NAME:MATH 103 Gateway Exam, version (a)31 October 2008100 pointsInstructions:1. This exam has 4 pages (including this one), which contain 10 questions. Please check that youhave all of the pages.2. Please do your work on scratch paper, not on this exam.3. When an answer box is given, write your answer in the box. Nothing outside the answer boxwill be graded.4. You do not need to simplify your answers.5. You may not use a book, notes, a calculator, or anything except a writing instrument, an eraser,and scratch paper for this exam.6. There will be no partial credit given. You must get 8 out of 10 questions completely correctin order to pass this exam. A passing score on this exam will give you 100 points toward yourgrade for this course.7. You have 50 minutes to complete this exam.CORRECTINCORRECTQuestion 1. Select all intervals for which |4y − 11| < 9 is true.(−1/2, 5)(−∞, −1/2)(−∞, 1/2)(5, ∞)(1/2, 5)CORRECTINCORRECTQuestion 2. Given the graph of y = f(x) below, select all intervals on which the function isdecreasing.(−4, 0)(−∞, −5)(−2, 2)(4, ∞)(−5, 0)Page 1CORRECTINCORRECTQuestion 3. What are cos θ, sin θ, and cot θ?ANSWERCORRECTINCORRECTQuestion 4. Find the equation for the secant line of y = 3xfrom (0, 1) to (2, 9).ANSWERCORRECTINCORRECTQuestion 5. Solve the equation F = mV − V0tfor t.(a) None of the others(b)Fm(V − V0)(c)F mV − V0(d)V − V0F m(e)m(V − V0)FCORRECTINCORRECTQuestion 6. What is tan(−2π/3)?(a) −√3/3(b)√3(c)√3/3(d) None of these(e) −√3Page 2CORRECTINCORRECTQuestion 7. Match the following graphs with their formulas.1. ln(x − 3)2.23x + 23.x − 2x − 14. −2x + 1CORRECTINCORRECTQuestion 8. Given the graph of y = f(x) below, select the graph of y = f (x −1).(a) (b)(c) (d)(e) None of the othersPage 3CORRECTINCORRECTQuestion 9. Which of the following graphs best represents y = −12cos(πx)?(a) (b)(c) (d)CORRECTINCORRECTQuestion 10. Find the solution(s) to the equation log(x + 5) + log(x + 2) = log(14x).ANSWERPage 4NAME:MATH 103 Gateway Exam, version (b)31 October 2008100 pointsInstructions:1. This exam has 4 pages (including this one), which contain 10 questions. Please check that youhave all of the pages.2. Please do your work on scratch paper, not on this exam.3. When an answer box is given, write your answer in the box. Nothing outside the answer boxwill be graded.4. You do not need to simplify your answers.5. You may not use a book, notes, a calculator, or anything except a writing instrument, an eraser,and scratch paper for this exam.6. There will be no partial credit given. You must get 8 out of 10 questions completely correctin order to pass this exam. A passing score on this exam will give you 100 points toward yourgrade for this course.7. You have 50 minutes to complete this exam.CORRECTINCORRECTQuestion 1. Solve the equation1R=1R1+1R2for R.(a) R1+ R2(b)1R1+ R2(c)R1+ R22(d)R1+ R2R1R2(e)R1R2R1+ R2Page 5CORRECTINCORRECTQuestion 2. Which of the following graphs best represents y = −3 sin(2x)?(a) (b)(c) (d)CORRECTINCORRECTQuestion 3. Match the following graphs with their formulas.1. 2(x − 1)2− 42. sin(2x)3.x − 2x − 14. (x + 1)3CORRECTINCORRECTQuestion 4. Given the graph of y = f(x) below, what is the range of the function?(a) (−∞, ∞)(b) [−10, 8](c) [−10, 8)(d) (−∞, 8)(e) (−12, 12)Page 6CORRECTINCORRECTQuestion 5. Select all intervals for which x2+ 4x − 12 ≤ 0 is true.[−2, 6][−2, ∞)[2, ∞)(−∞, −6][−6, 2]CORRECTINCORRECTQuestion 6. Which one of the following is true?43a27◦(a) a = 43 sin 27◦(b) a = 43 cos 63◦(c) a = 43 sec 63◦(d) a =43sin 27◦(e) a =43csc 63◦CORRECTINCORRECTQuestion 7. Find the solution(s) to the equation ln x + 3 ln 2 = ln2x.ANSWERCORRECTINCORRECTQuestion 8. Find the equation for the secant line of y = 8√x from (1, 8) to (4, 16).ANSWERPage 7CORRECTINCORRECTQuestion 9. Given the graph of y = f(x) below, select the graph of y = −f (x) + 5.(a) (b)(c) (d)(e) None of the othersCORRECTINCORRECTQuestion 10. What is sin π/4?ANSWERPage 8NAME:MATH 103 Gateway Exam, version (c)31 October 2008100 pointsInstructions:1. This exam has 4 pages (including this one), which contain 10 questions. Please check that youhave all of the pages.2. Please do your work on scratch paper, not on this exam.3. When an answer box is given, write your answer in the box. Nothing outside the answer boxwill be graded.4. You do not need to simplify your answers.5. You may not use a book, notes, a calculator, or anything except a writing instrument, an eraser,and scratch paper for this exam.6. There will be no partial credit given. You must get 8 out of 10 questions completely correctin order to pass this exam. A passing score on this exam will give you 100 points toward yourgrade for this course.7. You have 50 minutes to complete this exam.CORRECTINCORRECTQuestion 1. Select all intervals for which 4x + 5 > 1 −3x is true.[−4/7, ∞)(−∞, −4/7](−4/7, ∞)(−∞, −4/7)(−∞, 4/7)Page 9CORRECTINCORRECTQuestion 2. Given the graph of y = f(x) below, select the graph of y = −f (x + 1).(a) (b)(c) (d)(e) None of the othersCORRECTINCORRECTQuestion 3. Solve the equation ln(3x) + ln(3) = ln(x −3) for x.ANSWERCORRECTINCORRECTQuestion 4. Which of the following graphs best represents y = −cos(2πx)?(a) (b)(c) (d)Page 10CORRECTINCORRECTQuestion 5. What is tan 2π/3?(a) None of these(b)√3/3(c) −√3(d)√3(e) −√3/3CORRECTINCORRECTQuestion 6. If θ is an acute angle and tan θ = 7/3, then what are cos θ, sin θ, and csc θ? (Hint:Draw and label an appropriate triangle.)ANSWERCORRECTINCORRECTQuestion 7. Solve the equation E =12mv2+ mgh for m.(a) None of the others(b)E12v2+ gh(c) E −12v2− gh(d)E − gh12v2(e)2Ev2+ ghCORRECTINCORRECTQuestion 8. Find the equation for the secant line of y = log x from (1, 0) to (10, 1).ANSWERPage 11CORRECTINCORRECTQuestion 9. Given the graph of y = f(x) below, select all intervals on which the function isincreasing.(2, 6)(−1, 2)(1, 4)(−∞, 1)(4, ∞)CORRECTINCORRECTQuestion 10. Match the following graphs with their formulas.1. sin(2x)2. −2x + 13. x1/4+ 24. ln(x − 3)Page