You will be provided with the BCR/ECR scoring rubrics in your exam booklet. Your teacher can provide you with a copy.

Transcription

1 The Algebra 1 Semester B eamination will have the following types of questions: Selected Response Student Produced Response (Grid-in) Brief Constructed Response (BCR) Etended Constructed Response (ECR) Short Answer A calculator may be used on the eam. You will be provided with the BCR/ECR scoring rubrics in your eam booklet. Your teacher can provide you with a copy. The formulas below will be provided in the eamination booklet. Equations of a Line Standard Form: A + By = C where A and B are not both zero Quadratic Formula, Slope-Intercept Form: where m = slope and b = y-intercept Point-Slope Form: where m = slope, where Eponential Equations General Eponential Equation: Slope Formula Let and be two points in the plane. Eponential Growth Equation: Eponential Decay Equation: slope = MCPS

2 1. A catering company provides food for three family reunions on July 4 th every year. The matrices below represent the number of hamburgers and hot dogs ordered by three families in 009 and 010. Families Year 009 Year 010 Hamburgers Hot Dogs Hamburgers Hot Dogs Arnold Arnold Baker 40 5 Baker Carroll 15 0 Carroll 51 8 Families a. Write a matri that represents the total number of hamburgers and total number of hot dogs that each of the three families ordered for the years 009 and 010. b. How many more hot dogs did the Baker family order in 010 than in 009? c. The catering company predicts that in 014, each family will order five times as many hamburgers and hotdogs as they ordered in 010. Based on this prediction, write a matri that will represent the total number of hamburgers and total number of hot dogs each family will order in Stephan bowled 160, 180, and 15 in his first three games. What score would Stephan have to bowl in his fourth game for his 4-game BCR average to be 180? Eplain how you determined your answer. Use words, symbols, or both in your eplanation. 3. Jack plays basketball. After 9 games he is averaging 19 points per game. If represents the number of points that he scores in his tenth game, which of the following inequalities represents how many points that he must score in his 10 th game in order to average at least 0 points per game? A 0 B 0 C 9 D 9 MCPS

3 4. The bo-and-whiskers plot below show the number of hours Suchita worked each week for 5 weeks True or False: Justify your answer. a. The range is 7 hours. b. The interquartile range is 1 hours. c. Suchita worked the same number of weeks 14 hours or less as she did 5 hours or more. d. Suchita worked eactly 4 hours for 6 of the 5 weeks. 5. The bo-and-whiskers plots below show the points scored by two basketball BCR teams over the course of a season. DUKE Points MARYLAND Derek looked at the plots and stated that he thought that Maryland was the higher scoring team during the season. Is this a valid conclusion? Use mathematics to justify your answer. Give more than one reason. 6. Bobbie is making a sandwich. She can use one of four types of bread; rye, wheat, Italian, and white. She can make the filling either peanut butter, turkey,or tuna fish. Finally, she can toast the bread, or not toast the bread. How many ways can Bobbie make the sandwich? MCPS

4 7. The tree diagram below shows the ways that Jane can get dressed. Brown Skirt White Skirt Red Blouse Green Blouse Blue Blouse Red Blouse Green Blouse Blue Blouse Gray Shoes Black Shoes Gray Shoes Black Shoes Gray Shoes Black Shoes Gray Shoes Black Shoes Gray Shoes Black Shoes Gray Shoes Black Shoes a. How many different outfits of a skirt, blouse, and shoes can Jane wear? b. What is the probability that Jane will wear a white skirt, green blouse, and black shoes? 8. The Ice-Cream Shoppe states that you can get 40 possible sundaes consisting of one scoop of ice cream, a fruit topping, and either chocolate or caramel syrup. If there are 8 different fruit toppings, how many different flavors of ice cream can you get? 9. A bubble gum machine has 50 gumballs inside. There are red, 14 blue, 9 green, and 5 white gumballs. A child chooses one gumball at random. a. What is the probability that the gumball chosen is white? b. What is the probability that the gumball chosen is NOT green? MCPS

5 10. Bill recorded the color of the traffic light in front of his school when he arrived. The table below shows the results. Color Frequency Red 1 Yellow 3 Green 5 a. Based on the results in the table, what is the probability that the light will be red when Bill arrives? b. Bill goes to school 180 days in a school year. Based on the results in the table, how many days will the light be red when he arrives? 11. Louisa is interested in buying a scratch-off lottery ticket. She knows that a lot of her friends have bought the same ticket and has collected data. The chart below shows how many tickets have won each cash prize. Cash Prize Number of tickets $0 7 $1 18 $5 11 $10 3 $0 1 a. Based on the results of her data, what is the probability that Louisa will win at least $5? b. Louisa plans to buy 1 tickets. Based on the data above, how many tickets will win a cash prize of at least $5? c. Based on the results of her data in the table above, what is the total amount of cash won by her friends? 1. State whether each of the following sampling methods would provide a simple BCR random sample of 50 college students? Use the criteria for simple random sampling to justify your answer. Survey the first 50 students to enter the math building in the morning. Obtain a list of alphabetically assigned student ID numbers, and then select every 5 th student on the list until there are 50 students. Place the name of each student in a hat, and then draw 50 names. MCPS

6 BCR 13. Jack and Jill surveyed students in their school to estimate how many students listen to classical music. Jack s sample was to randomly select 50 orchestra students. Jill s sample was chosen by selecting students randomly from a list of all students in the school. Will Jack or Jill s sample be more likely to be representative of the school s population? Use mathematics to justify your answer. 14. The table below shows the results of Jill s survey from item 13. BCR Number of Students Who Number of Students Who Listen to Classical Music Do Not Listen To Classical Music Based on the results of the survey, if a student is chosen at random, what is the probability that a student listens to classical music? Eplain how you determined your answer. Use words, symbols, or both in your eplanation. Based on the results of the survey, if there are 800 students in her school, predict how many students listen to classical music. Eplain how you determined your answer. Use words, symbols, or both in your eplanation. 15. Hairless in Seattle, Inc. is marketing its hair growth cream. The two graphs below are being considered for use in magazine ads. 4 Graph One Hair Growth Cream 1.8 Graph Two Hair Growth Cream Hair Length (inches) 3 Hair Length (inches) Time (weeks) Time (weeks) The two graphs represent the same information. Why do the two graphs look different? MCPS

7 16. On the first 5 weeks of a job, Nancy earned $50, $50, $80, $90, and $300. Which measure of central tendency is best representative of Nancy s weekly income? Eplain your answer. 17. Nathan is conducting a simulation concerning seniors who ride a bus to school. He chooses to use a random number table with digits 0 9, where 0, 1,, and 3 represent a senior who rides a bus to school and 4, 5, 6, 7, 8, and 9 represents a senior who does not ride a bus to school. Based on this digit assignment, what is the probability that a senior rides a bus to school? A 6% B 30% C 40% D 60% 18. Describe a model you could use to simulate a probability that 5% of all students go to the movies each week. 19. Mr. VanDorn states that there is a 30% chance that a student is tardy to his class. Which of the following model(s) can be used to simulate this probability? A A random number table with digits 0 9 where 0, 1,, 3, 4, 5, and 6 represent a student that is tardy and 7, 8, and 9 represent a student who is not tardy. B C D A random number table with digits 0 9 where 0, 1,, 3, 4, and 5 represent a student that is tardy and 6, 7, 8, and 9 represent a student who is not tardy. A random number table with digits 0 9 where 7, 8, and 9 represent a student that is tardy and 0, 1,, 3, 4, 5, and 6 represent a student who is not tardy. A si-sided die where 3 represents a student that is tardy. For items 0 and 1, rewrite each polynomial in standard form MCPS

8 For items through 7, simplify. Your final answer should have only positive eponents y y 4. y 3 3 y y y y y y 3 y 3 3 For items 8 through 31, add or subtract as indicated m 6m1m m t 3t9 3t 4t 17 For items 3 through 39, multiply or divide as indicated y3 5y y 16 y 3 y 8y MCPS

9 40. Look at the rectangle below. 3 1 Which epression below could represent the perimeter of the rectangle? A 8 B 4 1 C D Look at the rectangle below. Which epression below could represent the area of the rectangle? A B C D Look at the figure below. Write an epression in terms of for the area of the shaded region. MCPS

10 43. Which binomial below is a factor of 1? A 4 B 3 C 3 D 6 For items 44 through 51, factor each of the following completely y 15 y a 14a For items 5 through 57, solve r t 10r9 0 6t MCPS

11 58. Let f 54 a. Sketch the graph of f below. Indicate the location of the vertices and all - and y- intercepts. y O b. Using the graph, write the verte form of the equation of the parabola. c. What are the zeros of the function? d. Write the equation for the ais of symmetry. MCPS

12 f Let a. What is the verte of the graph? b. What is the equation of the ais of symmetry of the graph? c. What is the y-intercept of the graph? d. What are the -intercepts of the graph? e. What are the zeros of the function? f. Write this function in verte form. You may choose to use your calculator or complete the square. 60. Look at the graph of the function g below. It is a translation of the graph of the parent function, f. g() a. Describe the translation of the graph from the parent function, f. b. Write an equation for g in verte form. c. Write an equation for g in standard form. d. What are the zeros of g? e. On what interval is g increasing? f. What is the equation of the ais of symmetry of the graph of g? MCPS

13 61. What is the equation of the ais of symmetry for the graph of the parabola represented by y 7 5? 6. What is the verte for the graph of the parabola represented by A 5, 6 B 5,6 C 5, 6 D 5,6 63. Jack kicked a football. The height, ECR y 4 5 6? htin feet, of the ball after t seconds is given by the quadratic function. ht () 16t 50t. Does the ball reach its maimum height at t seconds? Use mathematics to justify your answer. After how many seconds does the ball hit the ground? Eplain how you determined your answer. Use words, symbols, or both on your eplanation. 64. An animal makes a leap into the air. A function for the height ht, in meters of the animal s feet above the ground after t seconds is given by ht 5t 1.5t. a. What is the maimum height that the animal s feet reach? b. How long is the animal in the air? MCPS

14 65. The graph below represents y y Look at the graphs, labeled I, II, III, and IV below I y II y III y IV y Match the equations listed below with the graphs I, II, III, and IV above. 1 y y y 5 y MCPS

15 66. Complete the table below so that it represents an eponential function f Look at the eponential function graphed below. y a. Complete the values for the function in the table below f b. Write the function rule for the graph. c. Is the function increasing or decreasing? d. Is the function continuous? e. What is the domain of the function? f. What is the range of the function? g. What is the equation of the asymptote of the graph? MCPS

16 68. Look at the two functions below: f 43 g Which of the following statements are true? 57 I f is increasing at a faster rate than g. II The y-intercept of f is less than the y-intercept of III A I and II only B I and III only C II and III only D I, II, and III 69. Let f g. The graphs of both functions have the -ais as their asymptote Describe what happens to the values of the function as the 6 values of increase. Your answer should have two conclusions. 70. Let f 65. Describe what happens to the values of the function as the values of increase. MCPS

17 71. Sheila had 048 marbles. She gave marbles to her sister each day. The table ECR below shows the number of marbles Sheila had left after each day. # of Days d Number of marbles left Nd Write a function for the number of marbles remaining after d days. How many marbles will she have left after the 6 th day? After what day will she have marbles left? Eplain how you determined your answer. Use words, symbols, or both on your eplanation. As the value of d increases, what happens to the number of marbles? For items 7 through 74, classify each function below as linear, eponential, or quadratic. Use mathematics to justify your answers. 7. y 73. y 74. y A house was purchased for $00,000. It increases in value by 4% per year. a. Write an eponential function that gives the value (V) of the house t years after it was purchased. b. What is the value of the house 3 years after it was purchased? 76. A pool table was purchased for $,400. It depreciates (loses value) by 1% per year. a. Write an eponential function that gives the value (V) of the pool table t years after it was purchased. b. What is the value of the pool table 5 years after it was purchased? MCPS

18 Use the following graphs to answer items 77 and Complete the following with the correct type of function. a. f is a(n) function. b. g is a(n) function. c. h is a(n) function. d. j is a(n) function. 78. Which of the functions f, g, h, and/or j : a. have a domain of all real numbers? b. have a range of all real numbers? c. have a verte? d. increase on some interval? e. increase on the entire domain? f. decrease on some interval? g. decrease on the entire interval 1? h. are continuous? i. have a vertical ais of symmetry? MCPS

19 79. The curve of best fit on the scatter plot below shows the number of petals on a daisy as a function of time. Number of Petals on a Daisy As Time Passes Number of Petals Time (Days) a. According to the curve of best fit, when will the daisy have only 0 petals remaining? b. According to the curve of best fit, how many petals will be remaining after day one? 80. The amount of time it takes to complete a job varies inversely with the number of people on the job. If it takes 10 people a total of 15 hours to do a job, how long will it take 6 people to do the job? 81. The amount of time it takes for a car to travel one mile varies inversely with the average speed of the car. If it takes 60 seconds for a car averaging 60 miles per hour to travel one mile, how long will it take for a car averaging 75 miles per hour to travel one mile? MCPS

20 8. A weather station recorded the wind speed over a eight-hour time period as a hurricane approached. The graph shows the wind speed W as a function of time t where t is the number of hours since midnight. At t 8, the instrument for measuring the speed of the wind was destroyed. Wind Speed (in miles per hour) Time (in hours) since midnight (t) a. What is the domain of this function? b. What is the range of this function? c. What is the maimum value of this function? MCPS

21 83. A stock is being traded on the New York Stock Echange (NYSE). The price of the stock goes up and down as the day goes on. The net change C, in dollars per share, is graphed below as a function of the time t, in minutes, since the stock market opened. The graph below represents one day s trading. 5 4 Net Change in Price, in dollars per share C Time, in minutes, t 4 5 a. What is the domain of this function? b. What is the range of this function? c. What are the zeros of this function? d. What is the minimum value of this function? MCPS