Objective 1.01 ALGEBRA I EOC REVIEW PACKET Name 1. Circle which number is irrational? 49,. Which statement is false? A. a a a = bc b c B. 6 = C. ( n) = n D. ( c d) = c d. Subtract ( + 4) ( 4 + 6). 4. Simplify ( + 4 + ). 5. Simplify 84 16 9 1 6. Add ( 6 8 + 4) + ( 8 4 + ) 16 8, 1, 5 7. Which of the following is true? A. 6 4 y = B. = y y 8. Simplify 4y(y + y y 1). C. 0 m m m = D. d d 8 = 6 d 9. Write a simplified epression for the area of a rectangle with a length of (4 ) and a width of (5 ). 10. Factor 5 1. 11. (y + 4)(y a) = y 11y 0. What is the value of a? 1. Find the coefficient of the term in the product (6 4)(6 + 1). 1. Which of the following radical epressions is in simplified form? A. 1 B. 1 C. 19 D. 5 14. Simplify 160 10. 15. Simplify 15.
16. Simplify 4 4 9+ 5 16 6 5+ 7 6. 17. Valerie will use a 10-inch by 1-inch piece of rectangular cardboard to make a bo with no top. She will cut a square from each corner, as shown, then fold the sides up and tape them. Write an epression that describes the volume of the bo after the corners have been cut out. 18. What is the value of 6y if (y 4) + y =? 19. A side of a cube measures. Write a simplified epression for the volume of the cube? 0. Simplify 5 10 15 4 1y y + 1 y 5. y 1. Factor 4 4 16y completely. A. ( y)( + y)( + y) B. ( 4y)( + 4y) C. 4( y)( y) D. 4( y)( + y). Find the perimeter of a rectangle with length (9 10) and width (5 + ).. Write a simplified epression for the area of the rectangle in question. 4. For what value of p would ( + p)( + p) be the factored form of 4 + 144? Objective 1.0 5. At the local bakery, a small chocolate chip cookie has a -inch diameter. How much more cookie do you get if you buy a super cookie with a diameter of 6 inches? A. 8π in B. 10π in C. π in D. 40π in 6. If the height and diameter of a cylinder are doubled, how many times does the volume of the cylinder increase? 7. A rectangular planter can hold 04 cubic inches of soil. What is the height of the planter?
8. The height of an equilateral triangle can be determined by evaluating the epression n where n is the length of a side of the triangle. To the nearest tenth of an inch, what is the height of an equilateral triangle with sides 6.5 inches? 9. Construction slowed Jan s average speed on the 10-mile trip from Benson to Warsaw to 45 miles per hour. On her return trip, Jan was able to average 60 miles per hour. How much faster was her return trip? (d = rt) A. 7.5 hours B. 1.8 hours C. 1. hours D. 40 minutes 0. Arial is stacking wood at her mountain cabin. She begins with a row of 0 logs on the bottom layer. Each layer contains one log less than the layer below it. How many logs are in the pile? The formula for the sum of a series of consecutive integers beginning with 1 is n ( n+ 1). A. 10 logs B. 09 logs C. 190 logs D. 189 logs Objective 1.0 1. If a varies directly as b and a = when b = 1, what is the value of a when b = 18?. In which table of ordered pairs does n vary directly as m? A. B. C. D. m n - -1-1 - 1 m n - 4-1 1 - m n - -.5-1 -5 1 5 m n - - -1-4 1 4. The length a spring will stretch varies directly as the weight attached to the spring. If the spring stretches 1.6 inches when a 4-pound weight is attached, how far will it stretch when a 15-pound weight is attached? 4. Suppose that y varies directly as, and y = 5 when =. Find the constant of variation. What is the value of y when = 7? 5. The distance required for a car to stop is directly proportional to the square of its velocity. If a car can stop in 11.5 meters at 15 kilometers per hour, how many meters are needed to stop at 5 kilometers per hour? A 50.75 meters B. 98 meters C. 1.5 meters D. 7.5 meters
Objective.01 6. Gary s school has a rectangular courtyard that measures 6 meters by 48 meters. How much shorter is the walk from A to B along the diagonal sidewalk than through point P? 7. Find the midpoint of (4, 8) and (, 1). 8. Find the distance from ( 4, 4) to the intersection of the lines: + y=7 and y = 9. 9. Calculate the distance between (4, 1) and (6, ). Write your answer in both simplified radical form and as a decimal approimation to the nearest tenth. 40. A line has an endpoint at (5, ). The midpoint of the line is at (, 0). What are the coordinates of the other endpoint? 41. Square WXYZ has vertices W(1, 7), X(5, ), Y(1, 1), and Z(, ). Which is the area of WXYZ? A. 4 square units B. 16 square units C. square units D. 64 square units Objective.0 4. Line A passes through points (6, 8) and (1, 7). Line B is perpendicular to Line A. Line C is perpendicular to Line B. What is the slope of Line C? 4. Write the equation of the line through ( 4, 5) that is perpendicular to 4 y = 1. Write your answer in slope-intercept form. 44. Given points P (7, 5), Q (8, ), R (0, -1) and S (-1, 1) which statement is true? A. PQ is parallel to RS B. PQ is perpendicular to RS C. PR is perpendicular to QS D. PR is parallel to QS 45. Which of the following is an equation of the line perpendicular to + 6y = 1 and passing through (4, 0)? 1 A. y= + C. y= + 8 1 B. y= D. y= 8
Objective.01 46. Matri A shows the cost per pound of apples and oranges at three different markets during the first week of September. Matri B shows the prices one week later at the same three markets. Which matri correctly shows the difference in prices, B A? $1. 09 $1. 11 $0. 89 A = B = $1. 15 $1. 11 $0. 79 $1. 09 $1. 19 $1. 14 $1. 14 $0. 49 $0. 89 0 00. 040. 0 0 010. A. B. C. 004. 00. 010. 010. 0 040. 0 004. 00. 00. 040. 010. D. 18. 4. 5. 5. 18. 168. 47. Which element is in row 1, column of matri M? 8 0 M= 6 1 1 5 4 4 1 A. 5 B. 1 C. D. 4 Objective.0 0 5 48. Find 4B if B = 1. 4 1 4 8 49. If G = 1 and H = find G + H. 1 5 7 Objective.0 50. A tai company charges a flat rate of $1.66 plus $0.9 per mile. The total cost c is related to the number of miles. Show the relationship between these variables as a function. 51. A bank in Wilmington conducted a study to determine if it can predict the number of mistakes tellers will make during their first month of employment from the number of hours of training they receive. What is the dependent variable in the study?
5. Don s parents planted a redwood tree the day Don was born. They measured the tree s height each year on Don s birthday. The data gives four measurements. Don s Age 7 8 9 10 Tree Height 19 1 5 Assuming that the growth pattern you observe in the table does not change, find the seedling s height when Don was born? 5. The graph of y= + 1 is shown. If the line is shifted up units, which is the 4 equation of the new line? A. y= + C. y= + 4 4 B. y= + D. y= + 4 4 54. The table below shows the number of doctors in Bingham City from 1960 to 1986. If a linear regression model is fit to this data, which equation would best represent the data? (Let = the number of years after 1960.) Year 1960 1967 1970 1975 198 1985 1986 Doctors 97 511 754 417 4741 5019 510 A. y = 1.01 500 C. y = 8 + 99 B. y = 8 + 97 D. y = 8 + 944 55. The table shows the relationship between calories and fat grams contained in orders of fried chicken from various restaurants. Assuming the data can best be described by a linear model, how many fat grams would be epected to be contained in a 75-calorie order of fried chicken? Calories 05 410 0 500 510 440 Fat Grams 8 4 8 41 4 8 A. 8 fat grams C. 5 fat grams B. 7 fat grams D. fat grams Objective 4.01 56. Mark charges $50 for a private swimming lesson and $10 for a group class. One day Mark earned $190 teaching lessons. At most, how many students had private lessons? 57. A group of students are going on a field trip. It will cost $100 for the transportation plus $.75 for each student for a meal. The students have raised $10 to pay for the trip. What is the maimum number of students that can go on the trip? Write an inequality and solve.
58. How many integers are solutions to the inequality 19 < k + < 14? 59. Solve and graph on a number line 15 4 < 1 + 5. 60. Which property justifies the following statement? If a + b = 1 then (a + b) = 1. 61. Denisha bought a car for $15,000 and its value depreciated linearly. After the years, the value was $11,50. What is the yearly amount of depreciation? 6. In 1994, the average price of a new domestic car was $16,90. In 00, the average price was $19,16. Based on a linear model, what is the predicted average price for 008? A. $,969 B. $1, C. $0,77 D. $18,577 Objective 4.0 6. Which of the following is the equation of the graph? A. y = + 1 B. y = 1 C. y = 1 D. y = + 1 64. Which of the following equations has only one solution? A. 10 = 10 D. 18= 18 B. + 6 = 0 C. = 16 65. Which number is a solution of ( + ) = 5? A. 4 B. C. 1 D. 66. The dimensions of a rectangle are shown. If the area is 8 square units, what is the value of d? A. units d 1 B. 7 units C. 1 units d D. 14 units 67. If the area of a rectangle can be represented by 5, which could represent its length and width? A. ( 5) and ( 5) B. ( 5) and ( + 5) C. and 5 D. 5 and 5 68. The stress distribution on a structure is given by s = + 4 0 where s is the stress in pounds per square inch and is the distance in feet from a reference point. At what distance is the stress equal to 0?
69. Which function has a minimum value? A. y= 6+ 8 1 B. y= 8+ 5 C. y= 10+ 8 D. + y=6 70. If the area of the trapezoid is a b, which is the height of the trapezoid? A. (a + b) b B. (a b) C. 1 ( a+ b) h D. 1 ( a b) a Objective 4.0 71. The attendance at a ball game was 400 people. Student tickets cost $ and adult tickets cost $. $1050 was collected in ticket sales. Write a system of equations to model this situation in terms of the number of students, s and the number of adults, a. 7. A market charges $7.99 for a roll of 4-eposure film and $9.99 for a roll of 6- eposure film. Kim bought 9 rolls of film and spent $85.91. How many rolls of 6-eposure film did she buy? Set up a system of equations and solve. 7. What is the solution of the system y = 7 + 5 and y = +.5? 74. Suppose you have 1 coins that total $1.65. Some coins are dimes and some are quarters. Which of the following pairs of equations would you use to find out how many of each coin you have? A. 10d + 5q = 1 and 1(d + q) =1 65 B. d + q = 1.65 and d + q = 5 C. d + q = 1 and 10d + 5q = 165 D. d + q = 1 and 10q + 5d = 165 75. Write a system of inequalities for the graph to the right. 76. Last week, Reba s Reptiles Store received $1975 for selling 5 reptiles. Iguanas sell for $75 and corn snakes sell for $5. How many iguanas did Reba sell? Set up a system of equations and solve.
77. What system describes this graph? y A. 0 C. y> B. > < 0 D. y= 0 y> 0 Objective 4.04 78. On January 1, 1997, you deposited $00 in a bank account paying 5% interest compounded annually on December 1 of each year. What will the account balance be on January 1, 008? 79. Which of the following equations models eponential decay? A. y= 1 ( 4 500 ) B. y =05.( 8 ) C. y= 1 D. y=0. 004( ) 80. The population of a city can be modeled using the equation p = 40,000 9. 10 One year, the population was,60. Which of the following was the population a year later? A. 1, 58 D.,14 B. 7,60 E. 17,8 C. 19,60 81. Which is an equation of the function that is graphed? A. y = + 5 B. y = 5 C. y = 5 D. y= 5 + 8. The formula for calculating the amount A 1, after t years in a bank account that earns a compound annual interest rate r is A 1 = A 0 (1 + r) t, where A 0 is the initial amount in the account. How much money would you have in the account after 6 years if you initially deposited $800 in the account and it earns 4.5% interest annually?
8. You invest a certain amount of money. Your investment doubles each year for ten years. If you have $10,400 at the end of 10 years, what was your initial investment? A. $100 B. $00 C. $104 D. $510 84. Suppose an investment of $500 doubles in value every 15 years. How much is the investment worth after 0 years? After 45 years? 85. A population of 100 insects triples in size every month. The function 100() models the population after months. What is the population size after 6 months? 86. A population of 6000 doubles in size every 10 years; which equation relates the size of the population y to the number of 10-year periods? A. y = 6000(10) B. y = 10() C. y = 6000() D. y = (100) 87. Write an eponential model for the following situation: A population of,000,000 decreases 1.4% annually for 10 years. 88. Write an eponential model for the following situation: A $400 principal earns 7% compounded annually for 10 years. 89. The function 5(0.8) models the amount y of a 5mg dose of medicine remaining in the bloodstream after hours. How many milligrams of medicine remain in the bloodstream after 5 hours? 90. For which function will values of y decrease as values of increase? A. y = 1.5(1.5) B. y = 00(1.06) C. y = 5000(0.98) D. y = 1.0