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Chapter 3Practice Test 1

222222222MATHEMATICSLEVEL 2—ContinuedMATHEMATICSLEVEL 2For each of the following problems, decide which is theBEST of the choices given. If the exact numerical value is notone of the choices, select the choice that best approximatesthis value. Then fill in the corresponding oval on the answersheet.Notes: (1) A scientific or graphing calculator will be necessary for answering some (but not all) of the questions on thistest. For each question, you will have to decide whether ornot you should use a calculator.(2) The only angle measure used on this test is degree measure. Make sure that your calculator is in degree mode.(3) Figures that accompany problems on this test are intended to provide information useful in solving the problems.They are drawn as accurately as possible EXCEPT when itis stated in a specific problem that its figure is not drawn toscale. All figures lie in a plane unless otherwise indicated.(4) Unless otherwise specified, the domain of any functionf is assumed to be the set of all real numbers x for which f(x)is a real number. The range of f is assumed to be the set of allreal numbers f(x), where x is in the domain of f.THISinformationSPACE FOR(5)USEReferencethatSCRATCHWORK.may be useful in answeringthe questions on this test can be found below.THE FOLLOWING INFORMATION IS FOR YOURREFERENCE IN ANSWERING SOME OF THE QUESTIONS ON THIS TEST.Volume of a right circular cone with radius r and height h:V 1 22pr r hh3Lateral area of a right circular cone with circumference of1c 24 33 rVolume of a sphere with radius r: V pr3the base c and slant height : S Surface area of a sphere with radius r: S 4πr2Volume of a pyramid with base area B and height h:V 1Bh3USE THIS SPACE FOR SCRATCHWORK.c1. If 2 y 6 ( y 3) for all y, then c 91(A)9(B) 2(C) 9(D) 15(E) 18GO ON TO THE NEXT PAGE24 Cracking the SAT Subject Test in Math 2

222222222MATHEMATICS LEVEL 2—Continued2. The relationship between a temperature F in degrees Fahrenheit and a temperature C in degrees9Celsius is defined by the equation F C 32 ,5and the relationship between a temperature in de-USE THIS SPACE FOR SCRATCHWORK.grees Fahrenheit and a temperature R in degreesRankine is defined by the equation R F 460.Which of the following expresses the relationship between temperatures in degree Rankine anddegrees Celsius?9(A) R C 32 46059(B) R C 32 46059(C) R C 32 46059(D) R C 86059(E) R C 82853. What is the slope of a line containing the points(1, 13) and ( 3, 6)?(A)(B)(C)(D)(E)0.140.571.751.8364. If a b c 12, a b 4, and a c 7, what isthe value of a ?(A) 2(B) 1323(D) 2(C)(E)233GO ON TO THE NEXT PAGEPractice Test 1 25

22222222MATHEMATICS LEVEL 2—Continued5. If g(x) 2ex 2 and h(x) ln(x), then g(h(7)) (A)(B)(C)(D)(E)USE THIS SPACE FOR SCRATCHWORK.7.69121426.4331.986. The intersection of a cylinder and a plane couldbe which of the following?I.II.III.(A)(B)(C)(D)(E)A circleA triangleA rectangleI onlyII onlyI and III onlyII and III onlyI, II, and III72.4ºX50.8ºY7. The figure above shows a helium balloon risingvertically. When the balloon reaches a height of54 inches, the angles of elevation from points Xand Y on the ground are 72.4 and 50.8 , respectively. What is the distance, in inches, betweenpoints X and Y ?(A)(B)(C)(D)(E)26 61.1772.2984.15124.72236.44Cracking the SAT Subject Test in Math 2GO ON TO THE NEXT PAGE2

222222222MATHEMATICS LEVEL 2—Continued8. What is the value of y2 if y 34 2 30 2 ?USE THIS SPACE FOR SCRATCHWORK.(A) 2562(B) 256(C) 16(D) 4(E)29. The points in the xy-plane are transformed so thateach point A (x, y) is transformed to A’ (3x, 3y).If the distance between point A and the origin isc, then the distance between the point A’ and theorigin is1cc(B)3(C) c(A)(D) c 3(E) 3c10. If p(q( x )) 3 x2 2 2x 2 22and p( x ) 3x 2,x 2then q(x) (A) x2 – 2(B) x2(C) x(D)x2 2(E)xGO ON TO THE NEXT PAGEPractice Test 1 27

22222222MATHEMATICS LEVEL 2—Continued11. If x is the degree measure of an angle such that0 x 90 and cos x 0.6, then sin(90 x) (A)(B)(C)(D)(E)USE THIS SPACE FOR SCRATCHWORK.0.40.50.60.70.812. The set of points defined by the equationx2 y2 z2 4 is(A)(B)(C)(D)(E)a pointa linea circlea planea sphere13. The graph of the function g, where7g( x ) 2, has a vertical asymptotex 6x 9at x (A)(B)(C)(D)(E)0 only3 only7 only0 and 3 only0, 3, and 7GO ON TO THE NEXT PAGE28 Cracking the SAT Subject Test in Math 22

222222222MATHEMATICS LEVEL 2—ContinuedUSE THIS SPACE FOR 8–80–120–160–20014. The graph of y x4 8x3 – 4x2 64x k is shownabove. Which of the following could be the valueof k?(A)(B)(C)(D)(E)1,24052014 –14 –1,24015. If sin x 0.6743, then csc x (A)(B)(C)(D)(E)0.64810.83741.29531.48301.9637GO ON TO THE NEXT PAGEPractice Test 1 29

22222222MATHEMATICS LEVEL 2—Continued16. Sarah is planning a vacation at a hotel that costs 80 per night. Sarah must also pay the 170 airfare to get there and will also pay for an equallypriced hotel room for a friend who will be visitingher on three of the nights. Which of the followingcorrectly expresses the average cost, in dollars,for each night as a function of n, the number ofnights of the vacation?(A) f (n) 80 n 410n 3(B) f (n) 80 n 170n 3(C) f (n) 80 n 410n 3USE THIS SPACE FOR SCRATCHWORK.80 n 410n80 n 170(E) f (n) n(D) f (n) 17. Which of the following is an equation whosegraph is a set of points equidistant from the points(0, 0) and (6, 0)?(A)(B)(C)(D)(E)x 3y 3x 3yy 3xy 3x 3GO ON TO THE NEXT PAGE30 Cracking the SAT Subject Test in Math 22

222222222MATHEMATICS LEVEL 2—Continued18. What is the sum of the infinite geometric seriesUSE THIS SPACE FOR SCRATCHWORK.1111 . ?9 27 81 2435361(B)61(C)3(A)(D) 1(E)4319. Which of the following is equivalent to a – b a b?(A)(B)(C)(D)(E)a ba 0b ab 0b 020. If m and n are in the domain of a function g andg(m) g(n), which of the following must be true?(A)(B)(C)(D)(E)mn 0m nm nm nm nGO ON TO THE NEXT PAGEPractice Test 1 31

22222222MATHEMATICS LEVEL 2—Continued21. In a certain office, the human resources department reports that 60% of the employees in theoffice commute over an hour on average each day,and that 25% of those employees who commuteover an hour on average each day commute bytrain. If an employee at the office is selected atrandom, what is the probability that the employeecommutes over an hour on average by train?(A)(B)(C)(D)(E)USE THIS SPACE FOR SCRATCHWORK.0.100.150.200.250.3022. To the nearest degree, what is the measure ofthe second smallest angle in a right triangle withsides 5, 12, and 13 ?(A)(B)(C)(D)(E)23 45 47 60 67 23. Which of the following is an equation of a lineperpendicular to y 3x – 5 ?(A) y 5x – 3(B) y 3x 51(C) y x 531(D) y – x 431(E) y 3 x 5GO ON TO THE NEXT PAGE32 Cracking the SAT Subject Test in Math 22

222222222MATHEMATICS LEVEL 2—Continued24. What is the range of the function g(x) 2 5cos(3x 7π) ?(A)(B)(C)(D)(E)USE THIS SPACE FOR SCRATCHWORK. –1 g(x) 1 –5 g(x) 1 –5 g(x) 5 –7 g(x) 3 –7 g(x) 525. Of the following list of numbers, which has thegreatest standard deviation?(A)(B)(C)(D)(E)1, 2, 32, 2, 22, 4, 64, 7, 106, 8, 1026. The formula F Ie0.06y gives the final amountF that a bank account will contain if an initialinvestment I is compounded continuously at anannual interest of 6% for y years. Using this formula, after how many years will an initial investment of 100 be worth approximately 600?(A)(B)(C)(D)(E)5.26.013.022.429.7GO ON TO THE NEXT PAGEPractice Test 1 33

22222222MATHEMATICS LEVEL 2—ContinuedUSE THIS SPACE FOR SCRATCHWORK.yIIIxIIIIVsin θ 0 , then θ must be incos θwhich quadrant in the figure above?27. If cos θ 0 and(A)(B)(C)(D)(E)IIIIIIIVThere is no quadrant in which both conditions are true.28. If g( x) g(x) for all real numbers x and if (4, 9)is a point on the graph of g, which of the following points must also be on the graph of g ?(A)(B)(C)(D)(E)( 9, 4)( 4, 9)( 4, 9)(4, 9)(9, 4)If a is a multiple of 10, then a is a multiple of 5.29. If a is an integer, which of the following CANNOT be inferred from the statement above?(A) If a is a multiple of 5, then a is a multipleof 10.(B) If a is not a multiple of 5, then a is not amultiple of 10.(C) a is a multiple of 10 implies that a is amultiple of 5.(D) A necessary condition for a to be a multiple of 10 is that a is a multiple of 5.(E) In order for a to be a multiple of 5, it issufficient that a be a multiple of 10.34 Cracking the SAT Subject Test in Math 2GO ON TO THE NEXT PAGE2

222222222MATHEMATICS LEVEL 2—Continued30. In how many different orders can 8 different colors of flowers be arranged in a straight line?USE THIS SPACE FOR SCRATCHWORK.(A)8(B)64(C) 40,320(D) 80,640(E) 16,777,2162x31. What value doesapproach as xapproaches 0 ? ln( x 1)(A)(B)(C)(D)(E)00.512It does not approach a unique value32. If f(x) 7 – 5x , then f(1) (A) f( 1)(B) f(0) 3 (C) f 5 (D) f(2) 9 (E) f 5 33. What is the period of the graph of y 3tan(2πx 9) ?π21(B)2(A)(C) 3323π(E)2(D)GO ON TO THE NEXT PAGEPractice Test 1 35

22222222MATHEMATICS LEVEL 2—ContinuedX Maple StreetUSE THIS SPACE FOR SCRATCHWORK.10 kmY Elm Street34. The figure above shows a map of Maple Streetand Elm Street. Katherine is biking from Point Xto Point Y. The straight-line distance from PointX to Point Y is 40 kilometers. If Katherine bikesat an average speed of 15 km per hour alongMaple Street and Elm Street, how long will it takeKatherine to get to Point Y ?(A)(B)(C)(D)(E)40 minutes2 hours and 35 minutes2 hours and 40 minutes3 hours and 15 minutes3 hours and 35 minutesx 2 1012g(x)0 320035. If g is a polynomial of degree 4, five of whosevalues are shown in the table above, then g(x)could equal 1 2(A) g( x ) x ( x 1)( x 2 ) 2 (B) g(x) (x – 2)(x – 1)(x 2)(x 3) 1 (C) g( x ) ( x 2 ) x ( x 1)( x 2 ) 2 (D) g(x) (x – 3)(x – 2)(x – 1)(x 2)36 1 (E) g( x ) ( x 2 )( x 1) x ( x 2 ) 2 Cracking the SAT Subject Test in Math 2GO ON TO THE NEXT PAGE2

222222222MATHEMATICS LEVEL 2—Continued36. The only prime factors of an integer m are 2, 3, 5,and 13. Which of the following could NOT be afactor of m ?(A)(B)(C)(D)(E)USE THIS SPACE FOR SCRATCHWORK.69122635π37. If 0 x and cos x 4sin x, what is the value2of x ?(A)(B)(C)(D)(E)0.2450.2500.3281.2171.32638. If g(x) 3 5x , what is the value of g 1(15) ?(A)(B)(C)(D)(E)0.041.733.175.0025.9839. The Triangular Number Sequence Tn can be defined recursively asT1 1Tn Tn –1 n for n 1What is the 11th term of the sequence?(A)(B)(C)(D)(E)4555667891GO ON TO THE NEXT PAGEPractice Test 1 37

22222222MATHEMATICS LEVEL 2—Continued40. If f(x) x3 x2 – 16x 12, which of the followingstatements are true?USE THIS SPACE FOR SCRATCHWORK.I. The equation f(x) 0 has three realsolutionsII. f(x) 8 for all x 0III. The function is increasing for x 2(A)(B)(C)(D)(E)I onlyIII onlyI and III onlyII and III onlyI, II, and III onlyGO ON TO THE NEXT PAGE38 Cracking the SAT Subject Test in Math 22

222222222MATHEMATICS LEVEL 2—Continued10–1USE THIS SPACE FOR SCRATCHWORK.g01h–141. Portions of the graphs of g and h are shownabove. Which of the following could be a portionof the graph of gh (E)0–11–101–1001–1GO ON TO THE NEXT PAGEPractice Test 1 39

22222222MATHEMATICS LEVEL 2—ContinuedUSE THIS SPACE FOR SCRATCHWORK.242. The set of all real numbers y such that y y is(A)(B)(C)(D)(E)all real numbersno real numbersnegative real numbers onlynonnegative real numbers onlyzero only12560 x 43. In the triangle shown above, sin x 5135(B)12(A)(C)5 3125 32412(E)13(D)44. The length, width, and height of a rectangularsolid are 6, 3, and 2. What is the length of thelongest segment that can be drawn between twovertices of the solid?(A) 6(B) 3 5(C) 7(D) 12(E) 1840 Cracking the SAT Subject Test in Math 2GO ON TO THE NEXT PAGE2