Math 102 Sample Final Exam PDF

Math 102 - Sample Final Exam This exam consists of 40 multiple choice questions. In each case, select a single answer (A-F). Each correct answer is worth 2.5 marks, for a total of 100 marks. There are no penalties for incorrect answers. Note:...

Math 102 - Sample Final Exam This exam consists of 40 multiple choice questions. In each case, select a single answer (A-F). Each correct answer is worth 2.5 marks, for a total of 100 marks. There are no penalties for incorrect answers. Note: Questions #1-#5 are based on the following information: In its first year, the weight of a terrier puppy increases at a constant rate. At age ten weeks the puppy weighs 8.2 kg and at age twenty weeks the puppy weighs 16.2 kg. 1. If we model the weight of the puppy in its first year (y, in kg) as a function of its age (x, in weeks), what equation is most appropriate given that its weight increases at a constant rate? (A) This is linear, i.e. y=mx+b (B) This is parabolic, i.e. y=ax2+bx+c (C) This is exponential, i.e. y=cerx (D) This is circular, i.e. x2+y2=r2 (E) This is trigonometric, i.e. y=sin(x) (F) This is ridiculous, e.g. y=x1/2+ðx!3x7.1 ( 2. What is the slope in the above model equation, expressed as a fraction? (A) m=3/5 (B) m=4/5 (C) m=!5/4 (D) m=5/4 (E) m=!3/5 (F) m=!4/5 3. What is the y-intercept of the above model equation, expressed as a fraction? (A) b=2/5 (B) b=!2/5 (C) b=!1/3 (D) b=2/3 (E) b=3/5 (F) b=1/5 4. What does the model predict the puppy will weigh at age 52 weeks? (A) 40.5 kg (B) 41.2 kg (C) 41.8 kg (D) 42.0 kg (E) 43.1 kg (F) 43.7 kg 5. At what age will the puppy weigh exactly 30 kg, rounded to two decimals? (A) 36.00 weeks (B) 36.50 weeks (C) 37.25 weeks (D) 38.05 weeks (E) 38.45 weeks (F) 38.95 weeks 6. Simplify the expression by writing it as a single exponential xn. What is n? (A) n=3/2 (B) n=9/2 (C) n=!3/2 (D) n=5/2 (E) n=!5/2 (F) n=!9/2 7. Solve the inequality. Write the answer in interval notation. (A) [1/3 , 1] (B) (1 , 4) (C) [-1 , 1) (D) (1/3 , 1] (E) (2/3, 5/3] (F) (-1/3 , 2/3] 8. Solve the equation. (A) x=1/4 , x=!1 (B) x=!1/4 , x=1 (C) x=1/3 , x=!4 (D) x=!1/3 , x=4 (E) x=4/3 , x=1/4 (F) x=!4/3, x=1/4 9. Fully factor the expression (A) x3(x2!1)(2x+1) (B) x3(2x-1)(x+1) (C) x2(x2+1)(2x!1)2 (D) x3(x!1)(x+1)(2x+1) (E) x3(x2+1)(2x!1) (F) x2(x!1)(2x-1)(2x+1) 10. Solve. Write your final answer in interval notation. (A) (!2/3 , 2) (B) (!2 , 2/3) (C) (1/3 , 1/2) (D) (!2/3 , 1/2) (E) (2/3 , 2) (F) There is no solution Note: Questions #11-#14 are based on the following information: Two planes are flying towards each other at the same altitude, but at slightly different angles, resulting in a relatively close pass-by. The direct distance between the two planes (in km) as a function of time (in minutes) is given by the quadratic equation 11. How far apart are the planes at t=2 minutes? (A) 30.75 km (B) 11 km (C) 32.50 km (D) 12.75 km (E) 15.25 km (F) 20.6 km 12. Complete the square to write D(t) in vertex form: (A) D(t)=(t!11)2 + 30.75 (B) D(t)=(t!11/2)2 + 11 (C) D(t)=(t!1/2)2 + 30.75 (D) D(t)=(t!11/2)2 + 1/2 (E) D(t)=(t!1/2)2 + 1/2 (F) D(t)=(t!11/2)2 + 11/2 13. At what time will the two planes be closest to each other? (A) In 5 ½ minutes from now. (B) In 11 minutes from now. (C) In ½ minute from now. (D) In 30.75 minutes from now. (E) In 25 minutes from now. (F) In 40.25 minutes from now. 14. How close will the two planes be at that time, i.e. what is their closest distance? (A) 30.75 km (B) 12.75 km (C) 11 km (D) 5.5 km (E) 500 m (F) They will crash into each other, i.e. 0 m. Note: Questions #15-#16 are based on the following information: Moss is growing on the forest floor in a perfectly circular area. Right now, the area of the moss circle is 40 m2. Over the next four months, the radius of the circle will increase by 5 metres. 15. What is the radius of the moss circle right now? (Round to two decimals) (A) 3.57 m (B) 8.00 m (C) 12.73 m (D) 4.12 m (E) 6.37 m (F) 5.00 m 16. What is the area of the moss circle four months from now? (Round to the nearest square metre) (A) 45 m2 (B) 56 m2 (C) 231 m2 (D) 82 m2 (E) 100 m2 (F) 186 m2 17. Consider the function. State the domain of this function. (A) All x except x=2. (B) All x except x=0 and x=2. (C) All x except x=!2 and x=2. (D) All x except x=!2 and x=0. (E) All x except x=!2 and x=0 and x=2. (F) There are no domain restrictions. 18. Consider the function. State all x- and y-intercepts. (A) The x-intercept is x=0. There is no y-intercept. (B) The x-intercept is x=0. The y-intercept is y=0. (C) The y-intercept is y=0. There is no x-intercept. (D) The x-intercepts are x=!2 and x=2. The y-intercept is y=0. (E) The x-intercepts are x=!2 and x=2. There is no y-intercept. (F) There is no x-intercept. There is no y-intercept. 19. In your own words, describe the transformations in the correct order that would produce the graph of given the original graph. (A) Shift the graph one unit right, stretch vertically by two, move the graph one unit up. (B) Flip the graph vertically and stretch by two, move the graph one unit up. (C) Stretch the graph vertically by two, shift the graph one unit left, move it one unit up. (D) Shift the graph one unit left, flip and scale vertically by two, move it one unit up. (E) Flip the graph horizontally, stretch vertically by two, move one unit up. (F) Flip the graph horizontally, move it two units right, then move it one unit up. 20. The point with coordinates (x,y)=(1,1/3) is a point on the graph of. What are the coordinates of the corresponding point on the the graph of ? (A) (!1 , 5/3) (B) (1 , 5/3) (C) (1 , !5/3) (D) (5/3 , 1) (E) (5/3 , !1) (F) (!5/3 , 1) 21. Consider the function. Simplify the expression for. (A) (B) (C) (D) (E) (F) 22. What is the symmetry of the function ? (A) The function is even. (B) The function is odd. (C) The function is neither even nor odd. (D) The function is both even and odd. (E) The function is symmetric across the x-axis. (F) The function is circular. 23. Given the polynomial , find the degree and leading coefficient. (A) degree = 3, leading coefficient = 2 (B) degree = 3, leading coefficient = !1 (C) degree = 3, leading coefficient = !4 (D) degree = 6, leading coefficient = 2 (E) degree = 6, leading coefficient = !1 (F) degree = 6, leading coefficient = !4 24. Given the polynomial , which of the following graphs best represents this function? 25. Consider the given graph. What equation best represents this graph? (A) (B) (C) (D) (E) (F) 26. Write the expression as a single logarithm. (A) (B) (C) (D) (E) (F) 27. Solve the equation (A) x=(ln 3 ! 1) / 2 (B) x=ln(3/2) ! 1 (C) x=(ln 2 ! 1) / 3 (D) x=ln(2/3) + 1 (E) x=ln(2/3) ! 1 (F) x=(ln 2 + 1) / 3 28. Find the value of (A) 4 (B) 16 (C) 2 (D) 3 (E) 8 (F) 256 Note: Questions #29-#31 are based on the following information: The size of an animal population is decaying exponentially. Every five years, the population loses 25% of its members (that is, 75% of the population remain after five years). Let N(t) be the population size after t years, and let No be the initial population size. Let r be the continuous population decay rate. 29. The general formula for this population decline will be (A) (B) (C) (D) (E) (F) 30. Find the continuous decay rate r for this population. (A) r=!0.27726 (B) r=!0.76234 (C) r=!0.15267 (D) r=!0.07634 (E) r=!0.05754 (F) r=!0.04438 31. After what time will the population size be exactly half of its current size? Round your answer to two decimals. (A) After 10.09 years. (B) After 10.95 years. (C) After 11.30 years. (D) After 11.38 years. (E) After 11.82 years. (F) After 12.05 years. 32. Convert 80o to radian measure. (A) ð/8 (B) ð/4 (C) ð/9 (D) 4ð/9 (E) 9ð/4 (F) 8ð/9 33. Find and state the value of (A) !1 (B) 0.2086 (C) 0.2693 (D) 0 (E) 0.5432 (F) 0.4531 34. Find all x-values in [0,2ð] such that (A) x=2ð/3 , x=4ð/3 (B) x=ð/6 , x=5ð/6 (C) x=ð/6 , x=11ð/6 (D) x=5ð/6 , x=11ð/6 (E) x=4ð/3 , x=5ð/3 (F) x=7ð/6 , x=11ð/6 35. If sin(x)=z, what is cos2(ð-x)=? (A) -z (B) z-ð (C) 1-z2 (D) z2 (E) -z2 (F) (z-ð)2 36. Which of the following statements is correct? (A) sin(x) is an odd function, cos(x) is an odd function (B) sin(x) is an even function, cos(x) is an odd function (C) sin(x) is equal to cos(-x) for any x (D) sin(-x) is equal to sin(x) for any x (E) cos(-x) is equal to cos(x) for any x (F) sin(x+y)=sin(x)+sin(y) for any x Note: Questions #37-#38 are based on the following information: A 25 metre long rope is attached to the top of a vertical pole and anchored to a spot on the ground some distance away. Assume the rope is tightly drawn, that is we can model it as a perfectly straight line without any sagging. The angle the rope makes with the horizontal is 32o. 37. What is the angle that the rope makes with the vertical pole? (A) 32o (B) 64o (C) 148o (D) 58o (E) 122o (F) 23o 38. How tall is the pole? (A) 21.2 m (B) 13.25 m (C) 32.0 m (D) 25.0 m (E) 12.51 m (F) 18.32 m Note: Questions #37-#38 are based on the two points A: (x,y)=(4,-5) and B: (x,y)=(-2,3) 39. What is the distance between the two points A and B? (A) 100 (B) 10 (C) 5 (D) 3 (E) 2 (F) 1 40. What is the equation of the circle that has points A and B as its diameter? (A) (x!1)2 + (y+1)2 = 25 (B) (x+1)2 + (y!1)2 = 5 (C) (x!1)2 + (y!1)2 = 100 (D) (x+1)2 + (y+1)2 = 25 (E) (x!1)2 + (y+1)2 = 100 (F) (x!1)2 + (y!1)2 = 1  Answer Sheet - Record all answers here 1 A B C D E F 21 A B C D E F 2 A B C D E F 22 A B C D E F 3 A B C D E F 23 A B C D E F 4 A B C D E F 24 A B C D E F 5 A B C D E F 25 A B C D E F 6 A B C D E F 26 A B C D E F 7 A B C D E F 27 A B C D E F 8 A B C D E F 28 A B C D E F 9 A B C D E F 29 A B C D E F 10 A B C D E F 30 A B C D E F 11 A B C D E F 31 A B C D E F 12 A B C D E F 32 A B C D E F 13 A B C D E F 33 A B C D E F 14 A B C D E F 34 A B C D E F 15 A B C D E F 35 A B C D E F 16 A B C D E F 36 A B C D E F 17 A B C D E F 37 A B C D E F 18 A B C D E F 38 A B C D E F 19 A B C D E F 39 A B C D E F 20 A B C D E F 40 A B C D E F Math 102 Sample Final Answer Key 1. (A) This is linear, i.e. y=mx+b 2. (B) m=4/5 3. (F) b=1/5 4. (C) 41.8 kg 5. (C) 29.75 weeks 6. (B) n=9/2 7. (D) (1/3 , 1] 8. (A) x=1/4 , x=!1 9. (D) x3(x!1)(x+1)(2x+1) 10. (E) (2/3 , 2) 11. (D) 12.75 km 12. (D) D(t)=(t!11/2)2 + 1/2 13. (A) In 5 ½ minutes from now. 14. (E) 500 m 15. (A) 3.57 m 16. (C) 179.9 m2 17. (C) All x except x=!2 and x=2. 18. (B) The x-intercept is x=0. The y-intercept is y=0. 19. (E) Flip the graph horizontally, stretch vertically by two, move one unit up. 20. (A) (!1 , 5/3) 21. (F) 22. (B) The function is odd. 23. (F) degree = 6, leading coefficient = !4 24. (C) 25. (D) 26. (E) 27. (A) x=(ln 3 ! 1) / 2 28. (D) 3 29. (A) 30. (E) r=!0.05754 31. (F) After 12.05 years. 32. (D) 4ð/9 33. (A) !1 34. (F) x=7ð/6 , x=11ð/6 35. (C) 1-z2 36. (E) cos(-x) is equal to cos(x) for any x 37. (D) 58o 38. (B) 13.25 m 39. (B) 10 40. (A) (x!1)2 + (y+1)2 = 25