ALGEBRA II 2016 Summer Packet

Transcription

1 ALGEBRA II 016 Summer Packet Introduction: This summer packet is intended to help prepare you for the new version of the math portion of the SAT Test, as well as to review important basic algebra and geometry topics prior to your Algebra II class next school year. Some of the questions may deal with topics unfamiliar to you, but you should use your prior knowledge to try to answer each question. Expectations: You may print out the questions if you choose, but you can certainly work on the packet without doing so (to save paper). The packet itself will not be handed in. You are to do all of your work on lined notebook paper, in pencil, in the order in which they appear in the packet, with your answer clearly indicated. Please be neat and organized. The questions were drawn from a variety of sources, and so they may seem to be numbered a bit oddly. On your paper, number them with the large number at the top of the page followed by the question number. For example, the first question in the packet would be -1. Although many of the questions are multiple-choice, you are to show your work and/or write an explanation for each of your answers. Simply giving the letter of your answer (or just the answer for open-ended questions) will not be acceptable. Your work will be collected on the first day of class, and will be graded based on effort, amount of detail, organization and neatness. Your grade will not be based on the number of correct answers however, we will review the correct answers over the course of the year. The grade for the packet will be worth the same as a test grade.

2 Unapproved reproduction or distribution of any portion of this material is unlawful. 1. If p = 5.5, what is the value of p 1 p? (A) 1.5 (B) 1 (C) 5.5 (D) If (3x + )(5x + 1) = ax + bx +, what is the value of a b? (A) (B) 8 (C) (D) 8 y 4. Leo is manufacturing 1 meter rulers. If the ruler differs from the expected length by more than 1 mm, he needs to throw it away. If x is the length of the ruler in meters, what absolute value inequality represents the rulers that Leo does NOT throw away? O x (A) x (B) x (C) x (D) x Which of the following equations best describes the function in the figure above? (A) y = x + (B) y = x (C) y = x + (D) y = x 5. If x = 0.1, what is the value of x 4? (A) 1 (B) 10 (C) 100 (D) 1000 GO ON TO THE NEXT PAGE Ivy Global

3 Unapproved reproduction or distribution of any portion of this material is unlawful. 6. If 4n(n + 8) = 36, what is the product of the two solutions to this equation? 8. Which of the following represents the solution set to the inequality x + 1 9? (A) 1 (B) 9 (C) 0 (D) 9 (A) (B) (C) (D) y 50 x 9. f (x) = x 1, and g (x) is a linear function that is perpendicular to f (x). If (0,4) is a point of g (x), at what point do f (x) and g (x) intersect? 7. Every year, the population of Dwarf lop rabbits doubles in a certain country, as shown in the graph above. If there were 50 Dwarf lop rabbits last year, how many Dwarf lop rabbits will there be 4 years from now? (A) (0, 1) (B) (1, 1) (C) (, 3) (D) (3, ) (A) 00 (B) 50 (C) 800 (D) 1600 GO ON TO THE NEXT PAGE Ivy Global

4 Unapproved reproduction or distribution of any portion of this material is unlawful. 1. Which of the following is equal to 6x 11x 7? (A) (6x 1)(x + 7) (B) (6x + 1)(x 7) (C) (x 1)(3x + 7) (D) (x + 1)(3x 7) The graph shown above represents f (x) = 4x 3. If f (a + 4) = 5, what is the value of a? (A) (B) 1 (C) 1 (D) x x 13. What is the arc length of the figure above? (A) 180 (B) 90 (C) π (D) π x The triangle above has an area of x x and a base of x + 1. What is the height of the triangle? (A) 1 (x ) (B) x (C) (x ) (D) (x )(x + 1) GO ON TO THE NEXT PAGE Ivy Global

5 Unapproved reproduction or distribution of any portion of this material is unlawful. O y x 15. Which of the following expressions is equivalent to 15x 7x 6? x (A) (5x + 1) (B) 3(5x + 1) (C) 15x 8x 4 (D) 15x Which of the following equations could represent an expression for the function in the figure above? (A) f (x) = x + 4 (B) f (x) = x 4 (C) f (x) = (x 4) (D) f (x) = (x + 4) GO ON TO THE NEXT PAGE Ivy Global

6 Unapproved reproduction or distribution of any portion of this material is unlawful. 16. What is a value of y that satisfies the inequality y 5 1? n + 1 n + 8 = What value of n satisfies the equation above? 0 x What is the value of x in the number line above? 5x 4x 0. If the perimeter of the above triangle is 7, what is the value of x? 18. A psychological research study at a local university pays participants $15 if they are students and $10 if they are non-students. If the research study pays 10 participants a total cost of $10, how many of the participants were students? S T O P If you complete the problem set before time elapses, you may review your responses for this section. Do not view or begin working on any other sections. Ivy Global

7 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. 1. If f (x) = x + 1 and g (x) = 4x 4, what is f (0) g (0)? (A) 5 (B) 4 (C) 4 (D) 8 4. A printer can print at a rate of 5 pages per minute. How many hours will it take to print 300 pages? If y : z is equal to 1 : 3, and z : a is equal to : 3, what ratio is equal to y : a? (A) (B) (C) (D) : 9 1 : 3 1 : : 3 Books Read Per Month (E) (F) (G) (H) Number of Students Internet Usage 3 or more books 0 books Time (hours) 3. A group of people are surveyed about the number (C) of books they read each month, and the results are (A) (D) graphed above. If the sample accurately represents (B) (C) the 40,000 people in the city of Omaha, how many (D) people in Omaha can we expect to read 3 or more books per month? 84, , ,000 18,000 1 to books (A) (B) 5. Administrators at Washington High School have noticed that students are downloading and watching movies while in class. They want to determine whether it is only a few kids who are using the internet for long periods of time at school. The above graph is the result of an anonymous student survey, representing the number of hours spent on the internet per day by students at Washington High School. Which of the following statements is INCORRECT? The mode of this data set is 3 hours. The range of this data set is 3 hours. 60% of the students surveyed use the internet 3 or 4 hours per day. The median is smaller than the mean for this set of data. GO ON TO THE NEXT PAGE Ivy Global

8 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. x + 1 = 6 6. Which of the following is a value of x for the equation above? If f (x) is a linear function that passes through the points (4,3) and ( 4, 9), what is the y-intercept of f (x)? (0, ) (, 0) (0, 3) ( 3, 0) (I) (J) (K) (L) (M) (N) (O) (P) y 9. Which of the following equations represents the function f (x) = x 1 shifted units to the left on the xy-plane? g(x) = x 5 (A) g 3x = x (B) g(x) = x + 1 (C) (D) g(x)= x + 3 O x (A) 7. Which of the following equations could represent the (B) linear equation above? (C) (D) y = x 1 y = x + 1 y = x 1 y = x + 1 (Q) (R) (S) (T) 10. What is the average of x + 4, 5x 1, and x + 3? x + x x + x GO ON TO THE NEXT PAGE Ivy Global

9 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. University Students' Sleep Habits Hours of Sleep University A University B Average 6 8 Median 4 7 Mode 5 7 Standard Deviation A random sample of students in two different universities were surveyed for their sleep habits. The results are shown in the table above. Which of the following statements is supported by the information in this table? (A) (B) (C) (D) The hours of sleep per night varies more among students at University A than students at University B. More students attend University B than University A. More than half of the students at University B get 7 hours of sleep per night. Half of the students at University A get 6 hours of sleep per night. Year Number of Colonies , , , , The table above shows the number of fire ant colonies found in Greenville from 199 to Which of the following graphs best represents the number of fire ant colonies in Greenville? (A) (B) Number of Colonies Number of Colonies Year Year (U) 1. Logan bought 36 pieces of bubble gum, which was (V) 40% of the store s stock. How much bubble gum is (W) remaining in the store? (X) (C) (D) Number of Colonies Number of Colonies Year Year GO ON TO THE NEXT PAGE Ivy Global

10 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. 14. For the inequality x + y > 15, when x = 3, which of the following CANNOT be a possible value of y? x + 3 y + 5 xy = A xy (Y) (Z) (AA) (BB) (A) (B) (C) (D) 17. What is the expression for A? x + 3y + 5xy y + 3x + 5 x + y xy 15. The sum of the digits in a two digit number is 8. If 18 is subtracted from this number, the numbers digits are reversed. Which of the following could be the original number? (CC) (DD) (EE) (FF) 71 (GG) (HH) (II) 16. If x + ax + b = (x 9)(x + 9), what is the value of ab? (JJ) (KK) (LL) (MM) (NN) 18. A company polls a group of 1,067 people randomly selected to represent New York City. The company determines that 10% of the sample group does not like cheese, while the remaining 90% does like cheese. The poll is true with a 3% margin of error 19 times out of 0. If there are 8.5 million people in New York City, what is the best estimate for the number who do not like cheese? 850,000 people Between 45,000 and 1,75,000 people Between 595,000 and 1,105,000 people Between 7,500 and 977,500 people GO ON TO THE NEXT PAGE Ivy Global

11 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. 19. f () = 3 and f ( 6) = 13. If f (x) is a linear function, what is the y-intercept of f (x)? Sam can run 4 miles in 48 minutes. If Ahn can run twice as fast as Sam, how many minutes does it take Ahn to run 6 miles? (OO) (PP) (QQ) (RR) (SS) (TT) (UU) (VV) 6x 0. What is the perimeter of the figure outlined by the solid line, in terms of x? (A) (B) (C) (D) (A) (B) (C) (D) 5x + 3πx 5x + 6πx 10x + 3πx 10x + 6πx 4x 1. If 5 x + 4 = 5 x + 3, what is the value of x? (A) (B) (C) (D) Drink Sales for July Drink Flavor 16 oz. 4 oz. Vanilla Mocha m 175 Espresso s 4500 Total A beverage company offers three different flavors of energy drinks. Each flavor is also offered in two different sizes. The table above shows the number of cans sold in each category during the month of July. If 16oz cans represented 0% of the total Espresso cans sold, how many 16 oz. cans of Mocha, m, did the company sell? GO ON TO THE NEXT PAGE Ivy Global

12 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. 4. If (x + ) = 4, what is a solution for x? (WW) (XX) (YY) (ZZ) 4 8 Questions 5 and 6 refer to the following information. Scientists study a group of large dogs, allocating each of them 1600 calories per day. ½ of these calories come from carbohydrates, and ¼ of these calories come from fats. 5. How many more carbohydrate calories than fat calories is each dog allocated per day? (A) (B) 400 (C) (D) When the dogs are active, the scientists increase the dogs daily caloric intake by 5%. Of these (FFF) calories, 1,000 are from carbohydrates. What percentage (GGG) of the (AAA) (BBB) remaining calories come from other, non-carbohydrate (HHH) (CCC) sources? (DDD) (A) (B) (C) (D) (EEE) 5x + 3y = 3c y = c 4x 7. If x + y = 6, what is the value of c for the system of equations above? Hours of Exercise Per Week Number of Students Hours Per Week Class A Class B The table above shows the number of hours spent exercising per week by students in Class A and Class B. Which statement best describes the relationship of the median and mean of the hours of weekly exercise between the two classes? Class A has a higher median than Class B and Class B has a higher mean than Class A. Class B has a higher median than Class A and Class B has a higher mean than Class A. Class A and B have the same median, and Class B has a lower mean than Class A. Class A and B have the same median, and Class A has a lower mean than Class B. GO ON TO THE NEXT PAGE Ivy Global

13 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. x y 4 9. In the figure above, what is the value of sin(x)? 3 x (A) The function f (x) = ax + bx + c is graphed above. Which of the following must be positive? (B) 3 4 (C) 4 5 (D) 5 3 (A) (B) (C) (D) ab b a c ac GO ON TO THE NEXT PAGE Ivy Global

14 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. 31. Linda works 6 hours a day on Monday and Wednesday, 8 hours a day on Thursday and Friday, and 5 hours on Sunday. If she is paid $495 at the end of the week, what is Linda s hourly wage? x 3 1 4x 3. If the ratio of A to B is :3 and the ratio of A to C is 5:6, what is B C? 33. The figure above is an example of a completed bubble square. The numbers next to the line connecting the two adjacent circles is the sum of the numbers inside each of the two circles. What is the value of x? 5 x + 6x + 8 = A x + + B x In the above equation, what is the value of A + B? GO ON TO THE NEXT PAGE Ivy Global

15 4 4 Unapproved reproduction or distribution of any portion of this material is unlawful. Speed (miles per hour) Running Speeds Time (in hours) 35. The graph above shows Rebecca s running speeds during a hour run. What is the total distance, in miles, that Rebecca ran during the first hour of her run? 36. If a sector of a circle with an angle of 60 has an area of 4π, what radius of the circle? Questions 37 and 38 refer to the following information. In a psychology experiment, participants are asked to solve simple math problems presented on a computer screen. The data is analyzed by calculating what percentage of the questions that the participant answers correctly during one trial. The trials are presented back to back with no breaks in between. The results are shown below. Percent Correct Math Problem Accuracy Trial Number Participant 1 Participant 37. The duration of the experiment is 50 minutes and consists of 10 trials each lasting 5 minutes. If a new math problem is presented every 6 seconds, how many math problems are presented during one trial? 38. Trials 6 through 8 focus on spatial reasoning problems in math. The lab wants to determine whether the average accuracy is greater for Participant 1 or for Participant during these trials. The percent of math problems correct for both participants during trials 6 through 8 is always divisible by 5. What is the difference between the average number of problems correct for Participant 1 and Participant during trials 6 through 8? (Round your answer to the nearest integer.) S T O P If you complete the problem set before time elapses, you may review your responses for this section. Do not view or begin working on any other sections. Ivy Global

16 Madison leaves her house and bikes north at a constant speed of 10 miles per hour. If her dad leaves the same house two hours later, driving north at a constant speed of 15 miles per hour, how long will it take him, in hours, to reach Madison? A) B) 3 C) 4 D) 5 3 Bats detect the locations of objects by bouncing sound waves off of objects, in a process known as echolocation. The speed of a sound wave is approximately 350 meters per second. A bat emits a sound wave towards a tree 55 meters away. What is the time, in seconds, that it takes for the sound wave to reach the tree? A) 0.5 B) 1 C) 1.5 D) If x 1 x + 4 = 0, what are the values for x? I. 4 II. 1 III. 1 IV. 4 A) I and III B) II and IV C) III and IV D) I and II 4 w = 8 h = 3w An engineer determined that a bridge he is designing has maximum stability when its length, l, width, w, and height, h, are defined by the equations above. If he wants to build a bridge with a height of 9 meters, what should be the length of the bridge, in meters? A) 48 B) 4 C) 1 D) 6 50 Ivy Global

17 If the sum of two consecutive integers is 15, what is their product? A) 36 B) 48 C) 56 D) 64 7 In DNA sequencing, a machine is able to identify the sequence of units of DNA, called base pairs. It costs approximately 10 cents to sequence 1000 base pairs. If an investigator would like to sequence a gene consisting of 10,000 base pairs from each of 100 samples, how much would it cost for him to obtain the sequences? A) $10 B) $480 C) $70 D) $100 x f (x) Which of the following equations describes the chart above? A) f (x) = x x B) f (x) = x 1 C) f (x) = x 1 D) f (x) = x 8 x x = 15 Which of the following is a correct value for x in the equation above? A) 3 B) C) D) 4 Ivy Global 51

18 The velocity of a ball that is thrown upwards is represented by the equation v = 5t 0t + 60, where v represents velocity and t represents time, in seconds. After how many seconds does the velocity of the ball become zero? y A) B) 3 C) 6 (, 0) O (4, 0) x D) 1 The graph above could be a representation of which of the following equations? 10 If x = 4y + 3 and y = x 3, what is the value of xy? A) 1 B) 0 C) 1 D) 3 A) y = x 1 B) y = x x 9 C) y = (x 1) 9 D) y = x 5 Ivy Global

19 If 3 x + = 7, what is the value for x? A) 0 B) 1 C) D) 3 If 1 k = 6a, what is the value of k in terms of a? A) 3a B) 3a C) 9a D) 9a 4 Ivy Global 53

20 If the sum of the even integers between 1 and k, inclusive, is equal to k, what is the value of k? f (x) = x + d and g (x) = x, where d is a constant. f (g ()) If = 4, what is the value of d? f () 15 If a is a non-zero digit in the numbers 1aa and a31, what is the value of a when 1aa + a31 = 659? 17 A 160 B 30 C What is the length of AC in the diagram above? S T O P If you complete this section before the end of your allotted time, check your work on this section only. Do NOT use the time to work on another section. Ivy Global 55

21 Which of the following expressions is equivalent to (3x )(x + 1)? x y = x 3y A) 3x B) 4x C) 3x x D) 3x + x If x and y are integers in the diagram above, what is the value of 3 4? A) 18 B) 6 C) 6 D) 18 An athlete throws a javelin, a long metal spear, at a track and field competition. The javelin s height in feet, h, as a function of the number of seconds since it was thrown, t, is modelled by the equation h (t) = 16t + 18t. What is the height of the javelin after 5 seconds? A) 0 feet B) 8 feet C) 40 feet D) 480 feet 4 Depreciation is the decrease in value of an item. Three years ago, Aaron bought a computer for $930. The computer is now worth $570. Assuming that the value of the computer depreciates linearly, what is its yearly depreciation? A) $10 B) $180 C) $00 D) $40 60 Ivy Global

22 On a house blueprint, feet is represented by 1 inch. If a room on the blueprint measures 5 inches by 6 inches, what is the area of the actual room? A) 30 square feet B) 60 square feet C) 90 square feet D) 10 square feet 7 y (3, 8) O x Club Participation at a School Which of the following equations best describes the trend line for the scatterplot above? A) y = 3x + 1 B) y = x + C) y = 3x + 1 D) y = 3x Number of Students The graph above shows the student participation for 4 school clubs. Each student is allowed to participate in only one club. If the school has 50 students, how many students are not in a club? A) 0 B) 90 C) 60 D) 30 0 Debate Student Council Orchestra Choir Item Costs Comparison of Tools Cost at John s Tools Cost at Lin s Tools Hammer $15 $18 Drill $50 $55 Electric saw $30 $5 If a distributor receives a 10% discount from John s Tools and a 15% discount from Lin s Tools, how much more would they pay, in dollars, to buy a drill and electric saw from John s Tools than Lin s Tools? A) 4 B) 5 C) 6 D) 7 Ivy Global 61

23 4 4. Questions 9 and 10 refer to the following information. Percent Distribution Negative and Even Number Distributions Set A Set B Set C Negative Numbers Even Numbers 11 One byte is a unit of memory size used with computers. One megabyte contains approximately 10 6 bytes and Paul s computer hard-drive accesses information at a rate of 150 megabytes per second. If Paul wants to work with 5 files on his computer that are, bytes each, approximately how long will it take his computer to access them? A) 15.6 seconds B) 39 seconds C) 1.3 minutes D) 78 minutes The graph above shows the distribution of negative and even numbers in three sets of numbers. 9 How many sets had more even than negative numbers? A) 0 B) 1 C) D) 3 10 If Set B has 00,000 elements, how many more negative numbers than even numbers would we expect to find in the set? A) 5,000 B) 50,000 C) 100,000 D) 155,000 6 Ivy Global

24 cent coins 10 cent coins 5 cent coins Total coins Offer Offer Total Maria has been offered an exchange of coin collections for her wood carving. A summary of the coin collections is found in the table above. If she evaluates the offers based only on the face value of the coins, which collection is Maria most likely to choose? A) The coins are worth the same so Maria is equally likely to pick either one. B) Offer 1 is worth more than Offer, so Maria will pick Offer 1. C) Offer is worth more than Offer 1, so Maria will pick Offer. D) Offer 1 has the greater number of coins, so Maria will pick Offer 1. Questions 14 and 15 refer to the following information. The pie chart above shows the distribution of immigrants in a city, based on continent of origin Immigration Demographics Other 5% of the immigrant population originated in which of the following continents? A) Asia and Europe B) Asia and Africa C) Africa and Europe D) Other Europe Africa Asia 13 During the first month of life, a newborn s weight increases by 30%. If a newborn weighs w pounds when it is one month old, which of the following expressions represent the baby s weight at birth? A) 0.3 w B) 1.3 w C) w 1.3 D) 1.3 w 0% of the immigrant population from Europe are from France. If there are a total of 1500 immigrants in the city, how many immigrants are from France? A) 50 people B) 75 people C) 100 people D) 10 people Ivy Global 63

25 If 10% of a number is 1, then what is the value of 5% of half of the original number? A) B) 3 C) 4 D) 5 19 x 7x 3x What is the value of the largest angle in the triangle above? 17 a = b 3 b a = 4 What is the value of a + b in the system of equations above? A) 7 B) 9 C) 6 D) 15 0 A) 10 degrees B) 115 degrees C) 110 degrees D) 105 degrees The average in Set A is 85 and the average in Set B is 65. If the combined average of all the elements in Set A and Set B is 70, and Set A has 5 elements, how many elements are in Set B? 18 Which of the following is the sum of 3 consecutive odd integers? A) 45 B) 30 C) 15 D) 5 A) 3 B) 6 C) 105 D) Ivy Global

26 A species of shark spends 5% of a day, d, sleeping, and 50% of the remaining time hunting. Which of the following expressions represents how many hours in one day are left for other activities? A) 3d B) 3d 4 C) 3d 8 D) 3d 1 Age Male Female Total 0-18 years old years old years old years old Total The age of a random sample of people from a population is summarized in the table above. The whole population consists of 31,000 people. Which of the following statements is true? A) We expect that there are 15,00 females in the population. B) We expect there to be 5580 females 65 years old and younger in the population. C) We expect there to be 9300 females between 19 and 65 years old in the population. D) We cannot determine the number of females in the population with the information given. 3 If x y = 7 and x + y = 18 what is the value of x y? A) B) 4 C) 6 D) 8 Ivy Global 65

27 If 10x + 35 = x + 6 what is/are the value(s) of x divided by two? A) 1 B) 7 C) 1 and 7 D) 0 and 1 f (x) = x + a If a is a constant and f () + f (3) = f (5), what is the value of a? A) 6 B) 1 C) 4 D) 48 5 Employees at a Hospital 7 3x + 4y = 1 4x + 3y = 5 Years Worked Nurse Doctor Technician Total Less than to to More than Total What is the value of x + y, in the system of equations shown above? A) 4 B) 3 C) D) 1 The table above shows the years worked by employees at a hospital. What is the probability that a technician has worked for 6 or more years? A) 90% B) 75% C) 65% D) 50% 66 Ivy Global

28 If x + 5 = 7 and x + 5 k = 1, what is the value of k? There are 4 integers in a group. If there are 5 times as many odd integers as there are even integers, how many numbers are even integers? 68 Ivy Global

29 4 4. Questions refer to the following information. One Hz is a measure of frequency and is equal to one cycle per second. The A string on a violin is tuned to a resonant frequency of 440Hz. If the string length is decreased, its resonant frequency, measured in Hz, is increased. The decrease in string length changes the string frequency according to the equation f = v l, where f is the frequency in Hz, v is a constant, and l is the string length. An application of this equation is demonstrated in the diagram below: 31 The violin has another string, called the D string, which is tuned to resonate at 93.7Hz. If the lengths of a violin A and D string are decreased by half, what is the difference in resonant frequency between these two strings? (Round your answer to the nearest Hz.) String with a resonant frequency of 440Hz The same string is decreased by half, resulting in a resonant frequency of 880Hz 30 If the length of an A string on a violin is decreased by one quarter, what is the resonant frequency of the string, rounded to the nearest Hz? STOP If you complete the problem set before time elapses, you may review your responses for this section. Do not view or begin working on any other sections. Ivy Global 69

30 3 3 1 If 5 x +6 = 10, what is the value of 10 x + 3? A) 4 B) 9 C) 11 D) 0 x + y = 0 3x y = 10 Which of the following ordered pairs (, x y)satisfies the system of equations above? A) (3, ) B) (, ) C) (, ) D) (, ) A landscaping company estimates the price of a job, in dollars, using the expression nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 1 in the expression? A) The company charges $1 per hour for each landscaper. B) A minimum of 1 landscapers will work on each job. C) The price of every job increases by $1 every hour. D) Each landscaper works 1 hours a day a +1 a b +4b Which of the following is equivalent to the expression shown above? A) (3 a + b ) B) (3 a+ b) C) (9 a + 4 b ) D) (9 a+ 4 b) Unauthorized copying or reuse of any part of this page is illegal. 33

31 k +17 x = 0 If k >0 and x =7 in the equation above, what is the value of k? A) B) 3 C) 4 D) 5 ( 5, 0) O y l (0, ) (0, 4) ( p, 0) In the xy-plane above, line is parallel to line k. What is the value of p? A) 4 B) 5 C) 8 D) 10 k x If x x a b 16 = x, x >1, and a+ b =, what is the value of a b? A) 8 B) 14 C) 16 D) 18 na = 360 The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50, what is the greatest number of sides it can have? A) 5 B) 6 C) 7 D) 8 Unauthorized copying or reuse of any part of this page is illegal. 34

32 The graph of a line in the xy-plane has slope and contains the point (1, 8). The graph of a second line passes through the points (1, ) and (, 1). If the two lines intersect at the point (, ab), what is the value of a+ b? A) 4 B) 3 C) 1 D) 4 Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to 1? A) y = x B) y = x C) y =( x ) 3 D) y = x Which of the following complex numbers is 3 5i equivalent to? (Note: i = 1) 8+ i A) B) C) D) 3 i i i i F R = N+ F A website uses the formula above to calculate a seller s rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of the other variables? RN A) F = R 1 RN B) F = 1 R N C) F = 1 R N D) F = R 1 Unauthorized copying or reuse of any part of this page is illegal. 35

33 What is the sum of all values of m that satisfy m 16 m+8 = 0? A) 8 B) 4 3 C) 4 3 D) 8 A radioactive substance decays at an annual rate of 13 percent. If the initial amount of the substance is 35 grams, which of the following functions f models the remaining amount of the substance, in grams, t years later? A) f( t) = 35(0.87) t B) f( t) = 35(0.13) t C) f( t) = 0.87(35) t D) f( t) = 0.13(35) t The expression following? A) 5 3 B) 5 3 C) D) 5 x x +3 5 x x +3 is equivalent to which of the Unauthorized copying or reuse of any part of this page is illegal. 36

34 The sales manager of a company awarded a total of $3000 in bonuses to the most productive salespeople. The bonuses were awarded in amounts of $50 or $750. If at least one $50 bonus and at least one $750 bonus were awarded, what is one possible number of $50 bonuses awarded? x(3 x+5)+3(3 x+5)= ax + bx + c In the equation above, a, b, and c are constants. If the equation is true for all values of x, what is the value of b? A C B In the figure above, AE CD and segment AD intersects segment CE at B. What is the length of segment CE? D E Unauthorized copying or reuse of any part of this page is illegal. 38

35 y A( 3, 1) x O B In the xy-plane above, O is the center of the circle, and the measure of AOB is π radians. What is a the value of a?... 0 ax + by = 1 x +8 y = 60 In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a b? STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section. Unauthorized copying or reuse of any part of this page is illegal. 39

36 4 4 1 A musician has a new song available for downloading or streaming. The musician earns $0.09 each time the song is downloaded and $0.00 each time the song is streamed. Which of the following expressions represents the amount, in dollars, that the musician earns if the song is downloaded d times and streamed s times? A) 0.00 d+ 0.09s B) 0.00d 0.09s C) 0.09 d+ 0.00s D) 0.09d 0.00s A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate, how many lightbulbs will be inspected if the factory produces 0,000 lightbulbs? A) 300 B) 350 C) 400 D) =4+3.5m One end of a spring is attached to a ceiling. When an object of mass m kilograms is attached to the other end of the spring, the spring stretches to a length of centimeters as shown in the equation above. What is m when is 73? A) 14 B) 7.7 C) 73 D) 79.5 Unauthorized copying or reuse of any part of this page is illegal. 41

37 4 4 Questions 4 and 5 refer to the following information. The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns $10 at a performance where 8 people attend. 4 How much money will the performer earn when 0 people attend a performance? A) $960 B) $480 C) $300 D) $40 5 The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performer s profit. What is the profit the performer makes at a performance where 8 people attend? A) $51.60 B) $57.00 C) $68.40 D) $ When 4 times the number x is added to 1, the result is 8. What number results when times x is added to 7? A) 1 B) 5 C) 8 D) 9 y = x 6 x+8 The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients? A) y 8= x 6x B) y+1=( x 3) C) y = x( x 6)+8 D) y =( x )( x 4) Unauthorized copying or reuse of any part of this page is illegal. 4

38 4 4 8 In a video game, each player starts the game with k points and loses points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 00 points, what is the value of k? A) 0 B) 150 C) 50 D) A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of,400 pounds. Which of the following systems of inequalities represents this relationship? A) 40 x+ 65y,400 x+ y 45 B) C) x y ,400 x+ y x+ 65y 45 x+ y,400 D) x+ y, x+ 65y, A function f satisfies f () = 3 and f (3) = 5. A function g satisfies g(3) = and g(5) = 6. What is the value of f( g(3))? A) B) 3 C) 5 D) 6 Number of hours Tony plans to read the novel per day 3 Number of parts in the novel 8 Number of chapters in the novel 39 Number of words Tony reads per minute 50 Number of pages in the novel 1,078 Number of words in the novel 349,168 Tony is planning to read a novel. The table above shows information about the novel, Tony s reading speed, and the amount of time he plans to spend reading the novel each day. If Tony reads at the rates given in the table, which of the following is closest to the number of days it would take Tony to read the entire novel? A) 6 B) 8 C) 3 D) 34 Unauthorized copying or reuse of any part of this page is illegal. 43

39 4 4 1 On January 1, 000, there were 175,000 tons of trash in a landfill that had a capacity of 35,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 000, which of the following inequalities describes the set of years where the landfill is at or above capacity? A) 35,000 7,500 y B) 35,000 7,500y C) 150,000 7,500y D) 175, ,500y 35, A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town? A) Sample size B) Population size C) The number of people who refused to respond D) Where the survey was given Number of miles traveled (billions) Miles Traveled by Air Passengers in Country X, 1960 to Year According to the line of best fit in the scatterplot above, which of the following best approximates the year in which the number of miles traveled by air passengers in Country X was estimated to be 550 billion? A) 1997 B) 000 C) 003 D) 008 Unauthorized copying or reuse of any part of this page is illegal. 44

40 The distance traveled by Earth in one orbit around the Sun is about 580,000,000 miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun? A) 66,000 B) 93,000 C) 10,000 D) 40,000 Results on the Bar Exam of Law School Graduates Took review course Did not take review course Passed bar exam 18 7 Did not pass bar exam The table above summarizes the results of 00 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course? 18 A) 5 7 B) 5 5 C) 00 7 D) The atomic weight of an unknown element, in atomic mass units (amu), is approximately 0% less than that of calcium. The atomic weight of calcium is 40 amu. Which of the following best approximates the atomic weight, in amu, of the unknown element? A) 8 B) 0 C) 3 D) A survey was taken of the value of homes in a county, and it was found that the mean home value was $165,000 and the median home value was $15,000. Which of the following situations could explain the difference between the mean and median home values in the county? A) The homes have values that are close to each other. B) There are a few homes that are valued much less than the rest. C) There are a few homes that are valued much more than the rest. D) Many of the homes have values between $15,000 and $165,000. Unauthorized copying or reuse of any part of this page is illegal. 45

41 4 4 Questions 19 and 0 refer to the following information. A sociologist chose 300 students at random from each of two schools and asked each student how many siblings he or she has. The results are shown in the table below. Number of siblings Students Sibling Survey Lincoln School Washington School There are a total of,400 students at Lincoln School and 3,300 students at Washington School. 19 What is the median number of siblings for all the students surveyed? A) 0 B) 1 C) D) Based on the survey data, which of the following most accurately compares the expected total number of students with 4 siblings at the two schools? 1 A) The total number of students with 4 siblings is expected to be equal at the two schools. B) The total number of students with 4 siblings at Lincoln School is expected to be 30 more than at Washington School. C) The total number of students with 4 siblings at Washington School is expected to be 30 more than at Lincoln School. D) The total number of students with 4 siblings at Washington School is expected to be 900 more than at Lincoln School. A project manager estimates that a project will take x hours to complete, where x > 100. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time? A) x+ y < 10 B) y > x+10 C) y < x 10 D) 10 < y x < 10 Unauthorized copying or reuse of any part of this page is illegal. 46

42 4 4 Questions and 3 refer to the following information. P I = 4 πr At a large distance r from a radio antenna, the intensity of the radio signal I is related to the power of the signal P by the formula above. Which of the following expresses the square of the distance from the radio antenna in terms of the intensity of the radio signal and the power of the signal? IP A) r = 4π B) r C) r D) r P = 4πI πi = 4 P I = 4πP... 3 For the same signal emitted by a radio antenna, Observer A measures its intensity to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna? 1 A) 4 4 B) C) D) x + y +4x y = 1 The equation of a circle in the xy-plane is shown above. What is the radius of the circle? A) B) 3 C) 4 D) 9 Unauthorized copying or reuse of any part of this page is illegal. 47

43 The graph of the linear function f has intercepts at (,0)and a (0, b) in the xy-plane. If a+ b = 0 and a b, which of the following is true about the slope of the graph of f? A) It is positive. B) It is negative. C) It equals zero. D) It is undefined. 1 O y 1 y = f(x) The complete graph of the function f is shown in the xy-plane above. Which of the following are equal to 1? I. f ( 4) II. 3 f III. f (3) A) III only B) I and III only C) II and III only D) I, II, and III x... 7 Temperature ( C) insulated non-insulated Time (minutes) Two samples of water of equal mass are heated to 60 degrees Celsius ( C). One sample is poured into an insulated container, and the other sample is poured into a non-insulated container. The samples are then left for 70 minutes to cool in a room having a temperature of 5 C. The graph above shows the temperature of each sample at 10-minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change? A) In every 10-minute interval, the magnitude of the rate of change of temperature of the insulated sample is greater than that of the non-insulated sample. B) In every 10-minute interval, the magnitude of the rate of change of temperature of the non-insulated sample is greater than that of the insulated sample. C) In the intervals from 0 to 10 minutes and from 10 to 0 minutes, the rates of change of temperature of the insulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude. D) In the intervals from 0 to 10 minutes and from 10 to 0 minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the insulated sample are of greater magnitude. Unauthorized copying or reuse of any part of this page is illegal. 48

44 4 4 8 B A 4 6 y In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7, ) and (1, 0), respectively. Which of the following is an equation of the line that passes through points B and D? A) y = 3x 1 B) y = 3( x 1) C) y = 1 x+4 3 D) y = 1 x E D C x y =3 y = ax + b In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions? A) a =, b = B) a =, b =4 C) a =, b =4 D) a =4, b =3 The figure above shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is square inches, what is the area, in square inches, of the square? A) 56 B) 19 C) 64 3 D) 16 3 Unauthorized copying or reuse of any part of this page is illegal. 49

45 A coastal geologist estimates that a certain country s beaches are eroding at a rate of 1.5 feet per year. According to the geologist s estimate, how long will it take, in years, for the country s beaches to erode by 1 feet? If h hours and 30 minutes is equal to 450 minutes, what is the value of h? In the xy-plane, the point (3, 6) lies on the graph of the function fx ( ) = 3x bx+1. What is the value of b? In one semester, Doug and Laura spent a combined 50 hours in the tutoring lab. If Doug spent 40 more hours in the lab than Laura did, how many hours did Laura spend in the lab? Unauthorized copying or reuse of any part of this page is illegal. 51

46 a =18 t+15 Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount to the account. The equation above models the amount a, in dollars, that Jane has deposited after t weekly deposits. According to the model, how many dollars was Jane s initial deposit? (Disregard the $ sign when gridding your answer.) L 60 M O N In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of minor arc LN? Unauthorized copying or reuse of any part of this page is illegal. 5

47 4 4 Questions 37 and 38 refer to the following information. A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, N next year, can be estimated from the number of plants this year, N this year,bythe equation below. N N = N +0.( N next year this year this year) 1 this year The constant K in this formula is the number of plants the environment is able to support. 37 K According to the formula, what will be the number of plants two years from now if K = 4000? (Round your answer to the nearest whole number.) The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanist s goal is that the number of plants will increase from 3000 this year to 3360 next year, how many plants must the modified environment support? STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section. Unauthorized copying or reuse of any part of this page is illegal. 53

48 3 3 1 A babysitter earns $8 an hour for babysitting children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned? A) 8 x +3, where x is the number of hours B) 3 x +8, where x is the number of hours C) x(8 + ) + 3, where x is the number of children D) 3 x +(8+), where x is the number of children 3( x + y) = y If (, x y)is a solution to the equation above and y 0, what is the ratio x y? A) 4 3 B) 3 C) D) x 1 y = x 1 y = Which ordered pair (, x y)satisfies the system of equations above? A) ( 11, 64) B) (64, 88) C) 3 3, 4 3 D) (88, 536) Unauthorized copying or reuse of any part of this page is illegal. 33

49 3 3 4 B E D A Note: Figure not drawn to scale. Triangle ABC above is isosceles with AB = AC and BC =48. The ratio of DE to DF is 5 : 7. What is the length of DC? A) 1 B) 0 C) 4 D) 8 5 In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve? A) 10 B) 15 C) 5 D) 35 F C x +7x 15 = 0 If r and s are two solutions of the equation above and r > s, which of the following is the value of r s? A) B) C) D) To cut a lawn, Allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn. Taylor charges a fee of $1 for his equipment and $9.5 per hour spent cutting a lawn. If x represents the number of hours spent cutting a lawn, what are all the values of x for which Taylor s total charge is greater than Allan s total charge? A) x >4 B) 3 x 4 C) 4 x 5 D) x <3 Unauthorized copying or reuse of any part of this page is illegal. 34

50 3 3 8 n = 456 3T The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation? A) For every increase of 3 F, one more cup of hot chocolate will be sold. B) For every decrease of 3 F, one more cup of hot chocolate will be sold. C) For every increase of 1 F, three more cups of hot chocolate will be sold. D) For every decrease of 1 F, three more cups of hot chocolate will be sold. 9 A truck enters a stretch of road that drops 4 meters in elevation for every 100 meters along the length of the road. The road is at 1,300 meters elevation where the truck entered, and the truck is traveling at 16 meters per second along the road. What is the elevation of the road, in meters, at the point where the truck passes t seconds after entering the road? A) 1, t B) 1, t C) 1,300 4t D) 1,300 16t If f ( x 1) = x+3 for all values of x, what is the value of f ( 3)? A) 7 B) 5 C) 3 D) 1 s Which of the following is equivalent to ( s t) ()? t A) B) C) D) s t s t s t s t s st s s t Unauthorized copying or reuse of any part of this page is illegal. 35

51 3 3 1 p( x) = 3( x + 10 x+ 5) 5( x k) In the polynomial p( x) defined above, k is a constant. If p( x) is divisible by x, what is the value of k? A) 3 B) C) 0 D) In the xy-plane, if the parabola with equation y = ax + bx + c, where a, b, and c are constants, passes through the point ( 1, 1), which of the following must be true? A) a b = 1 B) b+ c = 1 C) a+ b+ c = 1 D) a b+ c = 1 Unauthorized copying or reuse of any part of this page is illegal. 36

52 For what value of h is h 4 = 10 6? What is the value of a if ( a+ 3) (4a 8) = 7? If x is not equal to zero, what is the value of 17 4(3 x) ( x)? If x is a factor of x bx+ b, where b is a constant, what is the value of b? STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section. Unauthorized copying or reuse of any part of this page is illegal. 38

53 4 4 1 Tyra subscribes to an online gaming service that charges a monthly fee of $5.00 and $0.5 per hour for time spent playing premium games. Which of the following functions gives Tyra s cost, in dollars, for a month in which she spends x hours playing premium games? A) Cx ( ) = 5.5x B) Cx ( ) = 5 x+0.5 C) Cx ( ) = 5+0.5x D) Cx ( ) = 5+5x A grocery store sells a brand of juice in individual bottles and in packs of 6 bottles. On a certain day, the store sold a total of 81 bottles of the brand of juice, of which 9 were sold as individual bottles. Which equation shows the number of packs of bottles, p, sold that day? A) p = B) p = C) p = D) p = Rainfall (inches) Monthly Rainfall in Chestnut City Mar Apr May Jun Jul Aug Sep Oct Month The line graph above shows the monthly rainfall from March to October last year in Chestnut City. According to the graph, what was the greatest change (in absolute value) in the monthly rainfall between two consecutive months? A) 1.5 inches B).0 inches C).5 inches D) 3.5 inches Unauthorized copying or reuse of any part of this page is illegal. 41