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1、 . . . . 1 / 26 Math Test No Calculator 25 MINUTES, 20 QUESTIONS Turn to Section 3 of your answer sheet to answer the questions in this section. Directions For questions 1-15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sh
2、eet. For questions 16-20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work. Notes . The use of a calculator is not
3、 permitted. . All variables and expressions used represent real numbers unless otherwise indicated. . Figures provided in this test are drawn to scale unless otherwise indicated. . All figures lie in a plane unless otherwise indicated. . Unless otherwise indicated, the domain of a given function f i
4、s the set of all real numbers x for which f(x) is a real number. Reference . . . . 2 / 26 1. A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painters fee can be calculated by the expression nKlh, where n is the number of walls, K is a cons
5、tant with units of dollars per square foot, lis the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change? A) h B) l C) K D) n 2. If 3r = 18, what is the valu
6、e of 6r + 3 ? A) 6 B) 27 C) 36 D) 39 3. Which of the following is equal to a23, for all values of a ? A) a13 . . . . 3 / 26 B) a3 C)a123 D) a23 4. The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states jo
7、ined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true? A) 30x=2 B) 2x=30 C) x2=30 D) x+30=2 5. If 5x15x20 , what Is the value of 5x? A) 10 B) 5 C) 2 D)12 6. x 3y = 14 3x 2y = 6 If (x, y) is a solution to the system of equatio
8、ns above, what is the value of xy ? A) 20 . . . . 4 / 26 B) 8 C) 4 D) 8 7. The function f is defined by a polynomial. Some values of x and f (x) are shown in the table above. Which of the following must be a factor of f(x)? A) x 2 B) x 3 C) x 4 D) x 5 8. The line y=kx+4,where k is a constant, is gra
9、phed in the xy-plane. If the line contains the point (c, d), where c 0 and d 0, what is the slope of the line in terms of c and d ? A) d4c B) c4d C) 4dc D) 4cd 9. . . . . 5 / 26 10. In the xy-plane, the parabola with equationy = (x 11)2 intersects the line with equation y=25at two points, A and B. W
10、hat is the length of AB ? A) 10 B) 12 C) 14 D) 16 11. In the figure above, lines k, l, and m intersect at a point. If x+y=u+w, which of the following must be true? I. x=z . . . . 6 / 26 II. y=w III. z=t A) I and II only B) I and III only C) II and III only D) I, II, and III 12. y = a(x 2)(x+4) In th
11、e quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c, d). Which of the following is equal to d ? A) 9a B) 8a C) 5a D) 2a 13. The equation true for all values of 24x225x47ax28x353ax2, where a is a constant. What is the value of a
12、? A) 16 B) 3 C) 3 D) 16 14. What are the solutions to 3x2+12x+6=0 ? A) x22 B) x2303 . . . . 7 / 26 C) x62 D) x6 6 2 15. C = 59 ( F 3 2 ) The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which
13、 of the following must be true? I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of 59 degree Fa
14、hrenheit is equivalent to a temperature increase of 1 degree Celsius. . A) I only . B) II only C) III only D) I and II only 16. x3(x2 5) = 4x If x 0, what is one possible solution to the equation above? 17. If79x49x14512what is the value of x? . . . . 8 / 26 18. Two isosceles triangles are shown abo
15、ve. If 180z=2y and y=75,what is the value of x ? 19. At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have? 20. In triangle ABC, the measure of B is 90, BC = 16, and
16、 AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 13the length of the corresponding side of triangle ABC. What is the value of sin F ? Math Test No Calculator . . . . 9 / 26 55 MINUTES, 38
17、QUESTIONS Turn to Section 4 of your answer sheet to answer the questions in this section. Directions For questions 1-30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31-38, solve the problem and enter y
18、our answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work. Notes . The use of a calculator is not permitted. . All variables and expressions used repres
19、ent real numbers unless otherwise indicated. . Figures provided in this test are drawn to scale unless otherwise indicated. . All figures lie in a plane unless otherwise indicated. . Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) is a rea
20、l number. Reference . . . . 10 / 26 1. The graph above shows Marilyns distance from her campsite during a 3hour hike. She stopped for 30 minutes during her hike to have lunch. Based on the graph, which of the following is closest to the time she finished lunch and continued her hike? A) 12:40 P.M. B
21、) 1:10 P.M. C) 1:40 P.M. D) 2:00 P.M . . . . 11 / 26 2. The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40 or a male age 40 or old
22、er? A)425 B) 1025 C)1125 D) 1625 3. The graph below shows the total number of music album sales, in millions, each year from 1997 through 2009. . . . . 12 / 26 Based on the graph, which of the following best describes the general trend in music album sales from 1997 through 2009 ? A) Sales generally
23、 increased each year since 1997. B) Sales generally decreased each year since 1997. C) Sales increased until 2000 and then generally decreased. D) Sales generally remained steady from 1997 through 2009. 4. The table above shows some values of the linear function f. Which of the following defines f ?
24、 A) f(n)=n 3 B) f(n)=2n 4 C) f(n)=3n 5 D) f(n)=4n 6 5. At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled seniors were inducted into the National Honor Society last year. If there were 562 juniors and 602 seniors enrolled at Lincoln High School last year, w
25、hich of the following is closest to the total number of juniors and seniors at Lincoln High School last year who were inducted into the National Honor Society? A) 140 B) 69 . . . . 13 / 26 C) 39 D) 30 6. 3x2 5x + 2 5x2 2x 6 Which of the following is the sum of the two polynomials shown above? A) 8x2
26、 7x 4 B) 8x2+7x 4 C) 8x4 7x2 4 D) 8x4+7x2 4 7. If 35w43,what is the value of w ? A)920 B)45 C)54 D)209 8. The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, wherex represents the number of years since . . . . 14 / 26
27、 2000, andy represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation? A) The total number of students at the school in 2000 B) The average number of students per classroom in 2000 C) The estimated increase in the av
28、erage number of students per classroom each year D) The estimated difference between the average number of students per classroom in 2010 and in 2000 9. Nate walks 25 meters in13.7 seconds. If he walk sat this same rate, which of the following is closest to the distance he will walk in 4 minutes? A)
29、 150 meters B) 450 meters C) 700 meters D) 1,400 meters Questions 10 and 11 refer to the following information. . . . . 15 / 26 The chart above shows approximations of the acceleration due to gravity in meters per second squared (msec2)for the eight planets in our solar system. The weight of an obje
30、ct on a given planet can be found by using the formula W = mg, where W is the weight of the object measured in newtons, m is the mass of the object measured in kilograms, and g is the acceleration due to gravity on the planet measured in (msec2) 10. What is the weight, in newtons, of an object on Me
31、rcury with a mass of 90 kilograms? A) 25 B) 86 C) 101 D) 324 11. An object on Earth has a weight of 150 newtons. On which planet would the same object have an approximate weight of 170 newtons? A) Venus B) Saturn C) Uranus D) Neptune 12. If the function f has five distinct zeros, which of the follow
32、ing could represent the complete graph of f in the xyplane? . . . . 16 / 26 13. h = 16t2 + vt + k The equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. Which of the following gives v in t
33、erms of h, t, and k ? A) v=h+k 16t B) vhk16t C) vhkt16t D) vhkt16t 14. The cost of using a telephone in a hotel meeting room is $0.20 per minute. Which of the following equations represents the total cost c, in dollars, for h hours of phone use? A) c = 0.20(60h) B) c=0.20h+60 C) c60h0.20 . . . . 17
34、/ 26 D) c0.20h60 15. In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and t
35、he other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?
36、 A) Treatment X is likely to improve the eyesight of people who have poor eyesight. B) Treatment X improves eyesight better than all other available treatments. C) Treatment X will improve the eyesight of anyone who takes it. D) Treatment X will cause a substantial improvement in eyesight. 16. . . .
37、 . 18 / 26 Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does f(x)+g(x)=0? A) 3 B) 2 C) 1 D) 0 Questions 17 and 18 refer to the following information. S ( P ) = 12P + 4 0 D(P) = 220 P The quantity of a product supplied and the quantity of the
38、 product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function S(P) gives the quantity of the product supplied to the market when the price is P dollars, and the function D(P) gi
39、ves the quantity of the product demanded by the market when the price is P dollars. 17. How will the quantity of the product supplied to the market change if the price of the product is increased by $10 ? A) The quantity supplied will decrease by 5 units. B) The quantity supplied will increase by 5
40、units. C) The quantity supplied will increase by 10 units. D) The quantity supplied will increase by 50 units. . . . . 19 / 26 18. At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market? . A) $90 . B) $120 . C) $133 . D) $155 19
41、. Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately 113acres, about how many acres could 48 ounces of graphene cover? A) 250 B) 350 C) 450 D) 1,350 20. . .
42、. . 20 / 26 Michael swam 2,000 yards on each of eighteen days. The scatterplot above shows his swim time for and corresponding heart rate after each swim. The line of best fit for the data is also shown. For the swim that took 34 minutes, Michaels actual heart rate was about how many beats per minut
43、es less than the rate predicted by the line of best fit? A) 1 B) 2 C) 3 D) 4 21. Of the following four types of savings account plans, which option would yield exponential growth of the money in the account? A) Each successive year, 2% of the initial savings is added to the value of the account. B)
44、Each successive year, 1.5% of the initial savings and $100 is added to the value of the account. C) Each successive year, 1% of the current value is added to the value of the account. D) Each successive year, $100 is added to the value of the account. 22. The sum of three numbers is 855. One of the
45、numbers, x, is 50% more than the sum of the other two numbers. What is the value of x ? A) 570 B) 513 C) 214 D) 155 . . . . 21 / 26 23. The angles shown above are acute andsin(a) = cos(b). If a = 4k 22 and b = 6k 13, what is the value of k ? A) 4.5 B) 5.5 C) 12.5 D) 21.5 24. Mr. Kohl has a beaker co
46、ntaining n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are
47、 in the class? A) 16 B) 21 C) 23 D) 26 25. . . . . 22 / 26 A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet? A) 261.8 B) 785.
48、4 C) 916.3 D) 1,047.2 26. In the xy-plane, the line determined by the points (2, k) and (k, 32) passes through the origin. Which of the following could be the value of k ? A) 0 B) 4 C) 8 D) 16 27. A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. I
49、f these alterations decreased the area of the rectangle by 12 percent, what is the value of p ? . . . . 23 / 26 A) 12 B) 15 C) 20 D) 22 28. In planning maintenance for a citys infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 p
50、ercent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineers estimate of the population of the city t years from now? A) 50,000(0.1)20t B) 50000(0.1)t20 C) 50,000(0.9)20t D) 50000(0.9)t20 29. The incomplete table above summarizes
51、 the number of left-handed students and right-handed students by gender for the eighth-grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-h
52、anded male students. If there is a total of 18 left-handed students and 122 right-handed . . . . 24 / 26 students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are bot
53、h right-handed and left-handed.) A) 0.410 B) 0.357 C) 0.333 D) 0.250 30. 3x+b=5x-7 3y+c=5y-7 In the equations above, b and c are constants. If b is c minus 12, which of the following is true? A) x is y minus 14 B) x is y minus 54 C) x is y minus 1 D) x is y plus 12 31. Tickets for a school talent sh
54、ow cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than $14 on x student tickets and 1 adult ticket, what is one possible value of x ? 32. . . . . 25 / 26 The table above lists the ages of the first 12 United States presidents when they began their terms in office. A
55、ccording to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.) 34. In a circle with center O, central angle AOB has a measure of 54radians. The area of the sector formed by central angle AOB is what fraction of t
56、he area of the circle? 35. An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have
57、 an average of at least 85 for the first 20 ratings? 36. In the xyplane, if a point with coordinates (a, b) lies in the solution set of the system of inequalities above, what is . . . . 26 / 26 the maximum possible value of b ? Questions 37 and 38 refer to the following information. If shoppers ente
58、r a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N = rT. This relationship is known as Littles law. The owner of the Good Deals Store estimates t
59、hat during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Littles law to estimate that there are 45 shoppers in the store at any time. 37. Littles law can be applied to any part of the store, such as a pa
60、rticular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average,
61、 are waiting in the checkout line to make a purchase at the Good Deals Store? 38. The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)
