ca c1 review fa12

College Algebra Chapter 1 Review

Plot the given point in a rectangular coordinate system.1) (5, 4)

2) (2, -3)

3) (-6, 0)

Graph the equation.4) y = x - 4

5) y = x2 - 5

6) y = 2|x|

1

7) y =1x

Use the graph to determine the x- and y-intercepts.8)

9)

Match the story with the correct figure.

10) Mark started out by walking up a hill for 5minutes. For the next 5 minutes he walkeddown a steep hill to an elevation lower thanhis starting point. For the next 10 minutes hewalked on level ground. For the next 10minutes he walked uphill. Determine whichgraph of elevation above sea level versus timeillustrates the story.

A)

B)

C)

2

D)

Solve and check the linear equation.11) 5x - 5 = 30

12) -3x + 5 + 6(x + 1) = -2x + 3

13) 32 - 2(11 - 8)2 = 36x

Find all values of x such that y = 0.14) y = 2[2x - (3x - 4)] - 5(x - 4)

Solve the equation.

15) x + 186

+x + 9

9= x - 3

Find all values of x such that y = 0.

16) y =x + 4

5+

x - 24

-34

First, write the value(s) that make the denominator(s) zero.Then solve the equation.

17) x - 82x

+ 4 =x + 3

x

Solve the equation.

18) 1x + 6

+3

x + 4=

-2x2 + 10x + 24

Find all values of x satisfying the given conditions.

19) y1 =2

x + 3, y2 =

5x - 3

, y3 =9

x2 - 9, and y1 -

y2 = y3

Determine whether the equation is an identity, aconditional equation, or an inconsistent equation.

20) 5x + 4x = 8x

21) 3x + 1 - 4x + 8 = 3x - 4x + 6

22) 7xx

= 7

23) 6xx - 7

=42

x - 7+ 8

24) -2x + 74

+54

= -3x2

25) 1x + 4

+2

x + 3=

-1x2 + 7x + 12

Solve the problem.26) The equation V = -2000t + 24,000 describes the

value in dollars of a certain model of car after itis t years old. If a car is worth $18,000,substitute 18,000 into the equation to find theage of the car.

Use the five-step strategy for solving word problems tofind the number or numbers described in the followingexercise.

27) 20% of what number is 58?

28) One number exceeds another by -4. The sumof the numbers is 10. What are the numbers?

Find all values of x satisfying the given conditions.29) y1 = 9x, y2 = (5x - 1), and y1 exceeds y2 by 2.

30) y1 =1

x + 6, y2 =

1x + 3

, y3 =-3

x2 + 9x + 18, and

the sum of y1 and 2 times y2 is y3.

3

Solve the problem.31) You inherit $70,000 from a very wealthy

grandparent, with the stipulation that for thefirst year, the money must be invested in twostocks paying 4% and 10% annual interest,respectively. How much should be invested ateach rate if the total interest earned for the yearis to be $4000?

32) An auto repair shop charged a customer $339to repair a car. The bill listed $99 for parts andthe remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did ittake to repair the car?

33) During a road trip, Tony drove one-third thedistance that Lana drove. Mark drives 18 moremiles than Lana drove. The total distance theydrove on the trip was 298 miles. How manymiles did each person drive?

34) Andrea is having her yard landscaped. Sheobtained an estimate from two landscapingcompanies. Company A gave an estimate of$220 for materials and equipment rental plus$65 per hour for labor. Company B gave anestimate of $300 for materials and equipmentrental plus $55 per hour for labor. Determinehow many hours of labor will be required forthe two companies to cost the same.

35) Sergio's internet provider charges itscustomers $13 per month plus 5¢ per minuteof on-line usage. Sergio received a bill fromthe provider covering a 2-month period andwas charged a total of $47.50. How manyminutes did he spend on-line during thatperiod? (Round to the nearest whole minute, ifnecessary.)

Solve the formula for the specified variable.

36) V =13

Bh for h

37) d = rt for r

38) A = P(1 + nr) for n

39) 1a

+1b

=1c

for c

40) P =A

1 + rtfor r

41) A =12

h(B + b) for B

42) P = s1 + s2 + s3 for s2

Add or subtract as indicated and write the result instandard form.

43) -7 - (- 2 - 7i) - (- 2 + 5i)

44) (-3 - 4i) + (-5 + 7i) + (3 + 7i)

Find the product and write the result in standard form.45) -6i(5i - 3)

46) 3i(-6i + 3)

47) (-3 - 7i)(2 + i)

48) (-6 + i)(-6 - i)

Perform the indicated operations and write the result instandard form.

49) (3 + i)2 - (2 - i)2

Divide and express the result in standard form.

50) 97 - i

51) 84 + i

52) 5i2 + i

53) 6 + 5i5 - 6i

54) 2 - 6i5 - 7i

4

Perform the indicated operations and write the result instandard form.

55) ( 6 - - 9)( 6 + - 9)

56) (5 + -2) (4 + -3)

57) -2 - -242

58) -64(5 - -36)

Solve the equation by factoring.59) x2 + 2x - 120 = 0

Solve the equation by the square root property.60) 8x2 + 4 = 76

Determine the constant that should be added to thebinomial so that it becomes a perfect square trinomial.Then write and factor the trinomial.

61) x2 -29

x

Solve the equation by completing the square.62) x2 + 4x = 7

63) x2 - 12x - 7 = 0

Solve the equation using the quadratic formula.64) 3x2 + x - 7 = 0

Compute the discriminant. Then determine the numberand type of solutions for the given equation.

65) x2 + 12x + 36 = 0

Solve the equation by the method of your choice.66) 7x2 - 21 = 0

67) x2 + 18x + 70 = 0

68) 1x + 13

+1x

=12

Find the x-intercept(s) of the graph of the equation.Graph the equation.

69) y = x2 - 2x + 1

Find all values of x satisfying the given conditions.70) y1 = 7 - 7x, y2 = (4x + 9)(x - 1), and y1 - y2 = 0

Solve the problem.71) A square sheet of paper measures 39

centimeters on each side. What is the length ofthe diagonal of this paper?

72) A 15-foot pole is supported by two wires thatextend from the top of the pole to points thatare each 15 feet from the base of the pole. Findthe total length of the two wires.

Solve the polynomial equation by factoring and thenusing the zero product principle.

73) 4x - 5 = 16x3 - 20x2

74) 12x3 + 84x2 + 120x = 0

Solve the radical equation, and check all proposedsolutions.

75) 26x - 39 = x + 5

76) x + 6 + 2 - x = 4

Find the x-intercepts of the graph of the equation.77) y = 2x + 3 - x + 1 - 1

78) y = x + 6 + 2 - x - 4

5

Solve and check the equation.79) (x + 7)3/2 = 27

Solve the equation by making an appropriate substitution.80) 2x - 11 x - 6 = 0

81) y -10y

2- 6 y -

10y

- 27 = 0

Match the graph with its function using the x-intercepts.82)

A) y = x4 + 5x2 + 4 B) y = x4 - 5x2 + 4C) y = x4 + 5x2 - 4 D) y = x4 - 5x2 - 4

83)

A) y = x1/2 + 5x1/4 - 6B) y = x1/2 + 2x1/4 - 1C) y = x1/2 - 5x1/4 - 6D) y = x1/2 + 2x1/4 + 1

84)

A) y = 2(x + 4)2 - 3(x + 4) - 5B) y = 2(x + 4)2 + 3(x + 4) - 5C) y = 2(x - 4)2 + 3(x - 4) - 5D) y = 2(x - 4)2 - 3(x - 4) - 5

Solve the absolute value equation or indicate that theequation has no solution.

85) 2(x + 1) + 6 = 10

Solve the problem.86) A formula for the length of a diagonal from the

upper corner of a box to the opposite lower

corner is d = L2 + W2 + H2, where L, W, andH are the length, width, and height,respectively. Find the length of the diagonal ofthe box if the length is 22 inches, width is 10inches, and height is 8 inches. Leave youranswer in simplified radical form.

87) For a cone, the formula r =3V

h describes the

relationship between the radius r of the base,the volume V, and the height h. Find thevolume if the radius is 7 inches and the cone is11 inches high. (Use 3.14 as an approximationfor , and round to the nearest tenth.)

6

Express the interval in set-builder notation and graph theinterval on a number line.

88) - , 75

89) [-2, 1]

Use graphs to find the set.90) (-10, 0) [-2, 7]

Solve the linear inequality. Other than , use intervalnotation to express the solution set and graph the solutionset on a number line.

91) 7x - 6 6x - 2

92) 15x + 15 > 3(4x + 7)

93) -6(2x + 6) < -18x - 42

94) -8x + 4 -2(3x + 1)

95) 6x + 10 2(2x + 11)

Solve the problem.96) ABC phone company charges $17 per month

plus 9¢ per minute of phone calls. XYZ phonecompany charges $13 per month plus 11¢ perminute of phone calls. How many minutes ofphone calls in a month make XYZ phonecompany the better deal?

Solve the linear inequality. Other than , use intervalnotation to express the solution set and graph the solutionset on a number line.

97) -4x -4(x - 5)

Solve the problem.98) Parts for an automobile repair cost $351. The

mechanic charges $27 per hour. If you receivean estimate for at least $486 and at most $594for fixing the car, what is the time interval, inhours, that the mechanic will be working onthe job?

Solve the absolute value inequality. Other than , useinterval notation to express the solution set and graph thesolution set on a number line.

99) |x - 9| < 0

100) |x + 2| < 7

101) |x + 2| + 6 11

102) 3(x + 1) + 6 15

103) 5 + 1 -x2

8

7

Answer KeyTestname: CA C1 REVIEW FA12

1)

2)

3)

8


4)

5)

6)

9


7)

8) x-intercept: -1; y-intercept: 59) x-intercepts: -8, 8; y-intercepts: -2, 2

10) C11) {7}

12) -85

13) -14

14) {4}

15) 12613

16) {1}17) x 0; 218)19) {-10}20) Conditional equation21) Inconsistent equation22) Identity23) Inconsistent equation24) Conditional equation25) Inconsistent equation26) 3 years27) 29028) 3 and 7

29) 14

30)31) $50,000 invested at 4%; $20,000 invested at 10%32) 6 hours33) Tony drove 40 miles, Lana drove 120 miles, and Mark drove 138 miles.34) 8 hours35) The number of minutes is 430.

36) h =3VB

10


37) r =dt

38) n =A - P

Pr

39) c =ab

a + b

40) r =A - P

Pt

41) B =2A - bh

h42) s2 = P - s1 - s343) -3 + 2i44) -5 + 10i45) 30 + 18i46) 18 + 9i47) 1 - 17i48) 3749) 5 + 10i

50) 6350

+950

i

51) 3217

-817

i

52) 1 + 2i53) i

54) 2637

-837

i

55) 1556) (20 - 6 )+ (5 3 + 4 2)i57) -1 - i 658) 48 + 40i59) {-12, 10}60) {-3, 3}

61) 181

; x2 -29

x +181

= x -19

2

62) {-2 - 5.5, -2 + 5.5}63) {6 - 43 , 6 + 43}

64) -1 - 856

, -1 + 856

65) 0; one real solution66) { - 3 , 3}67) {-9 - 11, -9 + 11}

68) -9 ± 1852

11


69) x-intercept: 1

70) -4, 171) 39 2 cm72) 30 2 ft

73) -12

, 12

, 54

74) {0, -5, -2}75) {8}76) {-2}77) 3, -178) -279) {2}80) {36}81) {- 5, - 1, 2, 10}82) B83) A84) B85) {-9, 1}86) 18 2 in.87) 564.2 cubic in.

88) x x <75

89) {x -2 x 1}

90) (-10, 7]91) [4, )

92) (2, )

12


93) (- , -1)

94) [3, )

95) (- , 6]

96) Less than 200 minutes97) ( , )

98) [5, 9]99)

100) (-9, 5)

101) [-7, 3]

102) [-8, 2]

103) (- , -4] [8, )

13

ca c1 review fa12

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