MTH 2001 Sample Final 1 PDF

Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 1 BARUCH COLLEGE MATH 2001, DAY, FORM A, PART 1 NAME: SIGNATURE: INSTRUCTOR/SECTION: PART 1: You are NOT ALLOW...

Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 1 BARUCH COLLEGE MATH 2001, DAY, FORM A, PART 1 NAME: SIGNATURE: INSTRUCTOR/SECTION: PART 1: You are NOT ALLOWED TO USE A CALCULATOR on this part of the exam. DIRECTIONS: Write your name and instructor/section number on the line above and sign your name. All exams are hand-graded by the instructor as well as machine graded, and the scores are compared. Students MUST SHOW ALL WORK in the area provided next to each problem. Students who do NOT provide supporting work WILL NOT receive credit for the problem. Problems 1 − 18 are multiple choice. CIRCLE your answer (A, B, C, D, or E) and MARK your answer on the Scantron sheet. Problems 19 − 24 are free response problems. WRITE your answer in the blank space to the right of the problem statement. You will have 90 minutes to complete Part 1. When you are finished with Part 1, also enter your answers on the Scantron sheet. After 90 minutes, the proctor will take this part of the exam from you and give you Part 2, which consists of 10 additional problems. You will keep the Scantron sheet. NO ANSWERS MAY BE CHANGED ON THE SCANTRON FOR PART 1 ONCE THIS EXAM HAS BEEN COLLECTED. Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 2 1. The graph of y = f (x) is sketched below. 1. 5 y 4 3 2 1 x −5 −4 −3 −2 −1 −1 1 2 3 4 5 −2 −3 −4 −5 −6 −7 −8 Identify the domain and range of f (x). (A) Domain: (−4, 3], Range: (−7, −6) ∪ [−5, 4] (B) Domain: (−4, −2) ∪ (−2, 3], Range: (−7, −6) ∪ [−5, 4] (C) Domain: [−4, −2) ∪ (−2, 3), Range: [−7, −6] ∪ (−5, 4) (D) Domain: (−4, 3], Range: [−7, 4] (E) Domain: (−4, −2) ∪ (−2, 3], Range: (−7, 4] 2. Find an equation of the line parallel to 2x + 5y = 7 passing through the 2. point (3, −4). −2 7 −2 14 5 (A) y = x+ (B) y = x− (C) y = x + 13 5 5 5 5 2 5 23 2 26 (D) y = x − (E) y = x − 2 2 5 5 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 3 3. Suppose f (x) is a polynomial. A complete graph of y = f (x) is sketched 3. below: 5 y 4 3 2 1 x −5 −4 −3 −2 −1 −1 1 2 3 4 5 −2 −3 −4 −5 Which of the following statements COULD be true? (A) The degree of the polynomial is 7 and the leading coefficient is positive (B) The degree of the polynomial is 4 and the leading coefficient is positive (C) The degree of the polynomial is 3 and the leading coefficient is negative (D) The degree of the polynomial is 6 and the leading coefficient is negative (E) The degree of the polynomial is 5 and the leading coefficient is negative f (x + h) − f (x) 4. Let f (x) = 3x2 + 1. Evaluate the difference quotient for 4. h h ̸= 0. Simplify your answer as much as possible. (A) 6x (B) 6x + 1 (C) 6x + 3h (D) 3h (E) 6x + 3h + 2 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 4 5. Given the right triangle below: 5. 2 θ 3 Evaluate sec θ. √ √ 2 3 13 1 13 (A) (B) (C) (D) (E) 3 2 2 2 3 x 6. Determine the domain of f (x) =. Write your answer in interval 6. 3x7 − 12x5 notation. (A) (−∞, −2) ∪ (−2, 0) ∪ (0, 2) ∪ (2, ∞) (B) (−∞, 0) ∪ (0, ∞) (C) (−∞, 0) ∪ (0, 2) ∪ (2, ∞) (D) (0, 2) ∪ (2, ∞) (E) (2, ∞) Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 5 7. The graph of a function of the form f (x) = A cos(Bx) is depicted below. 7. 4 y 3 2 1 x π π 3π 2π 5π 3π −1 2 2 2 −2 −3 −4 Determine A and B. 1 1 (A) A = 3, B = 2 (B) A = 3, B = (C) A = , B = 2 2 3 1 1 1 (D) A = , B = (E) A = , B = 3 2 3 2 3x − 3 8. Find ALL asymptote(s) to the graph of y = 8. x2 − 8x + 16 (A) y = 3, x = 4 (B) y = 0, x = 1, x = 4 (C) y = 3, x = 1 (D) y = 0, x = −4, x = 4 (E) y = 0, x = 4 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 6 a2   9. Suppose ln a = 0.1 and ln b = 0.3. Evaluate ln. 9. b HINT: Use properties of logarithms. (A) −0.2 (B) −0.1 (C) 0.1 (D) 0.2 (E) 0.5 10. Which of the following is an ODD function? 10. 1 (A) f (x) = (B) f (x) = 2 sin x + 6x (C) f (x) = cos x − 3x x6 (D) f (x) = ex − x4 (E) f (x) = 3x2 + 7 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 7 7 − 3x 11. Let f (x) =. Find the inverse function, f −1 (x). 11. x+5 3x − 7 x−5 x−7 (A) f −1 (x) = (B) f −1 (x) = (C) f −1 (x) = x−5 7 + 3x 5x − 3 7 − 5x 7 + 5x (D) f −1 (x) = (E) f −1 (x) = x+3 x−3 π cos x 12. Assuming 0 < x < , which of the following is equivalent to ? 12. 2 3 cot x csc x (A) 3 csc x (B) (C) 3 sin x 3 sin x sec x (D) (E) 3 3 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 8 13. Solve for x: 13. 2x x e − 3e − 10 = 0. (A) x = ln 2 only (B) x = ln 3 only (C) x = ln 5 only (D) x = ln 2 and x = ln 5 (E) x = ln 3 and x = ln 5 14. Find all x that satisfy 14. 2 2 cos x + cos x = 0 where 0 < x < 2π. π 2π 3π 4π (A) x = , , , 2 3 2 3 4π 5π (B) x = 0, π, , 3 3 π π 2π 3π (C) x = , , , 3 2 3 2 π 2π (D) x = 0, , , π 3 3 2π 3π 5π (E) x = 0, , , 3 2 3 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 9 15. Which of the following is the graph of y = 2 − ex ? 15. 3 y 5 y 6 y 2 4 5 1 3 4 x 3 2 −4 −3 −2 −1 1 2 2 −1 1 1 x x −2 −1 1 2 3 4 5 −3 −2 −1 1 2 3 (A) −3 (B) −1 (C) −1 3 y 6 y 2 5 1 4 x 3 −4 −3 −2 −1 1 2 2 −1 1 −2 x −3 −3 −2 −1 −1 1 2 3 (D) (E) 16. Solve the inequality 16. x3 + x2 ≥ 2x. Write your answer in interval notation. (A) (0, 1) (B) (−∞, −2] ∪ [0, 1] (C) (−∞, −2) (D) (−∞, −2] ∪ [1, ∞) (E) [−2, 0] ∪ [1, ∞) Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 10 √ ! − 3 17. Evaluate arccos using the standard domain of the arccos function. 17. 2 π π 2π 5π 4π (A) (B) (C) (D) (E) 6 3 3 6 3 18. A point (x, y) in the first quadrant on the line y = 6 − 2x is chosen, and a 18. rectangle in the first quadrant is formed as shown below: y 6 (x, y) x 3 Find a function P (x) that gives the perimeter of this rectangle as a function of the x-coordinate of the chosen point (for 0 < x < 3). (A) P (x) = 6 − x (B) P (x) = 12 − 2x (C) P (x) = 6x − 2 (D) P (x) = 12 + 2x (E) P (x) = 12x − 6 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 11 2 19. Suppose cos θ = for an angle θ lying in Quadrant IV. Find tan θ. 19. 3 20. Solve for x:  3x+2 20. 1 34x−1 =. 9 Write your answer as an integer or fraction in lowest terms. Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 12 21. Solve for x: 21. 2 log7 (x) + 5 = 9. Write your answer as an integer or fraction in lowest terms. 22. Suppose, for some constants b and c, the polynomial 22. f (x) = x2 + bx + c √ √ has zeros at x = 1 + 3 and x = 1 − 3. Find b. Write your answer as an integer or fraction in lowest terms. Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 1 Page 13 23. Evaluate √
23. ln e. Write your answer as an integer or fraction in lowest terms. 24. Evaluate each of the following.   5π (a) tan 24(a). 6 (b) sec(3π) 24(b). (c) sin(−225◦ ) 24(c). Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 2 Page 1 BARUCH COLLEGE MATH 2001, DAY, FORM A, PART 2 NAME: SIGNATURE: INSTRUCTOR/SECTION: PART 2: You ARE allowed to use a calculator on this part of the exam. DIRECTIONS: Write your name and instructor/section number on the line above and sign your name. All exams are hand-graded by the instructor as well as machine graded, and the scores are compared. Students MUST SHOW ALL WORK in the area provided next to each problem. Students who do NOT provide supporting work WILL NOT receive credit for the problem. Problems 101 − 106 are multiple choice. CIRCLE your answer (A, B, C, D, or E) and MARK your answer on the Scantron sheet as Problems 101 through 106 on the BACK of your Scantron. Problems 107 − 110 are free response problems. WRITE your answer in the blank space underneath the problem statement. You will have 30 minutes to complete Part 2. Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 2 Page 2 101. In the year that a certain cafe first opened, the price of a cup of coffee is 101. $2.25. 10 years after the cafe opened, the price of a cup of coffee is $2.65. Find a linear equation of the form P = mt + b which gives the relationship between the price of a cup of coffee, P, and the number of years since the cafe opened. (A) P = −0.04t + 2.65 (B) P = 25t + 2.65 (C) P = 0.04t + 2.25 (D) P = 0.04t − 0.09 (E) P = −0.04t + 3.05 102. Let √ 102. f (x) = 2 x − 23 and let g(x) = e2x. Evaluate g ◦ f (169). Round your answer to the nearest hundredth. (A) 492.81 (B) 562.34 (C) 421.98 (D) 403.43 (E) 598.02 Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 2 Page 3 103. Alice is investing money in an account that offers an annual interest rate of 103. 3% compounded continuously. What should Alice’s initial investment be if she wants to have $2, 000 in the account after 5 years? Round your answer to the nearest HUNDREDTH of a dollar. (A) $1672.90 (B) $1694.03 (C) $1721.42 (D) $1785.61 (E) $1839.01 104. A camera at ground level is 1000 feet away from the bottom of a building 104. which is 300 feet tall. The camera is pointed at the top of the building. Determine the the angle between the ground and the camera’s line of sight. Round your answer in degrees to the nearest hundredth. (A) 11.42◦ (B) 12.89◦ (C) 14.51◦ (D) 15.06◦ (E) 16.70◦ Math 2001 Sample Final 1 Final Exam Exam Number SF1(DAY) Form A Part 2 Page 4 105. Let ( 105. 2x + 1, x