algebra 1b study guide (part a) name: date:

Algebra 1B Study Guide (Part A)

Name: _______________________________________________ Date: __________

____ 1. The length of a rectangle is 2 cm more than three times the width. If the perimeter of therectangle is 36 cm, what are the dimensions?

A. width = 4 cm, length = 14 cm C. width = 8 cm, length = 28 cm B. width = 8 cm, length = 26 cm D. width = 4 cm, length = 28 cm

____ 2. Mr. Jarvis invested a total of $10,437 in two savings accounts. One account earns 8% simpleinterest per year and the other earns 9% simple interest per year. Last year, the twoinvestments earned a total of $849.52 in interest. Which of the following systems of equationscould be used to determine the amount Mr. Jarvis initially invested in each account? Let x represent the amount invested at 8% and let y represent the amount invested at 9%.

A. x + y = 849.52

8x + 9y = 10, 437

C. x + y = 10, 437

0.08x + 0.09y = 849.52 B. x + y = 849.52

0.08x + 0.09y = 10, 437

D. x + y = 10, 437

8x + 9y = 849.52

Solve by elimination:

____ 3. 2x + 2y = 43x − 2y = 16

A. (0, 2) C. (12, − 2) B. (4, − 2) D. no solution

____ 4. Solve the system using the addition method:2x − 4y = 123x + 4y = 8

A. (4, -1) C. (20, -1) B. (0, -3) D. no solution

Solve the system:

____ 5. 4x + 4y = − 123x − 4y = − 23

A. (0, -3) C. no solution B. (-5, 2) D. (-32, 3)

____ 6. A small airplane flies at 145 miles per hour in still air. It took 2.5 hours for the airplane to fly d miles against a headwind blowing toward the airplane at w miles per hour. Which of thefollowing equations can be used to represent this information?

A. d = (w − 2.5)145 C. 145 = (w − 2.5)d B. d = (145 − w)2.5 D. 145 = (d − w)2.5

Algebra 1B Study Guide (Part A), Version: 1 1


____ 7. Solve the system using the addition method:4x − 3y = 85x + 2y = 6

A. − 819

, 5823

C. 3423

, − 1623

B. 823

, 8823

D. no solution

____ 8. Marc sold 504 tickets for the school play. Student tickets cost $3 and adult tickets cost $5.Marc's sales totaled $2090. How many adult tickets and how many student tickets did Marcsell?

A. 284 adult, 220 student C. 215 adult, 289 student B. 220 adult, 284 student D. 289 adult, 215 student

____ 9. A chemistry teacher needs 2.5 liters of a sulfuric acid solution that is 20% sulfuric acid and80% water. He has 2 liters of a 15% sulfuric acid solution left over from earlier laboratoryexercises. He also has 4 liters of a 50% solution. Let x represent the number of liters of the15% solution that can be mixed with y liters of the 50% solution to make 2.5 liters of theneeded 20% solution. Which of the following shows a system of equations that could besolved to find the amounts of the 15% and 50% solutions that could be mixed to get therequired solution?

A. x + y = 2.5

0.15x + 0.50y = 0.20

C. x + y = 2.5

0.15x + 0.50y = 0.20(2.5) B. x + y = 0.20(2.5)

0.15x + 0.50y = 2.5

D. x + y = 0.65

x + y = 0.20(2.5)

____ 10. Which system of equations has no solution? A. 3x − 4y = 1

3x + 4y = 1 C. 3x − 4y = 1

12x − 16y = 4 B. 3x − 4y = 1

5x + 6y = 2 D. 3x − 4y = 1

3x − 4y = 2

Graph the system and describe its solution(s).

____ 11. 4x − 5y = – 216x − 20y = 5

A. −1, − 25

C. 5, 225

B. 1, 1120

D. no solution



____ 12. Determine if the system has no solutions, one solution, or many solutions.3x + 2y = 212x + 8y = 8

A. no solution C. many solutions B. (− 2, 4) D. (− 2, − 4)

____ 13. Graph: y ≤ 2x + 4 A. C.

B. D.



Graph:

____ 14. −y ≥ 2x − 7 A. C.

B. D.

____ 15. − y > 2x − 7 A. C.

B. D.



____ 16. − y ≥ 2x − 7 A. C.

B. D.



____ 17. x ≥ − 1 A. C.

B. D.



Solve the system of inequalities graphically:

____ 18. y ≤ 2x − 1y < − 3

A. C.

B. D.



____ 19. Graph the solution set of the system of inequalities 5x + 3y ≥ 15, x ≤ y, x ≤ 6 A. C.

B. D.



____ 20. The owner of a restaurant determines she can spend no more than $700 to buy coffee for thenext month. At wholesale prices, the regular coffee she uses costs $2.50 per pound and thedecaffeinated coffee costs $3.50 per pound. The owner estimates she will need at least 75pounds of coffee for the month. Which graph represents the possible combinations of thenumber of pounds of regular coffee, x, and the number of pounds of decaffeinated coffee, y,that meet these conditions?

A. C.

B. D.



____ 21. A salesman at a new car dealership gets paid a fixed commission above his base salary forany passenger car he sells and a different fixed commission for any sport utility vehicle hesells. In August, he sold 5 passenger cars and 5 sport utility vehicles and earned more than$2500 above his base salary. In September, he sold 8 passenger cars and 3 sport utilityvehicles and earned less than $3000 above his base salary.This information can be represented by the following inequalities and their graph, where p represents the number of passenger cars sold and s represents the number of sport utilityvehicles sold.5p + 5s > 25008p + 3s < 3000

Which region of the graph represents the possible commissions paid to the salesmanfor the two types of vehicles?

A. D C. A B. B D. C

Simplify. Leave your answer in exponential form.

____ 22. 44 × 47 A. 1611 C. 411 B. 43 D. 428



Simplify:

____ 23. v 3 ⋅ v 6 ⋅ v 3 A. v 54 C. 3v 12 B. v 12 D. 3v 54

____ 24. w3c −7w7c4

A. −7w10c5 C. −7w10c6 B. −7w11c6 D. −7w11c5

____ 25. −3c8 2c6d 8

A. −6c48d 8 C. 6c14d 14 B. −6c14d 8 D. 6c48d 14

Simplify. Write your answer using exponents.

____ 26.(34)

8

A. 364 C. 128 B. 332 D. 312

Simplify:

____ 27. c26

A. c64 C. c8 B. c1 /3 D. c12

____ 28. c610

A. c5 /3 C. c16

B. c3 /5 D. c60

____ 29. −2t 6r35

A. –32t 11r8 C. –32t 30r15 B. 32t 11r8 D. 32t 30r15

____ 30.Simplify the product: (3vw3)

3(vw)3

A. 27v 6w6 C. 3v 4w12 B. 27v 6w12 D. 3v 6w12



____ 31. Simplify 32 × 36 . A. 38 C. 98 B. 912 D. 312

____ 32.Simplify 22

6.

A. 212 C. 264 B. 21 /3 D. 28

33. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.

Evaluate the expression 5 − 36 ÷ r22⋅ 7, given r = 3 .

____ 34.Which is equivalent to 2

12

23?

A. 28 C. 215 B. 29 D. 23

Simplify the expression using positive exponents.

____ 35. −4q

8

A. 65, 536

q8 C. 32

8q

B. 32q8

D. 65, 5368q



____ 36.x3

y 8

4

A. x12 + y 32 C. x12

y 32 B. x7

y 12 D. x12

y 8

Multiply:

____ 37. 22 × 4 × 60 A. 96 C. 0 B. 16 D. 128

Simplify:

____ 38. a5 ⋅ a –8

A. a3 C. a40 B. 1

a40 D. 1

a3

____ 39. Which expression is equivalent to 30 ⋅ 3 –14? A. 314 C. 30 B. 1

314 D. 1

315

____ 40. Which of the following numbers when multiplied by −2 −2is equal to 1? A. 2 −2 C. − 2 −2

B. ( −2) 2 D. −22




What is the value of the expression ( 3) 2−1

?

42. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The table below shows the molecular masses of several samples of unidentified fluids used in achemistry laboratory quiz.Sample Molecular Mass (kg)

1 4.36 × 10 −24

2 5.14 × 10 −23

3 3.62 × 10 −24

4 6.29 × 10 −24

5 1.36 × 10 −23

If the samples are arranged on a shelf in order of their molecular masses from least to greatest,what is the sample number of the sample that will be in the middle?




What is the value of the expression 520

?

____ 44. Which expression is equivalent to 8 −6 × 89 ? A. 1

854 C. 815

B. 83 D. 183

45. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. What is the value of the expression ( −8) 0 + 29 + ( −29) ?



____ 46. Write 2,570 in scientific notation. A. 25.7 × 105 C. 0.257 × 104 B. 2.57 × 103 D. 257 × 10

____ 47. Write 0.00000258 in scientific notation. A. 258 × 10 −8 C. 0.258 × 10 −5 B. 2.58 × 10 −6 D. 258 × 10 −7

Multiply:

____ 48. (3.5 × 10 −7)(9.9 × 1010) A. 13.4 × 103 C. 34.65 × 103 B. 3.465 × 103 D. 34.65 × 104

____ 49. In astronomy, the immense distances between celestial bodies are measured in light-years,the distance that light can travel in one year. One light-year is approximately5,880,000,000,000 miles. If a star is 8.2 light-years from Earth, which expression in scientificnotation correctly represents the number of miles the star is from Earth?

A. 5.6 × 1013 C. 4.0 × 1013 B. 4.8 × 1013 D. 6.5 × 1013

____ 50. Ordinary conversation with another person typically has an intensity level of 65 decibels,which is equivalent to a power intensity of about 32 ten-millionths of a watt per square meter.Which expression represents the number 32 ten-millionths in proper scientific notation?

A. 3.2 × 10 −6 C. 3.2 × 10 −5 B. 32 × 10 −8 D. 3.2 × 10 −7



____ 51. Metal rods get shorter when they are cooled. In a science class experiment, identically-sizedmetal rods were cooled in ice-baths. The rods were all painted so there were no clues as towhat metal they were. Their length changes are shown in the table below.

The teacher told the students that the rod that showed the greatest change in lengthwould be the copper rod. Which rod was the copper rod?

A. rod #3 C. rod #1 B. rod #4 D. rod #2

____ 52. Which pair of numbers is NOT equal to −0.5 ? A. 0.5 and 50% C. − ( −0.5) and 5 × 10 −1 B. −0.5 and − 1

2 D. 0.5 and 1

2

53. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Sometimes it is easier to understand the size of a number given in scientific notation if it isconverted to fraction form. What simplified fraction is equivalent to 8.75 × 10 −3?



____ 54. The calorie and the BTU (British Thermal Unit) are two standard units of energy. Fourcalories is about 0.015872 BTU. How is this measure expressed in scientific notation?

A. 15.87 × 103 C. 15.87 × 10 −3 B. 1.587 × 10 −2 D. 1.587 × 102

____ 55. Deimos, a moon of Mars, takes about 1860 minutes to orbit the Mars. How is thismeasurement expressed in scientific notation?

A. 18.6 × 101 minutes C. 1.86 × 103 minutes B. 1.86 × 104 minutes D. 18.6 × 102 minutes

____ 56. Evaluate 49.5 ⋅ 104 .

A. 49,500 C. 4950 B. 4,950,000 D. 495,000

____ 57. Radio signals travel at a rate of 3.00 × 108 meters per second. How many seconds will it takefor a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at aheight of 1.02 × 108 meters?

A. 0.340 seconds C. 3.40 seconds B. 0.306 seconds D. 3.06 seconds



____ 58. Sketch the graph of the equation.y= − 3x2

A. C.

B. D.



____ 59. Sketch the graph of the equation y=0.75x2 . A. C.

B. D.



____ 60. Sketch the graph of the equation y= − 57x2 .

A. C.

B. D.



Graph:

____ 61. y = x2 − 3 A. C.

B. D.

____ 62. How would you translate the graph of y = x2 to produce the graph of y = x2 − 6? A. translate the graph of y = x2 down 6 units C. translate the graph of y = x2 right 6 units B. translate the graph of y = x2 up 6 units D. translate the graph of y = x2 left 6 units

____ 63. Predict how the graph of the equation y=7x2 will compare with the graph of the equationy = x2 .

A. The graph of y=7x2 will open downbecause coefficient is positive. The graphwill be wider because 7 is greater than 1.

C. The graph of y=7x2 will open downbecause coefficient is positive. The graphwill be narrower because 7 is greater than1.

B. The graph of y=7x2 will open up becausethe coefficient is positive. The graph will bewider because 7 is greater than 1.

D. The graph of y=7x2 will open up becausethe coefficient is positive. The graph will benarrower because 7 is greater than 1.



Graph:

____ 64. y = − x2 − 3x + 1 A. C.

B. D.



____ 65. Graph the parabola: y = − x2 + 3x − 2 A. C.

B. D.



66. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The area of a rectangle with a perimeter of 100 units can be described by y = x(50 − x), where x represents the width of the rectangle and y represents the area. The graph below shows how thearea of the rectangle depends on its width.

A farmer has 100 yards of fencing available and wishes to enclose a rectangular area. Tothe nearest 5 yards, what width gives the largest enclosed area?

____ 67. A rocket is launched from atop a 45-foot cliff with an initial vertical velocity of 137 feet persecond. The height of the rocket t seconds after launch is given by the equationh = − 16t 2 + 137t + 45 . Graph the equation to find out how long after the rocket is launchedit will hit the ground. Estimate your answer to the nearest tenth of a second.

A. 8.2 seconds C. 1.4 seconds B. 0.3 seconds D. 8.9 seconds

Solve:

____ 68. 9x2 – 4 = 0 A. – 3

2, 32

C. – 23

, 23

B. – 94

, 94

D. – 49

, 49



____ 69. Write the polynomial so that the exponents decrease from left to right. −3x2 + 2x − 3x3 − 4 A. 3x3 + 3x2 − 2x + 4 C. −4 + 2x − 3x2 − 3x3 B. 4 − 2x + 3x2 + 3x3 D. −3x3 − 3x2 + 2x − 4

Find the sum.

____ 70. (3x3 + 7x6 + 3) + ( − 5x6 + 9 + 5x3) A. −2x6 + 16x3 + 8 C. 2x6 + 8x3 − 6 B. 2x6 + 8x3 + 12 D. −2x6 + 16x3 + 12

Simplify:

____ 71. 3q3 + 5 − 3q2 + 3 + 8q3 − q2

A. 11q3 − 4q2 + 8 C. −5q3 − 4q2 + 8 B. 11q3 + 4q2 − 2 D. 11q3 − 4q2 + 2

____ 72. 3q3 + 5 − 3q2 + 3 + 8q3 − q2

A. 11q3 − 4q2 + 2 C. −5q3 − 4q2 + 8 B. 11q3 − 4q2 + 8 D. 11q3 + 4q2 − 2

Find the difference.

____ 73. (6x3 + 8x2 + 8) − (7x3 − 7x2 + 3x − 8) A. −x3 − 15x2 − 3x C. x3 − 15x2 + 3x B. −x3 + 15x2 − 3x + 16 D. −x3 − 15x2 + 3x + 16

____ 74. During the years 1992 through 1996, the average number of green grapes, G, sold by a largefarmer's market can be modeled by G = − 0.06t 2 + 1.63t + 45.16. The average number of redgrapes, R, sold by the farmer's market can be modeled by R = 0.009t 2 − 0.661t + 80.76. Determine the model representing the total number of grapes, N, sold from 1992 through1996.

A. N = – 0.051t 4 + 0.969t 2 + 125.92 C. N = 0.051t 2 + 2.291t + 125.92 B. N = 0.051t 4 + 2.291t 2 + 125.92 D. N = – 0.051t 2 + 0.969t + 125.92

Find the product.

____ 75. (x − 2)(x + 5) A. x2 + 7x − 10 C. x2 + 3x + 10 B. x2 − 7x − 10 D. x2 + 3x − 10



Multiply:

____ 76. (x + 4) (x + 7) A. x2 + 11x + 28 C. x2 + 28x + 28 B. x2 + 28x + 11 D. x2 + 28

____ 77. (4x + 1) (4x − 3) A. 16x2 − 8x − 3 C. 16x2 − 8x + 3 B. 16x2 − 16x − 3 D. 16x2 + 8x − 3

____ 78. (x + 5) x2 − 2x + 3 A. x2 − 3x + 15 C. x3 + 3x2 − 7x + 15 B. x3 + 3x2 − 10x + 15 D. x3 − 2x2 + 15

Find the product:

____ 79. (x + 4) x2 − 4x + 2 A. x3 − 16x + 8 C. x3 − 14x + 8 B. x2 − 5x + 8 D. x3 − 4x2 + 8

____ 80. The sides of a rectangle have length x + 7 and width x − 3. Which equation below describesthe area, A, of the rectangle in terms of x?

A. A= x2 + 4x − 21 C. A= 4x + 8 B. A= 2x + 4 D. A= x2 + 10x − 21

____ 81. A rectangular garden, with length three times its width, is to be expanded so that both sidesare increased by 8 yards.8 yd Which expression models the area of the expanded garden?

A. 4x + 16 C. 3x2 + 16x + 64 B. 3x2 + 64 D. 3x2 + 32x + 64

Factor:

____ 82. x2 − 7x + 10 A. (x − 2) (x + 5) C. (x + 2) (x − 5) B. (x + 2) (x + 5) D. (x − 2) (x − 5)



Performance Task:

____ 83. The volume of a cylinder is given by the formula V = πr2h, where r is the length of the radius ofthe base of the cylinder and h is the height of the cylinder. If the radius of a cylinder isincreased by 1 unit and the height remains the same, the ratio for the volume of the newcylinder to the volume of the original cylinder is 4:1. Find the length of the radius of the originalcylinder.

A. 2 units C. 1 unit B. 4 units D. 3 units

Solve:

____ 84. 9v 2 + 24v + 16 = 0 A. v = − 3

4 C. v = − 4

3 B. v = 4

3 D. v = 3

4

Solve for x:

____ 85. x3 + 4x2 − 25x − 100 = 0 A. −4, 25 C. 4, 5 B. −4, − 5, 5 D. −5, 4, 5

____ 86. Frances and Joyce decided to take a shortcut through the woods to go to their friend's house.When they went home they decided to take the long way around the woods to avoid gettingmuddy shoes. If the length of the shortcut is equal to the square root of the sum of the squaresof the other two sides, what total distance did they walk?

A. 1700 meters C. 2150 meters B. 1500 meters D. 1275 meters



____ 87. To get to the store from his house, Jack biked 5 kilometers due west and then 12 kilometersdue north. On the way back he cut across a field, taking the shortest possible route home.

How far did Jack bike on the round-trip?

A. 17 km C. 34 km B. 13 km D. 30 km

____ 88. A cable 27 feet long runs from the top of a utility pole to a point on the ground 16 feet from thebase of the pole. How tall is the utility pole?

A. 21.75 ft C. 21 ft B. 11 ft D. 31.38 ft

____ 89. Which set of side lengths cannot form a right triangle? A. 3

2 mm, 2 mm, 5

2 mm C. 4 mm, 4 mm, 5 mm

B. 6 mm, 8 mm, 10 mm D. 3 mm, 4 mm, 5 mm

____ 90. A cable 39 m long runs from the top of a utility pole to a point on the ground 24 m from thebase of the pole. How tall is the utility pole, to the nearest tenth of a meter?

A. 945 m C. 63 m B. 45.8 m D. 30.7 m



____ 91. Which is the approximate length of the hypotenuse of the right triangle?

A. 3.16 C. 22.67 B. 17.03 D. 15.3

In the drawing below, figures A, B, and C are squares.

____ 92. The perimeter of A is 24 inches, and the perimeter of B is 32 inches. What is the perimeter ofC?

A. 20 inches C. 56 inches B. 40 inches D. 100 inches



Graph the function.

____ 93. y = 13

x

A. C.

B. D.

____ 94. Write an exponential function to model the situation.A population of 250 animals that decreases at an annual rate of 19%.

A. y = 250(0.81) x C. y = 250(1.81) x

B. y = 250(0.19) x D. y = 250(1.19) x

____ 95. The table gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990.Year, t 1985 1986 1987 1988 1989 1990

Inner tubes, I 4 13 18 35 68 129

Determine which model best fits the data. A. absolute value C. quadratic B. linear D. exponential



____ 96. Use the terms linear or nonlinear and increasing, decreasing, or constant to describe thegraph.

A. constant, decreasing C. nonlinear, increasing B. constant, increasing D. nonlinear, decreasing

Writing:

____ 97. A salesperson earns a monthly salary of $750 a month plus a percentage of the proceedsfrom the number of items he sells. Which graph could be a model of this situation?

A. C.

B. D.

____ 98. Which of the following functions is linear? A. f (x) = 15

x+ 1 C. f (x) = 15

−14x + 1 B. f (x) = − 14

15x−1 + 1 D. f (x) = x

15+ 1


algebra 1b study guide (part a) name: date:

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