short answer. the word or phrase that best completes each ...€¦ · pound. if he buys s pounds of...

Exam Rev. 2018

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the equation.1) x - 944.623 = -983.556 1)

2) -77.935 = 258.173 + x 2)

Solve the problem.

3) The temperature, t, in degrees Fahrenheit, of water being heated is 67 + 13m where m is

the number of minutes since heating began. How long will it take for the temperature ofthe water to reach 70 degrees Fahrenheit?

3)

4) Mark has $75 to spend on salmon at $5.00 per pound and/or chicken at $3.00 perpound. If he buys s pounds of salmon and c pounds of chicken, the equation 5s + 3c = 75must be satisfied. How much salmon did Mark buy if he bought 20 pounds of chicken?

4)

Solve the formula for the specified variable.

5) V = 13Bh for h 5)

Use the appropriate formula to solve the problem.6) The length of a rectangular billboard is 7 inches more than the width. The perimeter ofthe billboard is 26 inches. Find the width of the billboard.

6)

7) The perimeter of a rectangle is 30 cm. One side is 7 cm longer than the other side. Findthe lengths of the sides.

7)

Use a graphing calculator to estimate the solution of the equation to two decimal places.8) 2.5 1.9x + 7.9 - 9.25 1.7x - 3.27 = 0 8)

Graph the linear equation.9) 9y = x - 6

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

9)

1

Find the domain and range.10) y = 2 + x 10)

Solve the problem.11) The graph shows the relationship between the area A of a rectangle and the length L, if

the width is fixed. Find the area if the length is 11 cm.

L-2 2 4 6 8 10 12 14 16 18

A320

240

160

80

L-2 2 4 6 8 10 12 14 16 18

A320

240

160

80

11)

Use the vertical line test to determine whether y is a function of x.12)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

12)

Graph the equation by plotting ordered pairs of numbers.13) 8x = y + 2

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

13)

Determine the order of the matrix.14) 3 -4 9 7 14)

2

15) 1 -4 6 0-6 8 4 -1

15)

Write the augmented matrix for the system.16) 2x + 4z = 22

9y + 2z = 42 4x + 3y + 7z = 53

16)

17) 9x + 5y + 2z = 47-2x + 8y - 2z = -32 9x - 2y + 6z = 86

17)

Write a system of equations associated with the augmented matrix. Do not try to solve.18) 9 6 2

14 12 1818)

Perform the indicated row operation on the given augmented matrix.19) R1 ↔ R2:

-6 -3 5 2 6 -9

19)

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

Find the indicated matrix.20) Let B = [-1 2 5 -3]. Find -2B.

A) [-2 4 10 -6] B) [-3 0 3 -5] C) [2 2 5 -3] D) [2 -4 -10 6]20)


Perform the indicated operation, if possible.21) [-5 8 3] - [4 3] 21)

22) -1 05 2

- -1 53 1

22)

Find the indicated matrix.23) Let A = -3 3

0 2. Find 5A. 23)

For the given matrix A, find -A.24) A = -5 3

8 724)

3

Find the sum, if possible.25) -2 1

2 5 + 6 2

5 -125)

Solve the system of equations corresponding to the given matrix equation.26) 4x + y

x - 9y = 0

7426)

27)x + y + z

-x - y + z2x + y - 2z

= -1622

27)

The order of two matrices is given. Find the order of the product AB and the product BA, if the products exist.28) A is 3 × 4, B is 4 × 3. 28)

Given matrices A and B, find the indicated matrix if possible.29) A = -5 0

1 2 , B = 2

5 Find AB. 29)

Solve the problem.30) At a store, Sam bought 4 batteries, 11 60-watt light bulbs, 43 100-watt light bulbs, 12

picture-hanging kits, and a hammer. Jennifer bought 9 batteries, 3 100-watt light bulbs,and a package of tacks. Write the information as a 2 x 6 matrix.

30)

Given matrices A and B, find the indicated matrix if possible.31) A = -1 3

2 2 , B = -2 0

-1 5 Find AB. 31)

Find the product.32) -1 3

2 2 -2 0

-1 132)

33) -1 31 2

0 -2 41 -3 2

33)

Find the product if possible.

34) 7 1 -40 6 -7

xyz

34)

Write the matrix equation as a system of linear equations.

35)-5 01 15 7

xy

= 2

-2-5

35)

36)-9 1 10 5 56 1 9

xyz

= 1

-1-7

36)

4

Write the linear system as a matrix equation of the form AX = B.37) x - 8y = 1

-6x - y = -737)

38) -5x + 9y - z = 9 x - y - z = 7

38)

Give the order of the matrix, and identify the given element of the matrix.39)

14 -8 5 -1 0-2 -e 15 4 !-3 -15 10 -2 1413

4 9 8 3; a34

39)

Find the domain of the function.40) f(x) = 3x - 5 40)

41) f(x) = x2

x2 + 1441)

42) f(x) = 1x + 6

42)

Solve.43) The average value of a certain type of automobile was $13,500 in 1993 and depreciated

to $7320 in 1996. Let y be the average value of the automobile in the year x, where x = 0represents 1993. Write a linear equation that models the value of the automobile interms of the year x.

43)

Use the graph of the given function to find any relative maxima and relative minima.44) f(x) = x3 - 3x2 + 1

x-4 -3 -2 -1 1 2 3 4

y

4

3

2

1

-1

-2

-3

-4

x-4 -3 -2 -1 1 2 3 4

y

4

3

2

1

-1

-2

-3

-4

44)

5

The graph of a function f is given. Use the graph to answer the question.45) Find the numbers, if any, at which f has a relative maximum. What are the relative

maxima?

x-4 -3 -2 -1 1 2 3 4

y

4

3

2

1

-1

-2

-3

-4

-5

x-4 -3 -2 -1 1 2 3 4

y

4

3

2

1

-1

-2

-3

-4

-5

45)

Determine whether the relation is a function.46) {(-3, 7), (2, 9), (6 , 4), (7, 5), (11, 1)} 46)

47) {(-5, -2), (-3, 5), (-1, 6), (8 , 5)} 47)

Evaluate the function at the given value of the independent variable and simplify.48) f(x) = -7x - 5 ; f(5) 48)

49) f(x) = x2 - 1; f(x - 4) 49)

Determine whether the equation defines y as a function of x.50) x + y = 16 50)

51) x2 + y = 1 51)

52) y = x2 52)

53) x + y3 = 27 53)

6

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.54)

x

y

x

y54)

55)

x

y

x

y55)

Identify the intercepts.56)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

56)

7

57)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

57)

Use the shape of the graph to name the function.58)

x

y

x

y58)

59)

x

y

x

y59)

8

60)

x

y

x

y60)

61)

x

y

x

y61)

62)

x

y

x

y62)

9

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph thegiven function.

63) h(x) = -(x + 2)2

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

63)

Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph thegiven function.

64) h(x) = - x - 6

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

64)

65) h(x) = 2 x + 3

x-10 -8 -6 -4 -2 2 4 6 8

y108642

-2-4-6-8

-10

x-10 -8 -6 -4 -2 2 4 6 8

y108642

-2-4-6-8

-10

65)

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinatesof the minimum or maximum point.

66) f(x) = x2 + 2x - 1 66)

10

67) f(x) = 2x2 - 2x - 1 67)

Determine the maximum possible number of turning points for the graph of the function.68) f(x) = - x2 - 4x - 5 68)

69) f(x) = 2x7 + 3x6 - 2x - 8 69)

70) f(x) = (x + 3 )(x - 7)(7x - 5 ) 70)

Graph the polynomial function.71) f(x) = x4 - 9x2

x-10-8 -6 -4 -2 2 4 6 8 10

y

8

6

4

2

-2

-4

-6

-8

x-10-8 -6 -4 -2 2 4 6 8 10

y

8

6

4

2

-2

-4

-6

-8

71)

Find the domain of the rational function.

72) h(x) = 9xx - 2

72)

73) g(x) = 4x2(x + 6 )(x - 6 )

73)

74) h(x) = x + 3x2 - 25x

74)

Find a rational zero of the polynomial function and use it to find all the zeros of the function.75) f(x) = x3 + 2x2 - 5x - 6 75)

76) f(x) = 2x3 - 11x2 + 17x - 6 76)

77) f(x) = x3 + 3x2 - x - 3 77)

11

Solve the problem.78) A company that produces inflatable rafts has costs given by the function

C(x) = 25x + 20,000 , where x is the number of inflatable rafts manufactured and C(x) ismeasured in dollars. The average cost to manufacture each inflatable raft is given by

_C (x) = 25x + 20,000

x.

Find _C (250). (Round to the nearest dollar, if necessary.)

78)

79) A company that produces inflatable rafts has costs given by the functionC(x) = 25x + 25,000, where x is the number of inflatable rafts manufactured and C(x) ismeasured in dollars. The average cost to manufacture each inflatable raft is given by

_C (x) = 25x + 25,000

x.

What is the horizontal asymptote for the function _C ? Describe what this means in

practical terms.

79)

80) A drug is injected into a patient and the concentration of the drug is monitored. Thedrug's concentration, C(t), in milligrams after t hours is modeled by

C(t) = 8t3t2 + 4

.

What is the horizontal asymptote for this function? Describe what this means inpractical terms.

80)

Approximate the number using a calculator. Round your answer to three decimal places.81) 41.9 81)

Solve the problem.82) The function f(x) = 500(0.5)x/70 models the amount in pounds of a particular

radioactive material stored in a concrete vault, where x is the number of years since thematerial was put into the vault. Find the amount of radioactive material in the vaultafter 200 years. Round to the nearest whole number.

82)

83) A city is growing at the rate of 0.8% annually. If there were 4,566,000 residents in the cityin 1993, find how many (to the nearest ten-thousand) are living in that city in 2000. Usey = 4,566,000(2.7)0.008 t.

83)

Approximate the number using a calculator. Round your answer to three decimal places.84) e2.8 84)

Solve the problem.85) The size of the coyote population at a national park increases at the rate of 4.6% per

year. If the size of the current population is 186, find how many coyotes there should bein 3 years. Use the function f(x) = 186e0.046 t and round to the nearest whole number.

85)

12

86) A sample of 1000 g of lead-210 decays to polonium-210 according to the function givenby A(t) = 1000e-0.032t, where t is time in years. What is the amount of the sample after40 years (to the nearest g)?

86)

Use the compound interest formulas A = P 1 + rnnt

and A = Pert to solve.

87) Find the accumulated value of an investment of $4000 at 8% compounded annually for16 years.

87)

88) Find the accumulated value of an investment of $16,000 at 4% compoundedsemiannually for 7 years.

88)

89) Find the accumulated value of an investment of $200 at 8% compounded quarterly for 4years.

89)

90) Find the accumulated value of an investment of $5000 at 7% compounded continuouslyfor 6 years.

90)

Write the equation in its equivalent exponential form.91) log5 125 = 3 91)

92) log4 x = 2 92)

Write the equation in its equivalent logarithmic form.93) 42 = 16 93)

94) 63 = x 94)

Evaluate the expression without using a calculator.95) log5 125 95)

96) log2 32 96)

Evaluate or simplify the expression without using a calculator.97) log 10,000 97)

98) log 103 98)

99) ln e10 99)

100) ln 1 100)

13

Solve the problem.101) The long jump record, in feet, at a particular school can be modeled by

f(x) = 20.4 + 2.5 ln (x + 1) where x is the number of years since records began to be kept atthe school. What is the record for the long jump 6 years after record started being kept?Round your answer to the nearest tenth.

101)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluatelogarithmic expressions without using a calculator.

102) log2 (7 ∙ 3) 102)

103) log3713

103)

104) logd x9 104)

105) log3 x2 105)

106) logb (yz4) 106)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithmwhose coefficient is 1. Where possible, evaluate logarithmic expressions.

107) logc m + logc n 107)

Solve the equation by expressing each side as a power of the same base and then equating exponents.108) 2x = 16 108)

109) 2(1 + 2x) = 8 109)

Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, forthe solution.

110) 10x = 3.89 110)

111) 4x = 12 111)

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmicexpressions. Give the exact answer.

112) log3 x = 5 112)

Solve.113) The value of a particular investment follows a pattern of exponential growth. In the year

2000, you invested money in a money market account. The value of your investment tyears after 2000 is given by the exponential growth model A = 8000e0.052t. How muchdid you initially invest in the account?

113)

14

114) The value of a particular investment follows a pattern of exponential growth. In the year2000, you invested money in a money market account. The value of your investment tyears after 2000 is given by the exponential growth model A = 8100e0.062t. By whatpercentage is the account increasing each year?

114)

Determine whether the given ordered pair is a solution of the system.115) (-3, 2)

x + y = -1x - y = -5

115)


Write the augmented matrix for the system of equations.116) 9x + 4y + 6z = 80

2x + 9y + 4z = 15 6x - 2y + 6z = 62A)

9 4 6 802 9 4 156 -2 6 62

B)9 2 6 804 9 -2 156 4 6 62

C)80 6 4 915 4 9 262 6 -2 6

D)9 4 62 9 46 -2 6

116)


Perform the matrix row operation (or operations) and write the new matrix.117)

40 12 -4 281 13 -3 02 -7 4 21

14R1

117)


118)4 -5 1 2

-4 0 5 -2-1 3 -3 -1

-5R1 + R2

A)4 -5 1 2

-24 25 0 -12-1 3 -3 -1

B)4 -5 1 216 -25 10 8-1 3 -3 -1

C)24 -5 -24 12-4 0 5 -2-1 3 -3 -1

D)-24 25 0 -12-4 0 5 -2-1 3 -3 -1

118)

15


Give the order of the matrix, and identify the given element of the matrix.119)

-9 -10 6 1512 0 -7 5

; a12

119)

Find values for the variables so that the matrices are equal.120)

x5

= 8y

120)

121)-3 3-6 5

= x y-6 z

121)

Solve the problem.122)

Let A = -9 12 5

and B = 6 23 1

. Find A + B.122)

123)

Let A = -1 30 4

8 -4 and B =

7 217 4 3 2

. Find A - B.

123)

124)Let A = -3 1

0 2. Find 3A.

124)

Solve the matrix equation for X.125)

Let A = 2 -5-2 -1

and B = -2 52 -4

; X + A = B125)

Find the product AB, if possible.126)

A = -1 32 2

, B = -2 0-1 5

126)

Write the first four terms of the sequence whose general term is given.127) an = 4n 127)

128) an = n - 5 128)

Find the indicated sum.

129)5

i = 26i∑ 129)

16

Answer KeyTestname: 2ND SEM #2018 REVIEW

1) -38.9332) -336.1083) 9 minutes4) 3 pounds

5) h = 3VB

6) 3 in.7) 4, 118) x ≈ 4.569)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

10) D = [-2, ∞); R = [0, ∞)11) 165 cm212) Yes13)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

14) 1 × 415) 4 × 216)

2 0 4 220 9 2 424 3 7 53

17)9 5 2 47

-2 8 -2 -329 -2 6 86

17


18) 9x + 6y = 214x + 12y = 18

19) 2 6 -9

-6 -3 520) D21) Not defined22)

0 -52 1

23)-15 150 10

24) 5 -3

-8 -725)

4 37 4

26) {(2, -8)}27) {(-3, -6, -7)}28) AB is 3 × 3, BA is 4 × 4.29)

-10 12

30)4 11 43 12 1 09 0 3 0 0 1

31)-1 15-6 10

32)-1 3-6 2

33)3 -7 22 -8 8

34) 7x + y - 4z 6y - 7z

35) -5x = 2 x + y = -2 5x + 7y = -5

36) -9x + y + z = 1 5y + 5z = -1 6x + y + 9z = -7

37)

1 -8-6 -1

xy

= 1

-718


38)

-5 9 -1

1 -1 -1 x

y

z

= 97

39) 4 × 5 ; -240) (-∞, ∞)41) (-∞, ∞)42) (-∞, -6) ∪ (-6, ∞)43) y = -2060x + 13,50044) maximum: (0, 1); minimum: (2, -3)45) f has a relative maximum at x = 0; the relative maximum is 146) Function47) Function48) -4049) x2 - 8x + 1550) y is a function of x51) y is a function of x52) y is a function of x53) y is a function of x54) function55) function56) (-1, 0), (0, 4)57) (4, 0), (0, 8)58) Constant function59) Identity function60) Standard quadratic function61) Standard cubic function62) Absolute value function63)

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

19


64)

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

65)

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

x-8 -6 -4 -2 2 4 6 8

y8642

-2-4-6-8

66) minimum; - 1, - 2

67) minimum; 12, - 32

68) 169) 670) 271)

x-8 -6 -4 -2 2 4 6 8

y161284

-4-8

-12-16

x-8 -6 -4 -2 2 4 6 8

y161284

-4-8

-12-16

72) {x|x ≠ 2}73) {x|x≠ -6, x ≠ 6}74) {x|x ≠ 0, x ≠ 25}75) {-3, -1, 2}

76) 12, 2, 3

20


77) {1, -1, -3}78) $10579) y = 25; $25 is the least possible cost for producing each inflatable raft.80) y = 0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream.81) 13.92982) 69 pounds83) 4,830,00084) 16.44585) 21486) 278 g87) $13,703.7788) $21,111.6689) False90) $7609.8191) 53 = 12592) 42 = x93) log4 16 = 2

94) log6 x = 3

95) 396) 597) 498) 399) 10100) 0101) 25.3 feet102) log2 7 + log2 3

103) log3 7 - log3 13

104) 9logd x105) 2 log3 x

106) logb y + 4 logb z

107) logc (mn)

108) {4}109) {1}110) 0.59111) 1.79112) {243}113) $8000.00114) 6.2%115) solution116) A117)

10 3 -1 71 13 -3 02 -7 4 21

118) A21


119) 2 × 4; -10120) x = 8; y = 5121) x = -3; y = 3; z = 5122)

-3 35 6

123)-8 1

-17 0 5 -6

124)-9 30 6

125)X = -4 10

4 -3126)

-1 15-6 10

127) 4, 8, 12, 16128) -4, -3, -2, -1129) 84

22

short answer. the word or phrase that best completes each ...€¦ · pound. if he buys s pounds of...

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