ALGEBRA I END-OF-COURSE, Lecture notes of Algebra

Download ALGEBRA I END-OF-COURSE and more Lecture notes Algebra in PDF only on Docsity! 5 l [ l [ l [ l [ l [ l [ i ALGEBRA | END-OF-COURSE TEST PREP Practice Packet Curriculum and Instruction Division of Mathematics, Science, and Advanced Academic Programs THE SCHOOL BOARD OF MIAMI-DADE COUNTY, FLORIDA Perla Tabares Hantman, Chair Dr. Lawrence S. Feldman, Vice Chair Dr. Dorothy Bendross-Mindingall Carlos L. Curbelo Renier Diaz de la Portilla Dr. Wilbert “Tee” Holloway Dr. Martin Karp Dr. Marta Pérez Raquel A. Regalado Hope Wilcox Student Advisor Alberto M. Carvalho Superintendent of Schools Milagros R. Fornell Associate Superintendent Curriculum and Instruction Dr. Maria P. de Armas Assistant Superintendent Curriculum and Instruction, K-12 Core Beatriz Zarraluqui Administrative Director Division of Mathematics, Science, and Advanced Academic Program ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 3 of 39  6. Pauola was given the equation y = –x + 3. Which of the following is an equivalent representation of this equation? A. f(x) = –x + 3 B. f(y) = x C. y = –f(x) + 3 D. f(y) = –x + 3 7. Dr. Chait is considering joining the Garden Club. If he pays a $25 membership fee, he can buy rosebushes from the club at a reduced price of $10 each. If he does not join the club, he can buy rosebushes from a local nursery for $15 each. The graph below compares the cost of buying rosebushes from the Garden Club and from the local nursery. How many rosebushes will Dr. Chait have to buy from the Garden Club before he would begin to save money? A. 5 B. 7 C. 25 D. 75 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 4 of 39  8. Diana is driving 182 miles to Orlando for a math convention. She has already driven x miles of the trip. If Diana drives below 70 miles per hour for the remainder of the trip, which inequality best represents the amount of time in hours, t, that it will take her to complete the remainder of her drive to Orlando? A. 70 182 xt − < B. x t − > 182 70 C. x t − < 182 70 D. 70 182 xt − > 9. The average daily high temperature for the month of May in Ocala, Florida is approximated by the function f(n) = 0.2n + 80, where n is the day of the month. May has 31 days. The maximum daily high temperature occurred on May 31st . What was the maximum temperature? 10. Guy keeps track of the amount of water he uses on his flower garden over the course of the summer. He finds that the less it rains, the more he needs to water the garden to keep his plants healthy and in bloom. This summer the two driest months were June and August, but it rained so heavily in September that he did not have to water his garden at all during that month. Which of the following graphs best represents Guy’s water usage this summer? ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 5 of 39  11. Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of greater length than the speech she gave the week before. The table below shows the lengths of several of her speeches. Alyssa’s Speeches Week Number 3 4 5 6 Length of Speech (seconds) 150 180 210 240 If this trend continues, in which week will she give a 12-minute speech? A. 22 B. 12 C. 15 D. 24 12. Brock is six feet tall. He climbs a ladder to paint some trim on his house. For each rung that he climbs, Brock is 1.2 feet higher above the ground. Which equation could you use to calculate the distance, d, from the top of Brock’s head to the ground if r represents the number of ladder rungs he has climbed? A. d = 1.2r + 6 B. d = 1.2r C. d = r +6 D. d = 6r + 1.2 13. Which sequence uses the algebraic expression 4n + 5 to describe the relationship between a term in the sequence and its position, n, in the sequence? A. 4, 9, 14, 19, 24 … B. 4, 8, 12, 16, 20 … C. 9, 13, 17, 21, 25 … D. 9, 10, 11, 12, 13 … 14. Which expression is equivalent to the following expression? )()( 1364 2 1 2 −+− xxx A. 5x2 – 3x + 3 B. x2 + 3x – 6 C. 5x2 – 3x – 3 D. –x2 + 3x + 3 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 8 of 39  19. A South Dade farmer knows that the number of potatoes harvested varies directly with the number of potato plants grown. Last year the farmer harvested 189 potatoes from 9 potato plants. If the farmer plants 14 potato plants this year, how many potatoes can he expect to harvest? A. 21 B. 23 C. 294 D. 2646 20. To which of the following situations can the function y = 5x + 10 best be applied? A. The number of miles a person walks if he walks for 5 hours at the rate of 10 miles per hour B. The total weight on a scale if 5 pounds is placed there initially and a series of 10-pound weights are added to it C. The total wages earned by a waiter who is paid $5 per hour and earns $10 in tips D. The combined length of 5 boards, each 10 feet longer than the width of a doorway 21. Gemma and her cousin went to a restaurant for dinner. Gemma’s dinner cost $5 more than her cousin’s. If their combined bill was under $25, which inequality best describes the cost of their dinners? A. x + 5 < 25x B. x + (x + 5) < 25 C. x + (x + 25) < 5 D. x - (x + 5) < 25 22. The population of Williston is currently 15,400 people. If the population increases at an average rate of 325 people per year, which equation could be used to find the approximate number of years it will take for the population to reach 18,000 people? A. 15,400 + 325n = 18,000 B. 325n = 18,000 C. 15,400n + 325 = 18,000 D. 15,400n = 18,000 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 9 of 39  23. Dosset’s Mobile Service Station uses the graph below to determine how much a mechanic should charge for labor for automobile repairs. If the labor charge on an automobile repair bill was $67.50, for approximately how many hours, h, did the mechanic work? A. 2.25 < h < 2.50 B. 2.75 < h < 3.00 C. 2.00 < h < 2.25 D. 2.50 < h < 2.75 24. The gas tank in Mina’s car holds 15 gallons. Her car gets between 25 and 30 miles to the gallon. If Mina fills up the gas tank and then drives until she runs out of gas, what is the least number of miles she can drive? A. 300 mi B. 375 mi C. 405 mi D. 450 mi ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 10 of 39  25. The cost of renting a van for one day includes a flat rental fee plus a charge for each mile the van is driven while it is rented. A van that is driven 107 miles costs $97.15. A van that is driven 127 miles costs $106.15. What is the flat rental fee? A. $19.00 B. $20.00 C.  $45.00  D.  $49.00  26. At a linen sale Mrs. Earle bought twice as many pillowcases for $2 each as sheets for $5 each. If she spent less than $40, not including tax, what is the maximum number of pillowcases she could have purchased? A. 3 B. 4 C. 6 D. 8 27. Given the system of equations below: 114 1223 =− =− yx yx What is the value of y in the solution? A. -3 B. -2 C. 2 D. 3 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 13 of 39  33. Let A = {0, 1, 2, 3, 4, 5} and B = {6, 7, 8, 9} How many distinct pairs are in A x B? 34. There are 32 students in the 10th grade class. There are 15 of those students on the basketball team and 23 of those students in the drama class. Which diagram correctly shows the number of students on the basketball team, in the drama class, and in both of these activities? A. C. B. D. 35. Given the set A = {1, 2, 3} and the set B = {-3, -2, -1, 0}, what is the total number of elements in A x B? ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 14 of 39  36. The Venn diagram below shows the number of web pages that were found by using the keywords “math” and “education” on Google in spring 2005. How many millions of web sites were found that contain the work “math”? 37. Twenty-eight girls went camping. The girls were able to choose to participate in volleyball and swimming. Fourteen girls went swimming, 5 participated in both activities, and 4 girls did neither. How many girls only played volleyball? 38. Let C = {1, 4, 5, 7, 9 10}, A = {1, 9, 17}, and T = {9, 10, 13}. What is the greatest value in the set CTA ∩∪ )( ? ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 15 of 39  39. Which expression represents 6 62 4 82 x xx ))(( in simplest form? A. 2x B. 9x C. 24x D. 94x 40. Which property is illustrated by the equation ax + ay = a(x + y)? A. Associative B. Commutative C. Distributive D. Identity 41. The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert ticket sales during two class periods. If x represents the cost for each adult ticket and y represents the cost for each student ticket, what is the cost for each adult ticket? A. $20 B. $10 C. $8 D. $4 42. Given: Set A = {(–2,–1), (–1,0), (1,8)} and Set B = {(–3,–4), (–2,–1), (–1,2), (1,8)}. What is ? A. {(1, 8)} B. {(–2,–1)} C. {(–2,–1), (1, 8)} D. {(–3,–4), (–2,–1), (–1, 2), (–1, 0), (1, 8)} ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 18 of 39  49. Mike’s solution to an equation is shown below. Which statement about Mike’s solution is true? A. Mike’s solution is correct. B. Mike made a mistake in Step 1. C. Mike made a mistake in Step 3. D. Mike made a mistake in Step 5. 50. What is the y-intercept of the graph of 4x + 2y = 12? ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 19 of 39  51. Which best represents the graph of y = 2x – 2? 52. Harry determined that every time he tapped his wand the sound increased 4 decibels. He noticed that after tapping his wand three times, the sound measured 34 decibels. Which equation best represents the sound when w represents a move of the wand and s represents the loudness of the sound? A. s = 4w – 22 B. s = 4w + 22 C. s = 4w – 43 D. s = 4w = 43 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 20 of 39  53. The data in the table show the cost of renting a bicycle by the hour, including a deposit. If hours, h, were graphed on the horizontal axis, and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data? A. hc 5= B. 5 5 1 += hc C. 55 += hc D. 55 −= hc 54. (4x2 – 2x + 8) – (x2 + 3x -2) = A. 3x2 + x + 6 B. 3x2 + x + 10 C. 3x2 - 5 x + 6 D. 3x2- 5x + 10 55. The equation of line j is 6x + 5y = 3, and the equation of line q is 5x – 6y = 0. Which statement about the two lines is true? A. Lines j and q have the same y-intercept. B. Lines j and q are parallel. C. Lines j and q have the same x-intercept. D. Lines j and q are perpendicular. ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 23 of 39  61. At a local grocery store, watermelons are sold for $4 each plus an additional $0.25 per pound. Write a function that describes the relationship between x , the number of pounds of a watermelon, and )(xf , the total cost of the watermelon. A. xxf 254.)( = B. xxf 2504 .)( += C. ).()( 12504 += xxf D. ).()( 42504 += xxxf 62. If x xxf − − = 3 3 )( 2 , what is )2(f ? A. -2 B. -1 C. 1 D. 2 63. What is the solution to the inequality below? 2x−7≥15 A. x ≤ 8 B. x ≥ 8 C. x ≤11 D. x ≥11 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 24 of 39  64. A long string with a balloon at the end was tied to the ground. After a breeze came up, the balloon was 55 feet to the right of where it was tied and 30 feet above the ground, as shown in the figure below. What is the slope of the line between the balloon and the point where it was tied? A. 11 6 B. 6 11 C. 30 D. 55 65. The time that it takes to fill a fish tank depends upon the rate at which the water is flowing. It takes 40 minutes to fill the fish tank at the rate of 3 gallons per minute. How many minutes will it take to fill the fish tank at the rate of 4 gallons per minute? A. 40 12 B. 30 C. 50 D. 3 153 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 25 of 39  66. Which is an equation of a line that is parallel to line MN ? A. 2x - y = 3 B. x - 2y = 3 C. 8x + 4y = 4 D. 9x + 18y = -9 67. A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same karate class for $95. What is the total cost for 1 child and 1 adult to take the karate class? A. $60 B. $55 C. $51 D. $48 ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 28 of 39  73. What is the solution to the inequality 145 >−x ? A. x > 9 B. x > 19 C. x < 9 D. x < 19 74. Which inequality is shown on the graph below? A. B. C. D. ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 29 of 39  75. Which best represents the graph of y = 2x −2? A C B D ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 30 of 39  76. Jorge graphed the line shown below. What is the slope of the line? 77. Which expression represents y4 - 36 in simplest factored form? A. ( y2 + 4)( y2 - 9) B. ( y2 + 4)( y - 3)( y + 3) C. ( y2 + 6)( y2 - 6) D. ( y4 - 36)( y +1) ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 33 of 39  84. Solve 6 – 3(4x – 5) = 7. A. 3 4 − B. 6 7 C. 6 11 D. 3 7 85. The formula below illustrates how to calculate body mass index (B), using weight (w) and height (h). 2 703 h wB = Which of the following shows this equation correctly solved for w? A. 7032 −= Bhw B. 7032 −+= hBw C. 703 2Bhw = D. 2 703 h Bw = ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 34 of 39  86. Which graph represents the solution set for 6 5 3 2 2 1 <− x ? A. B. C. D. 87. Which graph best represents 2x – y < 10? A. C. B. D. ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 35 of 39  88. Which of the following is the graph of the function 322 −+= xxy ? A. C. B. D. ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 38 of 39  95. Let G = {1, 3, 5} and H = {5, 9}. Which of the following represents the cross product of G and H? A. G x H = {5, 9, 15, 25, 27, 45} B. G x H = {(1,5), (1,9), (3,15), (3,27), (5,25), (5,45)} C. G x H = {(5,1), (5,3), (5,5), (9,1), (9,3), (9,5)} D. G x H = {(1,5), (1,9), (3, 5), (3,9), (5, 5), (5,9)} 96. Shelly has been asked to factor the following expression completely. yxy 28136 − Which answer choice shows her completely factored expression? A. ))(( xxy 9696 −+ B. ))(( xxy 32329 −+ C. )( 28136 xy − D. )( 2949 xy − 97. Kerry wants to simplify the following: x xx 5 520 2 + Which of the following is the correct result? A. x4 B. 14 +x C. 220x D. 120 2 +x ALGEBRA I END-of-COURSE PRACTICE Division of Mathematics, Science, and Advanced Academic Programs         Page 39 of 39  98. What is the range of the relation shown in the graph below? A. All 5≤y B. All 5≤x C. All values of y D. All values of x 99. The surface area, S , of a cylinder is calculated using the formula 222 rlrS ππ += . Which equation is equivalent to this formula solved for l , the length of the cylinder? A. r Sl 1− = B. 22 2 r rSl π π− = C. r rSl π2− = D. r rSl π π 2 2 2− = 100. What is the value of x in the equation shown below? 3662 2 12 3 =++ xx x x A. 2 B. 4 C. 8 D. 16