercept: -1 B) x-intercept: 8; y-intercept: -4

C) x-intercept: -1; y-intercept: 6 D) x-intercept: -4; y-intercept: 8

43) -2x - 5y = 10

A) x-intercept: 4; y-intercept: -3 B) x-intercept: 5; y-intercept: 2

C) x-intercept: -5; y-intercept: -2 D) x-intercept: -3; y-intercept: 4

Solve the problem.

44)

x1990 1991 1992 1993 1994 1995 1996 1997

y700

600

500

400

300

200

100

-100x1990 1991 1992 1993 1994 1995 1996 1997

y700

600

500

400

300

200

100

-100

Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a

function of time. What is the approximate number of cars sold in 1993?

A) 250 B) 600 C) 500 D) 650

45) Big "D" Sales

1989-1990

Month

Which month in 1989 had the lowest sales?

A) Month 8 B) Month 6 C) Month 3 D) Month 2

46) Big "D" Sales

1989-1990

Month

What was the increase in sales between month 5 and month 6 of 1990?

A) $4000 B) $800 C) $8000 D) $4

Find the slope of the line, if it is defined.

47) Through (8, -6) and (2, 6)

A) 6 B) 12 C) 2 D) -2

48) Through (-9, -8) and (-4, -1)

A) 15

2B) Undefined C) -9 D) 1

2

5

49) Through (-8, -7) and (-8, 8)

A) Undefined B) 15 C) 5 D) 3

50) Through (-2, 4) and (-6, 4)

A) 0 B) 3 C) 7 D) 1

51) Through the origin and (4, 7)

A) 13

4B) 7 C) Undefined D) 1

4

3

Write an equation in slope-intercept form of a line satisfying the given conditions.

52) m = - 7

2; b =

39

2

A) y = - 7

2x -

39

2B) y = -

7

2x +

39

2C) y =

7

2x -

39

2D) y =

7

2x +

39

2

53) m = 2

3; b = 2

A) y = - 2

3x + 2 B) y =

2

3x - 2 C) y =

2

3x + 2 D) y = -

2

3x - 2

Find the slope and the y-intercept of the line.

54) 3x + 5y = 16

A) m = 3

5; b = 16 B) m = -

3

5; b =

16

5C) m = -

5

3; b = 5 D) m =

5

3; b =

16

5

55) -3y = -2x - 16

A) m = - 2

3; b = -16 B) m = -

3

2; b = -3 C) m =

2

3; b =

16

3D) m =

3

2; b =

16

3

Identify whether the slope is positive, negative, zero, or undefined.

56)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) Positive B) Undefined C) Zero D) Negative

57)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) Negative B) Positive C) Undefined D) Zero

58)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) Positive B) Undefined C) Zero D) Negative

59)

x-10 -5 5 10

y

10

5

-5

-10

x-10 -5 5 10

y

10

5

-5

-10

A) Positive B) Zero C) Negative D) Undefined

Find an equation of the the line satisfying the given conditions.

60) Through (5, 4); m = - 2

3

A) 2x + 3y = -22 B) 2x - 3y = 22 C) 2x + 3y = 22 D) 3x + 2y = -22

61) Through (0, 3); m = 4

3

A) 3x - 4y = -9 B) 4x + 3y = -9 C) 4x - 3y = 9 D) 4x - 3y = -9

62) Through (5, 9); m = 0

A) y = 9 B) x = 5 C) 9x + 5y = 0 D) 5x + 9y = 0

Write an equation in standard form for a line passing through the pair of points.

63) (2, -2) and (-4, -7)

A) 4x + 3y = -5 B) -4x - 3y = -5 C) 5x + 6y = -22 D) -5x + 6y = -22

64) (-3, -9) and (6, -9)

A) 6x - 3y = 0 B) y = -9 C) -3x + 6y = 0 D) x = -3

Find an equation of the the line satisfying the given conditions.

65) Through (3, 7); perpendicular to 6x + 9y = 81

A) 3x - 2y = 1 B) 3x - 2y = -5 C) 3x + 2y = -5 D) 2x - 3y = -5

66) Through (-3, -14); parallel to -5x + 4y = -5

A) 4x - 5y = -14 B) -3x + 4y = -5 C) -5x + 4y = -41 D) -5x - 4y = -41

Solve the problem.

67) Let C(x) = 700 + 90x be the cost to manufacture x items. Find the average cost per item to produce 30 items.

A) $113 B) $2370 C) $243 D) $263

Convert the temperature. You may use the fact that 32°F = 0°C, and 212°F = 100°C.

68) 87°F = °C

A) 124.6°C B) 16.3°C C) 188.6°C D) 30.6°C

69) 6°C = °F

A) 32.5°F B) 68.4°F C) 42.8°F D) 35.3°F

Solve the problem.

70) Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 150x + 1000, where S(x)

represents the number of sales in year x, with x = 0 corresponding to 1982. Find the number of sales in 1989.

A) 1900 B) 3950 C) 4100 D) 2050

71) Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were

$3500 in 1982 and $72,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).

A) S(x) = 13,700x + 72,000 B) S(x) = 13,700x + 3500

C) S(x) = 68,500x + 72,000 D) S(x) = 68,500x + 3500

Solve and graph the inequality and graph the solution.

72) x - 4 < -7

A) [-3, ∞)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

B) (-∞, -3]

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

C) (-∞, -3)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

D) (-3, ∞)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

73) -4x - 12 ≥ -5x - 9

A) (-∞, -4)

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

B) (-∞, 3]

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

C) [3, ∞)

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

D) (-4, ∞)

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

Solve the problem.

74) The equation y = 0.002x - 0.40 can be used to determine the approximate profit, y in dollars, of producing x

items. How many items must be produced so the profit will be at least $3728?

A) x ≥ 1,864,200 B) x ≥ 1,863,800 C) x ≥ 1,957,410.00 D) 0 < x ≤ 1,864,199

75) The equation y = 0.002x - 0.30 can be used to determine the approximate cost, y in dollars, of producing x items.

How many items must be produced so the cost will be no more than $488?

A) 0 < x ≤ 244,151 B) 0 < x ≤ 256,357.50

C) 0 < x ≤ 244,150 D) 0 < x ≤ 243,850

Answer Key

Testname: MATH 1453 - PRACTICE EXAM #1

1) FALSE

2) FALSE

3) TRUE

4) C

5) B

6) D

7) B

8) C

9) C

10) B

11) D

12) B

13) C

14) C

15) D

16) D

17) C

18) B

19) D

20) D

21) D

22) A

23) C

24) D

25) A

26) C

27) A

28) A

29) D

30) B

31) B

32) C

33) A

34) C

35) B

36) C

37) C

38) C

39) C

40) C

41) C

42) D

43) C

44) D

45) C

46) A

47) D

48) D

49) A

50) A

51) A

52) B

53) C

54) B

55) C

56) A

57) A

58) C

59) D

60) C

61) D

62) A

63) D

64) B

65) B

66) C

67) A

68) D

69) C

70) D

71) B

72) C

73) C

74) A

75) C