Algebra I Regents Practice Test #1.pdf

Name ________________ Algebra I Regents Practice Test  35 Algebra 1 Regents Practice Test #1  Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial...

Name ________________ Algebra I Regents Practice Test  35 Algebra 1 Regents Practice Test #1  Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. 1 Which expression is an equivalent form of 𝑦 4 − 100? Use this space for computations. (1) (𝑦 2 − 10)2 (3) (𝑦 2 + 10)(𝑦 2 − 10) (2) (𝑦 2 − 50)2 (4) (𝑦 2 + 50)(𝑦 2 − 50) 2 Find the value of 𝑓(16) for the function 𝑓(𝑥) = 2𝑥 2 − 3√𝑥. (1) 315 (3) 500 (2) 307 (4) 523 3 Determine which of the following relations is not a function. (1) (3) (2) (4) Algebra 1 Regents Practice Test #1  4 Given the function 𝑔(𝑥) = 2𝑥 2 − 1, which of the following Use this space for functions, ℎ(𝑥), represent the result when 𝑔(𝑥) is translated 3 units computations. to the right? (1) 2(𝑥 − 3)2 − 1 (3) 2𝑥 2 + 2 (2) 2(𝑥 + 3)2 − 1 (4) 2𝑥 2 − 4 5 Which of the following expressions is equivalent to 6𝑥 5 + 8𝑥 − 3𝑥 3 + 7𝑥 7 when it is written in standard form? (1) 7𝑥 7 + 6𝑥 5 − 3𝑥 3 + 8𝑥 (3) −3𝑥 3 + 6𝑥 5 + 7𝑥 7 + 8𝑥 (2) 8𝑥 − 3𝑥 3 + 6𝑥 5 + 7𝑥 7 (4) 8𝑥 + 7𝑥 7 + 6𝑥 5 − 3𝑥 3 6 The function, 𝑉(𝑥), models the velocity of a motorcycle in meters per second, after 𝑥 seconds. Selected values from the function are in the table below. Which of the following equations and statements properly illustrate the approximate velocity of the motorcycle? (1) 𝑉(𝑥) = 4(0.65)! , and velocity is increasing (2) 𝑉(𝑥) = 4(0.65)! , and velocity is decreasing (3) 𝑉(𝑥) = 4(1.35)! , and velocity is increasing (4) 𝑉(𝑥) = 4(1.35)! , and velocity is decreasing 7 Which of the following expressions result in a rational number? (1) √2 ⋅ √18 (3) √2 + √2 (2) 5 ⋅ √5 (4) 3√2 + 2√3 Algebra 1 Regents Practice Test #1  8 A polynomial function is graphed on the coordinate plane below. Use this space for computations. Which of the following functions could this graph represent? (1) 𝑓(𝑥) = (𝑥 − 3)(𝑥 − 1)(𝑥 + 1) (2) 𝑓(𝑥) = (𝑥 + 3)(𝑥 + 1)(𝑥 − 1) (3) 𝑓(𝑥) = (𝑥 − 3)(𝑥 − 1)(𝑥 + 3) (4) 𝑓(𝑥) = (𝑥 + 3)(𝑥 + 1)(𝑥 − 3) 9 Bruno was given the following equation on his math homework. 12𝑥 2 − 7𝑥 = 6 − 2(𝑥 2 − 1) If Bruno’s first step was to write 12𝑥 2 − 7𝑥 = 6 − 2𝑥 2 + 2, which property justifies this step in his work? (1) subtraction property of equality (2) multiplication property of equality (3) associative property of equality (4) distributive property of multiplication over subtraction 10 The Little Tikes EasyScore Basketball Hoop has an adjustable height. The description on the side of the box states that the hoop can be “at least 45 inches tall, but no more than 60 inches tall.” Which inequality would model the height, ℎ, for this basketball hoop? (1) 45 ≤ ℎ ≤ 60 (3) 45 < ℎ 𝑜𝑟 ℎ ≤ 60 (2) 45 > ℎ ≥ 60 (4) 45 ≥ ℎ 𝑜𝑟 ℎ < 60 Algebra 1 Regents Practice Test #1  11 Which of the following situations could be modeled by a linear Use this space for function? computations. (1) The number of Tik Tok followers that a new artist has increases by 4.5% every day. (2) The population of a rabbit species doubles every day. (3) A concert venue allows 20 people to enter through the gates every 30 minutes. (4) The March Madness Basketball Tournament eliminates half of the teams after each round. 12 Success Academies sent a survey out to elementary school (ES) and middle school (MS) parents to see if they preferred in- person or remote learning for their scholars. The results are summarized below. In-Person Remote ES MS What percentage of parents who preferred remote learning are middle school parents? (1) 21.3 (3) 45.6 (2) 38.2 (4) 61.9 13 What is the solution to the inequality below? 4𝑥 + 2 < 2(𝑥 + 5) (1) 𝑥 > −6 (3) 𝑥 > 4 (2) 𝑥 < −6 (4) 𝑥 < 4 Algebra 1 Regents Practice Test #1  14 Which of the following statements is true about the three Use this space for functions described below? computations. (1) 𝑓(𝑥) and ℎ(𝑥) have the same zeros (2) 𝑔(𝑥) and 𝑓(𝑥) have the same y-intercept (3) 𝑓(𝑥) has a minimum, and ℎ(𝑥) has a maximum (4) ℎ(𝑥) has a maximum, and 𝑔(𝑥) has a minimum 15 Arielle is thinking of two numbers. The second number is seven less than twice the first. The sum of the two numbers is 45. Which equation could be used to find these two numbers? (1) 𝑥 + (7 − 2𝑥) = 45 (3) 2𝑥 − 7 = 45 (2) 𝑥 + (2𝑥 − 7) = 45 (4) 𝑥 = 2𝑥 − 7 Algebra 1 Regents Practice Test #1  16 The number of freshmen enrolled at Medaille College during four Use this space for different years is recorded in the table below. The year 2013 computations. represents 𝑥 = 0. The enrollment estimates 𝐸(𝑥), for these years can be modeled by the function 𝐸(𝑥) = 𝑎𝑏 ! , where 𝑏 is rounded to three decimal places. Which of the following statements about 𝐸(𝑥) are true? I. 𝑎 = 3810 II. 𝑎 = 4224 III. 𝑏 = 0.035 IV. 𝑏 = 1.035 (1) I and III (3) II and III (2) I and IV (4) II and IV 17 Which of the following is an equivalent form of the trinomial 𝑥 2 − 14𝑥 + 49? (1) (𝑥 − 7)2 (3) (𝑥 − 7)(𝑥 + 7) (2) (𝑥 + 7)2 (4) (𝑥 − 7)(𝑥 + 2) 18 Which of the following points would not be on the graph of the function 𝑓(𝑥) = 𝑥 2 − 3𝑥 + 4? (1) (0, 4) (3) (5, 14) (2) (1.5, 1.75) (4) (−1, 6) 19 Which of the following sequences are arithmetic? I. 2, 4, 6, 8, 10... II. 2, 4, 8, 16, 32... III. 𝑎, 𝑎 + 2, 𝑎 + 4, 𝑎 + 6, 𝑎 + 8... (1) I and II (3) II and III (2) I and III (4) I, II, and III Algebra 1 Regents Practice Test #1  20 Carmelo opens a lemonade stand in front of his apartment Use this space for building. The profit from his stand can be modeled by the computations. function 𝐿(𝑐) = 0.82𝑐 where 𝑐 corresponds to the number of cups of lemonade that he sells. What is an appropriate domain for this function? (1) an integer ≤ 0 (3) a rational number ≤ 0 (2) an integer ≥ 0 (4) a rational number ≥ 0 21 What are the roots of the quadratic equation 𝑥 2 − 5𝑥 − 4 = 0? (1) 1 and 4 (3) –1 and –4 5± 41 #5±√41 (2) √ (4) 2 2 22 How many real solutions does 4𝑥 2 + 2𝑥 + 9 = 0 have? (1) one (3) zero (2) two (4) infinitely many 23 The amount of a radioactive element can be modeled by the function 𝑟(𝑡) = 1000(0.98)" , where 𝑡 represents the time since the element started decaying, and 𝑟(𝑡)represents the amount of the element, in grams. What is the rate of decay of the element? (1) 98% (3) 0.98% (2) 2% (4) 0.02% 24 Evergreen trees grow the most during spring months. In May, these trees have been known to increase in height by up to 91 centimeters per day. Convert this measurement into inches per hour. (1) 1.49 (3) 9.63 (2) 3.79 (4) 35.83 Algebra 1 Regents Practice Test #1  Part II Answer all 8 6 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 25 Solve the equation below algebraically. 2 6 − (𝑥 + 5) = 4𝑥 3 Algebra 1 Regents Practice Test #1  26 𝐹 = 4𝑥 2 − 3𝑥 + 1 and 𝐺 = −2𝑥 2 + 5. Find the trinomial that represents 𝐻, if 𝐻 = 3𝐺 − 𝐹. Algebra 1 Regents Practice Test #1  27 Algebraically determine the zeros of the function 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 3. Algebra 1 Regents Practice Test #1  28 In February 2021, the state of Texas saw one of the worst snowstorms in its history. Snowfall totals recorded in Dallas, TX are shown in the table below. Dallas, TX Which of the following intervals had the greatest rate of snowfall, in inches per hour? 1 a.m. to 12 noon or 6 a.m. to 3 p.m. Justify your answer. Algebra 1 Regents Practice Test #1  $% % 29 The gravitational force between two objects can be calculated using the formula 𝐹# = &12 2. In the formula, 𝐺 is called the gravitational constant. The variables 𝑀1 and 𝑀2 represent the masses of the two objects between which the force is being measured. Lastly, 𝑟 is the distance between the objects. Solve for the positive value of 𝑟, in terms of the other variables. Algebra 1 Regents Practice Test #1  30 Four Seasons Landscaping is creating a rectangular flower bed at a customer’s home. The width of the flower bed will be half of the length. The total area of the flower bed is 38 square feet. Write and solve an equation to determine the width of the flower bed to the nearest tenth of a foot. Part III Algebra 1 Regents Practice Test #1  Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. 31 A couple planning a backyard wedding is researching different tent rental companies for their event. They contact two different companies. Buffalo Party Rental charges a $50 set-up fee, and $5 per square foot of tent space. Tent Genie charges a $25 set-up fee, and $6 per square foot of tent space. Write an equation for Buffalo Party Rental that could be used to determine the total cost 𝐵, when 𝑥 square feet of tent space is ordered. Write a second equation for Tent Genie that could be used to determine the total cost 𝑇, when 𝑥 square feet of tent space is ordered. Determine algebraically and state the minimum square feet, rounded to the nearest square foot, of tent space that must be ordered for Buffalo Party Rental to be the cheaper option. Algebra 1 Regents Practice Test #1  32 Graph the two functions on the coordinate plane below. Find all values of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥). Algebra 1 Regents Practice Test #1  33 The table below shows the number of hours ten different scholars at Marion P. Thomas Middle School spent studying and their scores on a recent history test. Write the linear regression for this data set. Round all values to the nearest hundredth. State the correlation coefficient rounded to the nearest hundredth. Explain what the correlation coefficient suggests in the context of the problem. Algebra 1 Regents Practice Test #1  34 A system of inequalities is graphed on the coordinate plane below. Write the system of inequalities that is represented by the graph above. What does region A represent? What does the gray region represent? Part IV Algebra 1 Regents Practice Test #1 Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. 35 The CoinStar machine at the local supermarket is broken. Instead of providing the exact number of each type of coin that is deposited, the machine can only display the total number of coins and total value. The machine shows 90 coins, with a value of $17.55. If Mr. Rogers only placed dimes and quarters in the machine, write a system of equations in two variables, or an equation in one variable that could be used to model this situation. Using your equation or system of equations, algebraically determine the number of quarters Mr. Rogers deposited in the machine. Algebra 1 Regents Practice Test #1  Mr. Rogers’ neighbor replaced each one of his dimes with a quarter. If he uses all of his coins, determine if Mr. Rogers would have enough money to buy a cardigan priced at $20.98 if he must also pay an 8% sales tax. Justify your answer. Algebra 1 Regents Practice Test #1 Algebra 1 Regents Practice Test #1