MHF4U1 Exam Review 1. For each of the following graphs, state: i) the maximum ii) the minimum iii) the interval(s) where the function is increasing iv) the interval(s) where the function is decreasing sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m v) the interval(s) where f(x)>0 vi) the interval(s) where f(x)<0 14 4 12 10 2 8 6 5 -5 -2 -4 2. determine the degree and type of each polynomial function. th a) f(x) =4x3 - 5x + d) x -1 0 1 3 y 11 36 https:> 0 https://www.coursehero.com/file/16818357/ExamReview/ b) x4 - 3x3 - 3x2 + 7x + 6 0 15. Solve each polynomial inequality algebraically and then graph your solution on a number line. a) x3 - 7x - 6 0 b) x3 - 4x2 + x + 6 0 16. For each function, determine the reciprocal function and then state the vertical and horizontal asymptote of each of the reciprocal functions. b) x2 - 16 a) x - 4 c) 5x - 7 17. For each function, determine: i) x-intercept and y-intercept sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m ii) equation of V.A. iii) equation of H.A. \u0001\u0002 a) f(x) = \u0003 \u0002 \u0004\u0001\u0002\u0005\u0006 \u0002 \u0003 \u0004\u0007\u0002\u0004\b b) g(x) = \u0003 \u0002 \u0005\u0006\u0002\u0005 18. Sketch each of the following rational functions: a) y = \u0002\u0004\u0001 b) y = \u0002\u0004 \u0006\u0002\u0005 19. Solve each of the following rational equations: a) x 2 x+ 4 = x+ 3 x1 b) 2x + 3 1 x + 1 + = x+ 3 2 x1 Th 20. Suppose that the temperature, T, in degrees Celsius, varies with the height h, in 60 . Find the kilometers, above the earth's surface according to the equation T (h) = h+ 2 average rate of change of the temperature at the height changes from 1 km to 3 km. Find the instantaneous rate of change of temperature with respect to height at a height of 3 km. 21. A parachutist jumps out of an airplane. The distance, s, (in meters), through which 6t she falls in t seconds is given by s(t ) = 10t . Determine the instantaneous rate of t+1 change of the distance through which she falls at 3 seconds. Determine the average rate of change of the distance which the parachutist falls from 1 - 2 seconds. https://www.coursehero.com/file/16818357/ExamReview/ 22. Convert each to radian measure: a) 85 b) 315 23. Convert to degree measure: a) 0.2 b) \u0007 24. Sketch the graph of each of the following from 0 to 2 a) y = sinx b) y = cosx c) y = tanx d) y = cscx e) y = secx f) y = cotx 25. For each of the following state: ii) period iii) phase shift iv) vertical shift sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m i) amplitude a) y = cos(x + /2) - 1 b) f(x) = 1/2sin(3x - ) 26. Sketch one cycle of each graph: a) f(x) = 3cos(4x - ) b) y = 1/2sin3x - 1 27. The depth of water at the end of a pier in vacation village varies with the tides throughout the day and can be modeled by the equation D = 1.5cos[0.575(t - 3.5)] + 3.8 a) Determine the average rate of change as t goes from 4.0 to 6.5. b) Determine the instantaneous rate of change at t = 6.5 28. Use special angles to determine the exact value of each of the following trigonometric ratios. a) cos0.524 b) tan5/6 c) sin 5.498 29. Use compound angles to evaluate the exact value of the following: Th a) sin /12 b) cos5/12 30. Prove each trigonometric identity: a) \u000e\u000f\u0010\u0002 \u0010\u0011\u0012\u0002 \u0005\u0014\u0015\u0012\u0003 \u0002 \u0013 \u0005\u000e\u000f\u0014\u0003 \u0002 b) \u0016 \u0013 2\u0018\u0019\u001a \u001b \u0004\u0014\u0015\u0012\u0002 \u0005\u0014\u0015\u0012\u0002 31. Solve each trigonometric equation for 0x2 a) 3 \u0016 2\u001a\u001e\u0018\u001b \u0013 0 b) 2cos2x + cosx - 1 = 0 c) 2sin2x +5sinx - 3 = 0 d) 2sinx - cos2x = 2 https://www.coursehero.com/file/16818357/ExamReview/ 32. Evaluate each logarithm: a) log4 \u0006 b) log8512 c) log28 + log39 d) log381 - log464 33. Write each as a single logarithm: a) 2log(x - 1) - log (3x - 6) b) 2log(2x + 5) + 5log(x - 8) 34. Solve using same base: a) 93x+1 = 27x b) 6(34f - 2) = 2 35. Solve: 52x - 1 = 7 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 36. Solve each of the following: a) log2(x - 2) + log2(x + 1) = 2 b) log5(x + 2) - log5(x - 1) = 2log53 37. For a biology experiment, there are 50 cells present. After 2 hours, there are 1600 bacteria. How many bacteria would their be in 6 hours? 38. A laboratory has 40 mg of iodine 131. After 24 days, there are only 5 mg remaining, What is the half-life of iodine 131? 39. The population of a fishing village is decreasing by 8%/year. In 1998, there were 4500 people living in the village. Estimate the population in 2004. Th 40. Compare the intensities of an earthquake of magnitude 7.2 on the Richter scale that occurred in Kobe, Japan, on Jan. 17, 1995, to an earthquake of magnitude 6.9 that occurred in northwest Armenia on Dec. 7, 1988. 41. The noise in the school cafeteria is recorded at 50 dB at 10:00. At 12:00, the noise is found to be 100dB. By what factor does the intensity of the sound increase at lunch? 42. A liquid has pH of 5.62. https://www.coursehero.com/file/16818357/ExamReview/ Find the hydrogen ion concentration [H+] 43. Describe the transformation that takes the graph of the first function to that of the second. a) y = log4x and y = log464x2 b) y = log2x and y = log2128x1/2 44. Describe the transformations being applied to f(x) = logx: a) f(x) = -3log(-3x + 6) - 1 b) f(x) = 1/4log(-x + 5) - 6 Hours Titer (cells/ml) sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 45. a culture bacteria was serial diluted and spread plated to get the following titer once an hour. 0 1 2 3 4 5 6 7 8 9 10 2 x 107 2.1 x 107 2.3 x 107 3.3 x 107 6.6 x 107 1.4 x 108 2.9 x 108 6.1 x 108 1.1 x 109 1.2 x 109 1.3 x 109 a) Calculate the average rate of growth over the 10 hours of the experiment b) Calculate the instantaneous rate of growth at hour 5. 46. For each of the following pairs of functions, find: i) (f + g)(x) ii) (g - f)(x) iii) (f - g)(x) iv) (fg)(x) v) (f/g)(x) vi) (g/f)(x) then state the domain for each combined function a) f(x) = -2x + 5 and b) f(x) = x2 + 2x + 1 g(x) =3x2 + 6 Th and g(x) = 4x - 4 47. Find an expression for f(g(x)) and g(f(x)) for each pair of functions and then state each domain. a) f(x) = x + 1 b) f(x) = \u001b c) f(x) = \u0002 1 and g(x) = x2 - 4 and g(x) = x - 2 and g(x) = x + 5 https://www.coursehero.com/file/16818357/ExamReview/ 48. If f(x) = 3x - 2 and g(x) = 2x - 3, calculate each of the following: a) f(g(1)) b) g(f(-1)) c) f o f (2) d) f o f-1(x) e) g-1 o f(x) 49. Let f = {(3, 1), (5, 2), (7, -2), (9, 6), (11, 0)} and g = {(1, 3), (-2, 5), (6, 0), (0, 9), (4, 8)} Evaluate each of the following, if possible. b) g(f(7)) c) f o g (6) d) g o f (-1) sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m a) f(g(1)) 50. The time, T, in seconds, taken for one complete swing of a pendulum is less if the length, L, in centimeters, of the pendulum is shortened. The relationship between T # and L is given by T = 2"$ % . The length, L, in centimeters, of a pendulum is related to the temperature by the following relationship. L = w + 0.035C where C is the temperature in degrees Celsius and w is the length at 0C. a) Find T(L(C)) b) A pendulum is 100cm in length when the temperature is 0C. Calculate the period, T, of the pendulum if the temperature is 0C. c) A pendulum is 100cm in length when the temperature is 0C. T, of the pendulum if the temperature is 80C. Textbook Questions Th Pg. 188 # 4, 6, 7, 20, 22 - 28 Pg. 380 # 1 - 3, 5, 8 - 11, 14, 16 - 19, 21, 23 - 26, 29 Pg. 580 # 1, 2, 7, 12 - 14, 16 - 18, 21 - 24, 26, 30, 31 https://www.coursehero.com/file/16818357/ExamReview/ Powered by TCPDF (www.tcpdf.org) Calculate the period