Algebra 1 Semester 1 Final Exam Study Guide PDF

Name:_________________________________________________ Period:_________ Key Algebra 1 Semester 1 Final Study Guide You may use a scientific calculator or the Desmos test mode (scientific) app (NO GRAPHING) 1. Select...

Name:_________________________________________________ Period:_________ Key Algebra 1 Semester 1 Final Study Guide You may use a scientific calculator or the Desmos test mode (scientific) app (NO GRAPHING) 1. Select all the equations that are equivalent to: 2" + 8 = 15 ABF mult alltermsby 2 0 a. −30 = −4" − 16 b. 2" + 8 − 8 = 15 − 8 frombothsides of equation subtract 8 c. 0.5(8" − 4) = 15 ifdistribute 4 2 15 only doubled 2xand15 needtodouble 8 aswell d. 4" + 8 = 30 ! e. 15 = " (4" + 16) + 2 distribute is equivalent but extra 2 on the right f. −2(−" − 4) = 5 − 3" + 8 + 3" + 2 distribute combine like terms 8 I initialvalue D 2. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, y, after x days. height losing L a. 1 = 34" +.050 decreasing KEY b. 1 = 0.5" + 34 c. 1 = 0.5" − 34 O d. 1 = −0.5" + 34 3. Using your equation from question 2, In what will the water level be after 16 days? Y 34 let x 16 99 26k 26 B 4. Hailey has saved up $225, but is spending $15 a month on a gym membership. After how many months will take she have $165 left? decrease by15 165 15 225 a. 3 months 225 4 15 225 225 0b.c. 4 months 15181s let 165 5 months d. 10 months 4months X 5. Identify the slope of each of the following lines. a. −2" + 31 = −10 b. 5" + 21 = 3 c. 3" − 31 = 6 2x 2x SX SX 3x 3x 34 25 5 21 2 3 Ez y 52 32 2 4 33 13 y 1 shope Z stopeff sto  Use the graph to answer questions #6-8 6. What is the vertical intercept (y-intercept)? B a. 150 0,140 Intercept 0b. 140 Yi c. 70 d. 80 2 slope 78 2 7. What is the slope of the graph? B a. −20 b. −2 ! c. − " ! d. − "# 8. Select all the statements that are true: a. As the number of adult tickets increases, the number of children tickets increases. b. As the number of adult tickets decreases, the number of children tickets also decreases. c. As the number of adult tickets increases, the number of children tickets decreases. 8d. The number of children tickets decreases at a rate of 2. e. When no children tickets are purchased, 140 adult tickets were purchased. f. When the number of children tickets decrease by 20, number of adult tickets decreased by 10. 9. Write the equation of the line that passes through the points (−2, 5) and (3, −1). B a. 1 = − % " + " $ & % !& slope m 22 2 y 5 651 2 O b. 1 = − $ " + point use as I fi $ % "& g pt.slopeformy c. 1 = $ " − $ y MCxx $ ' d. 1 = " − % " 10. Write the equation of the line that passes through the points (1, −3) and (4, −3). A Y Y H Oa. 1 = −3 b. 1 = 3 c. " = −3 g d. " = 3 11. Write the equation of the line that passes through the points (−2, −3) and (−2, 4). Yet redslope 12. Write the equation of the line that passes through (0, −1) and is perpendicular to the line shown? Givenline slope 32 1m 23 opposite fTa e 2n newline1m 23 3 newline point 10D ftp.gffffn.fi 4 3 6 13. Consider the equation −" + 21 = −8. For each question, explain or show your reasoning. a. If we graph the equation, what is the slope of the graph? 24 28 4 1 4 stope 4 1 E b. Where does the graph intersect the y-axis? ePt vq.IE ob D 0i4 8,4 4 c. Where does it intersect the x-axis? notYnÉe o 18,0J 8 14. Solve the equations: a. −3(23 − 3) = 25 − 83 b. −3" −3(−4" + 2) = 2" − 27 distribute distant 25 3 12 6 2 27 sep cs 6 27 1 4 I 7 28 I t.EE 4 15. Which linear system has exactly one solution? 1 =− "+7 " 3" − 21 = 4 gffin 1 = −2" + 6 3" + 51 = 2 a. 5 & b. 2C " c. " d. # 0 ( 1 =− "+7 & 6" − 41 = 8 1 = −2" − 5 −6" − 101 = 4 Taifferent slopes 8 44 Imesures 4 Pariftions manysolutions Pi 1 = −2" + 10 16. Solve the system of equations: 6 3" − 41 = 15 set.pt ubstitution s's In a s I could solve by elimination as well 1500 1 214" 2" + 31 = 10 17. Solve the system of equations: 6 + 61 = 15 sedimentation because set up 4 we 0 5 false statement nosolutionsf 216"3"−−4121==126 18. Solve the system of equations: 6 0 0 truestatement Infinitsolutions A gift Ie  19. Solve the inequalities: 14 172 3 !) &*+!" , &,-$ a. 84 < 4(1 + 4") b. − " ≥ ( c. ( −2≤ !" 84424 16 1214 2112 5112 1912 3 12 38 3 12 3h 24 3h 5 12 12 3h 3h Six 24 5 truestatement fff infnftymm.FI 20. Select all values that make the inequality true. M− ") < 3" + 6 −2(−4 6 MBEO a. " = 10 8T 34 b. " = 4 0 8 6 c. " = 2 6 6 d. " = −1 22 X e. " = 5 2 all valuesfor greater than 2 21. Select the inequality that matches the graph negativeslope ) D a. 1 ≤ − $ " + 5 If ) b. 1 < − $ " + 5 dashed ) c. 1 ≥ − $ " + 5 FLsive ) d. 1 > − $ " + 5 O  22. Select all the points that are solutions to the graph. CIF t a. (2, 0) onelineis dashed or not inclusive b. (0, 0) not in shadedarea 2,0 c. (0, −1) boundry ofshadedregionand solid inclusive co 4 0 45 d. (0, −4) oneline is dashed or not inclusive e. (−1, 3) shadedarea not in inshadedarea f. (−4, −5) bothnot orequalto so fathed 1 −2" A 0a. b. c. d. need F fa.int 24. Write a system of linear inequalities for the shaded region on the graph to the right. If Inequalities equations 1,4 4 2 4 2 1017 1112 stifferthan we's net dashedline so 25. Which of the following coordinates is a solution to the system of inequalities from the graph above (problem #24)? shadedarea a. (0, 0) not in a solution to b. (0, 2) only on a line y 2 notincluded in 4 2 and not line c. (1, 2) State intersection.sn sooEItoY unInnfot1Ysi if s've p the d. (1, 4) on thesolidlinefor and above in shadedareafor 4 2 26. You are managing a community garden and need to allocate space for growing two types of crops: tomatoes (T) and carrots (C). The available garden space is limited, and you want to ensure a balanced distribution. A Each square meter of tomatoes requires 2 hours of sunlight, and each square meter of carrots requires 3 hours of sunlight. The total sunlight hours available each day is 18 hours, and you have a maximum of 20 square meters of space. Which system of inequalities represents the constraints for the allocation of garden space for tomatoes and carrots? 2= + 3> ≤ 18 0 a. < = + > ≤ 20 Lgnf 2T 3C 18 2= + 3> ≥ 18 b. < = + > ≥ 20 3= + 2> ≤ 18 sq meters T C 20 c. < = + > ≤ 20 of space 3= + 2> ≥ 18 d. < = + > ≥ 20  27. This scatter plot shows the relationship between the weight of gravel in pounds and the cost in dollars. Which best describes C the relationship between the variables? a. No correlation b. Negative correlation O c. Positive correlation Use the graph to answer questions #28-29. 28. What does the slope represent? B a. The age that number of email decreases. Ob. The average number of emails decreases by for every one year. c. The years decrease by for each email sent. d. The total number of emails for each age. 29. Select all the statements that are true ABP $ a. Typically, the number of emails goes down by !" every year. 8b. 12 year olds typically get 30 emails a day. but there theft c. The correlation coefficient appears to be close to -0.5yesnegative 1 99 0 d. All of the emails received by 49-60 year olds was more than the number of emails received by 61-72 year olds.  30. Which of the functions best represents the equation of the line of best fit? B a. 1 = −0.5" + 17.5 graph haspositiveslope slope Amount of Bills 0b. 1 = 0.4" + 17.5 49 c. 1 = 2" + 18 bothslopestoolarge d. 1 = 4" + 17 Age (in years) Use the following information and table for questions #31-34 x 2.5 2.8 2.3 3.5 2.5 1.2 1.1 (gallons bought) y 10 11 9 13 7 5 4 (dollars spent) The table represents the number of gallons of gas purchased and the cost at 7 different gas stations. The data in the scatter plot suggests a linear association. A student put the data into the desmos graphing calculator and performed linear regression. 31. Using this information, write the equation of the line of best fit. Round values to the nearest hundredth (2 decimal places). 4 3.60 0.25 Write your equation on the line _______________________________________________ 32. What does the slope mean in terms of the situation? forevery 3.60 spent you canbuy 1 additional gallonofgas r 0.95 33. Identify the correlation coefficient: __________________________________ 34. Is the correlation between the variables: a. strong -OR- weak b. positive -OR- negative  35. The linear regression equation 1 = 2.15" + 63.75 represents the relationship between the number of D pages read and the reading comprehension score for students in Mr. Smith's literature class. Predict the reading comprehension score for a student who has read 10 pages. a. 2.15 10 b. 21.5 4 2.15 6 63.75 c. 63.75 d. 85.25 21.5 63.75 85.25 36. Given the equation: Q(") = −3" + 25, when is Q(") = 100? 100 3 25 25 25 3 256 4 15 5 37. Given the equation: Q(") = −2" + 30, find Q(") when " is −10. f 107 2610 30 20 30 f 10 50 Use the following situation to answer questions #38-40 Liam is working part-time during the summer to earn money in addition to his monthly allowance. Liam earns $12 per hour at his job, and his weekly allowance is $15. 38. Which function, R, represents theinitial amount total Liam earns in a week as a function of the hours he works, ℎ? Fyffe B a. R(ℎ) = 15ℎ + 12 O b. R(ℎ) = 12ℎ + 15 c. R(ℎ) = 27ℎ d. R(ℎ) = 27 + ℎ 39. What does the expression R(3) represent in this situation? The amount of money Liam earns afterworking 3 hours 40. What does the equation R(4) = 63 represent in this situation? Liam earned 63 after he worked 4 hours  41. Function T is the percentage of homes in the United States that have a landline phone in year U. Function > is the percentage of homes with only a cell phone. Here are the graphs of T and >. Select all true statements. ACID O 0,110 EF a. T(2006) > >(2006) 0 20061 b. T(2012) < >(2012) 8,80 for fanC O c. T(2008) = 80 0d. T(2015) = >(2015) 2006,4200 Oe. When U = 2012, T(U) = 60 O f. T(2004) = 95 g. >(2004) = 20 h. There are two values of time where Functions H and C have the same percentages. 42. Identify the domain and range of the linear function graphed. Be sure to use interval notation. x x Domain:__________________ Range:___________________ x x maxheight 55 43. The graph shows the attendance at a sports game as a function of time in minutes. a. What is the domain? Yefftion 0,70 b. What is the range? 0,55 44. Determine if the graph to the right is increasing or decreasing and if it is linear or exponential. a. Increasing Linear AO b. Decreasing linear c. Exponential growth d. Exponential decay  45. Determine if the graph to the right is increasing or decreasing and if it is linear or exponential. a. Increasing Linear b. Decreasing linear c. Exponential growth 0d. Exponential decay 46. Is the function 1 = 0.01(1.2)* an example of exponential growth or exponential decay? Factor 1 growth 47. Is the function 1 = 3(0.8)* an example of exponential growth or exponential decay? factors 1 decay 48. What is the equation of the asymptote for each function below? verticaltranslation amount added subtracted to function " * ! a. 1 = & (2)* b. 1 = 1.5(0.5) + 1 c. 1 = ( (4)* − 2 4 0 41 y 2 Exp functions have horizontal asymptotes boundaryline All horizontal lines are the equation y 49. When a new car is purchased, it begins to lose its values as soon as it leaves the car lot. Each year it loses 1/10 of its value. The table represents the value of the car for the following years after it has been decays purchased. Write an equation that shows the cost of a car, >, after each year 1? 1 0 1 2 3 y 40,000 Equation:__________________________ >(1) 40,000 36,000 32,400 29,160 480 Y.fTing this IE copaI 3mgrowfatfor 50. A bacteria population is 5,000. It triples each day. Write an equation relating the bacteria population, b, and the number of days, d, since it was measured to be 5,000. initialamount 0 3 d  Use the following information for questions #51-53 The value of a home in 2015 was $400,000. Its value has been doubling each decade. The equation W(X) = 400,000 ∙ 2. represents the value of the home, in dollars, in terms of d, the number of decades since 2015. 51. What does 400,000 represent in this context? the intial starting value of the home in 2015 52. What does the 2 represent in this context? The growth factor the value of the home doubles every decade 3 400,000 2 After3 decades the 53. What was the value of the home in the 3 decades later? 4001000 8 let d 3 3,200,000 Use the following information for questions #54-56 fy f ! / The remaining amount of a radioactive substance is represented by the equation Z(U) = 300 ∙ [ \ where U is the time " in years since the substance was initially measured. 54. What does 300 represent in this context? Theamount of radioactive substance when we first started measuring initialamount ! 55. What does the represent in this context? " Thedecayfactor the radioactive substance will half eachyear 56. How much radioactive substance is left 4 years after the substance was initially measured? Let t 4 A4 300 E Therewould be 18.75 radioactive 300 substanceremaining 4 years 18.75 after it was initially measured  Use the following information and table for questions #57-59 X (time in minutes) 0 4 10 15 18 24 29 y (temperature in 178.4 167.6 148.3 141.7 133.5 122.2 115.9 ℉) initialamount The table represents the cooling temperatures, in ℉, of a freshly brewed cup of coffee after it is poured into a cup after x minutes. decayfactor The data in the scatter plot suggests an exponential association. A student put the data into the desmos graphing calculator and performed exponential regression. 57. Using the information given, write the equation of the curve of best fit. Round values to the nearest hundredth (2 decimal places). Y 176.55 0.99 58. What does the initial value tell you about the situation? After 0 minutes orwhenthecoffeewasbrewed the temperature ofthe coffee wasabout 176.55 F 59. What does the growth factor mean in this situation? Fay Everyminute there is 991 of the previous temp remaining