Multiple Choice Practice (All Chapter).pdf

Pre-Calculus Honors Final Exam Review Chapter 1 Multiple Choice Questions 1. Solve for x: 2 x 2  3  2 x 1 5 1 5 1 7 1 7 1 2 7 A. B....

Pre-Calculus Honors Final Exam Review Chapter 1 Multiple Choice Questions 1. Solve for x: 2 x 2  3  2 x 1 5 1 5 1 7 1 7 1 2 7 A. B. C. D. E. 2 2 2 2 2 2. Solve for x: 32  8x  x 2 A. 3  3i B. 2  4i C. 1 2i D. 4  4i E. 3  4i 3. Find the range of the function f ( x)   x  3  1. A. y  1 B. y  3 C. y  1 D. y  1 E. y  3 4. Compare the graph of t ( x)   x 2 with s( x)  x 2. A. t is obtained by reflecting s over the x-axis B. t is obtained by reflecting s over the y-axis C. t is obtained by shifting s up D. t is obtained by shifting s down E. t is obtained by shifting s left 5. Given f ( x)  x 2 , find g(x) such that g ( x)   f ( x  1)  3. A. g ( x)  ( x  1) 2  3 B. g ( x)  ( x  1) 2  3 C. g ( x)  ( x  1) 2  3 D. g ( x)  ( x  1) 2  3 E. g ( x)  x 2  2 x  2 8  7x 6. Find the inverse of f ( x) . 6 8  6x 8  6x 8  6x A. f 1 ( x)  B. f 1 ( x)  C. f 1 ( x)  7 7 6 8  6x 8  7x D. f 1 ( x)   D. f 1 ( x)  7 6 7. Find the inverse of h( x)  x  9. 3 A. h 1 ( x)  x 3  9 B. h 1 ( x)  x 3  9 C. h 1 ( x)  3 x  9 D. h 1 ( x)  3 x  9 E. h 1 ( x)  ( x  9) 3 8. Which of the following functions is not one-to-one? 7 A. q( x)   x B. q( x)  x 2 , x  0 C. t ( x)  ( x  3) 3  5 2 1 D. q( x)  2 E. q( x)   x  3 , x  3 x 9. Find the x-intercepts of f ( x)   x 2  18x  80. A. (8, 0), (10, 0) B. (-8, 0), (-10, 0) C. (-8, 0), (10, 0) D. (8, 0), (-10, 0) E. (-16, 0), (5, 0) 2 2 10. Approximate the zero furthest to the right accurate to three decimal places for h( x)  x  7 x  12. 5 A. –1.573 B. –1.003 C. 7.332 D. 19.073 E. 20.001 7 2 5 11. Approximate the zero furthest to the left accurate to three decimal places for p( x)  x  x  2. 5 3 A. –1.741 B. –0.740 C. 1.742 D. 1.930 E. 2.741 12. Find the vertex of the function f ( x)  2 x 2  24 x  3. A. (-6, 69) B. (6, 69) C. (-6, -33) D. (-6, -69) E. (6, -33) 13. Approximate to three decimal places the minimum value of y  5x 2  7 x  15. A. –17.450 B. –1.700 C. –0.700 D. 1.700 E. 17.450 14. Given g ( x)  2 x and h( x)  1  x 2 , find ( g  h)(3). A. –16 B. –20 C. 16 D. –35 E. 37 15. Given f ( x)  3x  10 and g ( x)  9 x 2  x , find ( f  g )(5). A. 235 B. 225 C. –215 D. –225 E. -235 16. For what value(s) of x is the graph of y  ( x  2)( x  4) 2 above the x-axis? A. x  4 B.  4  x  2 C. x  2 D. x  4 E. none of these Pre-Calculus Honors Final Exam Review Chapter 3 Multiple Choice Questions 1. What is the remainder when 2 x³  7 x²  5 is divided by x  3. A. – 4 B. 5 C. 4 D. 0 E. none of these 2. Which of the following are factors of 2 x³  5x²  x  6 ? A. x + 2 B. x – 1 C. x – 2 D. all of these E. a and b 3. A polynomial function has a complex root of 5i – 3. Which of the following must also be a root? A. -3 + 5i B. -5i + 3 C. 5 + 3i D. -5i – 3 E. 3i – 5 4. Determine the remainder when 2 x 4  4 x³  5x²  3x  2 is divided by x²  2 x  3. A. 1 B. 2x² + 1 C. x + 1 D. 2x² - 1 E. x 5. Which of the following is an x-intercept of 2 x 4  7 x³  4 x²  27 x  18 ?  2   3  A. (-2 , 0) B. (3 , 0) C. (1 , 0) D.   ,0  E.   ,0   3   2  6. Simplify 6  3. A. -18 B.  3 2 C. 3 2 D. 18 E.  2 3 4 7. Which of the following is the horizontal asymptote for y  1. x A. y = 1 B. y = 4 C. y = 0 D. y = -1 E. none 8. Choose the appropriate statement for the graph of a parabola in the form f ( x)  a( x  h)  k where a, h and k are real numbers and x is a variable. A. vertex at (h , k) with an axis of symmetry of x  h B. vertex at (h , -k) with an axis of symmetry of x  h C. vertex at (-h , k) with an axis of symmetry of x  h D. vertex at (h , -k) with an axis of symmetry of x  k E. vertex at (h , k) with an axis of symmetry of x  k Pre-Calculus Honors Final Exam Review Chapter 4 Multiple Choice Questions 1 1. If  9 6 x , then what is the solution for x? 34 x 8 A. 0, 6 B. 6 C. -2 D.  E. -6 3 2. Given that e 2 x  3e x , find the value of x. A. 0, 3 B. 1, 3 C. 0, ln 3 D. 1, ln 3 E. ln 3 3. Condense 3 ln x  3 ln x  ln 9 x A. ln 9 x 7 B. ln( x 3  12 x) C. 3 ln 9 x 5 D. ln 27 x 5 E. ln(2 x 3  9 x) 1 4. Condense 2 log 3 x  log 3 27. 3  x2   x2  A. log 3 (2 x  3) B. 2 log 3 ( x  9) C. log 3 ( x 2  3) D. log 3  3  E. log 3    27   3  5. Solve for the exact solution of ln( x)  2. A. 2 B. e 2 C. 1, 0 D. 2 e E. none of these 6. Solve for the exact solution of e x  6. 6 A. 6 B. ln 6 C. e 6 D. E. none of these e 7. Solve for the exact value of ln x  ln 2  3. e3 e3 3e 3 A. B. C. D. E. none of these 2 ln 2 2 ln 2 8. Solve for the exact value of ln( x 2  1)  ln( x  1)  ln 4. 1  17 A. -2, 3 B. 3 C. ln 3 D. E. none of these 2 9. If log( 7  x)  1  log( 3x  2), then x is equal to what value? 27 13 9 13 19 A.  B. C. D.  E. 29 31 4 31 31 10. Find the domain of the graph of y  log 2 ( x  5). A. x < 5 B. x > -5 C. all real numbers D. x  5 E. x > 0 11. Solve the equation e 2 x1  e 4 x  e 3. A. 1 B. -1 C. 8 D. -8 E. none of these 12. Find the range of the function y  20.8x. A. y > 0 B. y < 0 C. y < -2 D. y > -2 E. y < 2 13. Solve to three decimal places 4 2 x3  9 x3. A. - 1.685 B. 1.685 C. 8.648 D. 18.648 E. 18.685 14. Simplify log 3 32 x 1. A. 6 2 x 1 B. 2x – 1 C. 32 x 1 D. 6x-3 E. none of these 15. Simplify e ln 2 x. A. 2x B. 2ex C. e 2 x D. ln2x E. none of these 16. Write log a b  c in exponential form. A. a b  c B. b a  c C. c b  a D. b c  a E. a c  b w 17. Evaluate ln  p  e   w A.  p  ln w B. ln w  p  C.  p D. ln   E. p  ln w  p 18. Solve for x: log b x  log b 5  log b 60. A. 10 B. 12 C. 120 D. 300 E. 65 19. Choose the expression that represents log n z changed to the natural base. log n log e n ln z log z ln n A. B. C. D. E. log z log e z ln n log n ln z 20. Choose the expression that represents log n z changed to the common log. log n log e n ln z log z ln n A. B. C. D. E. log z log e z ln n log n ln z 43 21. Evaluate log 7 to the nearest ten-thousandth. 5 A. 1.8837 B. 1.3102 C. 1.1803 D. 1.1072 E. 0.1679 1 22. If log w  log x  log y then w  5 1 1  x 5 1 1 x5 x A. x  y B. C. x  y 5 D.   E. 5 y  y 5y  1 23. Condense completely. 4 log 5 x  log 5 y 2 1 4 A. log 5 ( x  y ) 4 2 B. log 5 ( x 4 y ) C. 5 x y 1 D. log 5 ( x )  log 5 ( y ) 4 2 E. log 5 ( x 4  y ) 2 1 24. Condense completely. ln( x  3)  7 ln y  ln z 3 3   ( x  3) 2 y 7 3 ln 3 ( x  3) 2  y 7  3 ( x  3) 2 y 7  C.   3 z A. B. e ln ln 3 z  3 z      3 ( x  3) 2 y 7 D. ln 3 ( x  3) 2  y 7  3 z 3 z E. e  y3 8 x  25. Expand completely. ln    64 4 x  1    1  ln 8      ln 6  ln 4 x  ln 1 1 A. 3 ln y   2  ln x   4  B. 3 ln y  8  x   ln 6  ln 4 x  ln 1 1 1 2 4   C. 3 ln y  ln 8  ln x   ln 6  ln 4 x  ln 1 1 1 2  4  1  1  D. 3 ln y  ln 8  ln x  ln 6  ln 4  ln x  ln 1 2  4    E. 3 ln y  ln 8  x   ln 6  ln 4 x  1 1 1 2  4  3x 26. State the asymptote for h( x)  2  4 A. y  5 B. y  4 C. x  3 D. x  3 E. y  3 27. Compare the graph of p( x)  2  ln( x  5) with r ( x)  ln x. A. p is obtained by reflecting r over the y-axis, up two units and right five units B. p is obtained by reflecting r over the x-axis, up two units and right five units C. p is obtained by reflecting r over the x-axis, down two units and left five units D. p is obtained by reflecting r over the y-axis, down two units and left five units E. p is obtained by reflecting r over the x-axis, up two units and left five units. 28. Mrs. Higgins has $2500 to invest. If she would like to triple her money in 7.5 years, what interest rate must she obtain if the interest is to be compounded monthly? A. 0.1473793237% B. 0.1464816385% C. 14.74% D. 14.23% E. 14.61%  3 29. If log a 2  x and log a 3  y , write an expression for log a   in terms of x and y. 2 x y A. x – y B. C. D. x + y E. y – x y x 30. Choose the appropriate interval for the domain of f ( x)   log 2 ( x  1). A.  ,  B.  1,   C.  ,1 D.  ,1 E. 1,   31. If the graph of f ( x)  3 x is shifted 4 units to the right, the equation of the transformed graph would be: A. f ( x)  3 x  4 B. f ( x)  3 x 4 C. f ( x)  3 x  4 D. f ( x)  3 x  4   E. f ( x)  4 3 x 32. The numbers of United States citizens y (in millions) who traveled to foreign countries in the years 1988 through 1996 are shown in the table, where t  0 represents 1980. t 1988 1989 1990 1991 1992 1993 1994 1995 1996 y 40.7 41.1 44.6 41.6 43.9 44.4 46.5 50.8 52.3 Using an exponential model determine the number of travelers in 2005 to the nearest tenth. A. 66.1 million B. 56.7 million C. 66.2 million D. 62.8 million E. 52.2 million Pre-Calculus Honors Final Exam Review Chapter 5 Multiple Choice Questions 1. A tower that is 125 feet tall casts a shadow of 172 feet. Find the angle of elevation of the sun to the nearest degree. a. 40  b. 37  c. 36  d. 41 e. 48  2. A restaurant is building a wheelchair ramp that must rise 18 inches to meet its front door. If the ramp's angle of elevation is not allowed to exceed 6  , what is the minimum horizontal length of the ramp? a. less than 12 feet b. between 12 and 13 feet c. between 13 and 14 feet d. between 14 and 15 feet e. over 15 feet 3. For all angles  in degree measure, sin() = a. cos(90    ) b. sin(90    ) c. sec(90    ) d. sin(  90  ) e. cos( ) 4. If  is such that sin() = 3/5 and tan() = 3/4, then 4 5 4 5 5 a. cos   b. sec    c. csc   d. cos   e. cot   5 4 3 4 4 5. The period of y  5  3 cos4x  1 is  a. 4 b. 2 c. 8 d. e. 3 2  3 6. If arctan     then 5 3 3 3 3 a. cot    b. tan   c. sin   d. tan    e. sin   3 5 5 5 5 7. The horizontal translation of the function f ( x)  2  4 cos4 x  5 is a. exactly two units to the right b. exactly five units to the left  c. exactly 1.25 units to the right d. exactly units to the left 2 e. exactly five units to the right   3  8. Find the exact value in quadrant III of tan sin 1   .    2  1 1 2 a. b.  c. 3 d.  3 e. 3 3 3 9. A student looks out a second-story school window and sees the top of the school flagpole at an angle of elevation of 22o. The student is 18 ft. above the ground and 50 ft. from the flagpole. Find the height of the flagpole. a. 21.8 b. 23.5 c. 38.2 d. 48.6 e. 58.2 10. cos( ) is equivalent to which of the following? a.  cos  b. cos  c. sin  d.  sin  e.  cos( ) 11. Which of the following is an even function? a. sin  b. tan  c. csc d. cos(  1) e. sec 12. An airplane flying at 490 mph has a bearing of N 27E. After flying for two hours how far north and how far east has the plane traveled? a. 444.9 mi. N, b. 873.2 mi. N, c. 436.6 mi. N, d. 222.5 mi. N e. 237.1 mi. N, 873.2 mi. E 444.9 mi. E 222.5 mi. E 436.6 mi. E 452.8 mi. E 5 13. If sin(x)  then sin(x) equals: 7 5 5 a. b. 45.58 c. -45.88 d.  e.  74 7 7 2 14. If cos( x)  then sec(  x) equals: 3 2 3 2 3 a.  b.  c. d. 13 e. 3 2 3 2 15. A 50 meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of 71 with the ground. What is the height of the balloon? a. 16.3 m b. 47.3 m c. 145.2 m d. 39.7 m e. 24.8 m 16. Determine the exact value of csc given (7 , -10) on the terminal side of the angle in standard position. 10 51 149 7 51 a.  b.  c.  d.  e. 149 7 10 51 10 17. Determine the exact value of sec  given (-5 , 12) on the terminal side of the angle in standard position. 13 119 13 119 5 a.  b. c.  d.  e.  5 5 12 5 13 18. Determine the exact value of sin  given (-4 , -10) on the terminal side of the angle in standard position. 116 116 29 5 29 a.  b.  5 29 c.  d.  e.  10 4 5 29 19. Determine the exact value of cos  given (-2 , 3) on the terminal side of the angle in standard position. 2 5 2 13 3 5 3 13 a.  b.  c.  d.  e.  2 5 5 13 5 13 20. State the reference angle for   211. a. 149 b. 571 c. 59 d. 49 e. 31 21. State the reference angle for   315. a. 45 b. 135 c.  45 d.  75 e. 75 22. State the reference angle for   292. a. 112 b.  68 c. 22 d. 68 e.  22 23. State the reference angle for   153. a.  27 b. 63 c. 207 d. 27 e.  207  24. Determine the quadrant for  . 10 a. I b. II c. III d. IV 7 25. Determine the quadrant for  . 4 a. I b. II c. III d. IV 2 26. Determine the quadrant for   . 3 a. I b. II c. III d. IV 5 27. Determine the quadrant for   . 3 a. I b. II c. III d. IV 28. Determine the quadrant for   910. a. I b. II c. III d. IV 29. Determine the quadrant for   550. a. I b. II c. III d. IV  30. Find the complement and supplement for   3   2 5 7 2 5 a. , b. none ,  c. , d.  , e. , 2 6 3 3 3 3 3 11 31. Find the complement and supplement for   12 13 35    5 5 7 a.  , b. none , c. , d. , e. , 12 12 12 2 6 6 6 6  3 32. Express the angle in terms of degrees. Round if necessary. 2 a. 90 b. 180 c. 240 d. 300 e. 270 7 33. Express the angle  in terms of degrees. Round if necessary. 6 a.  420 b.  315 c.  330 d.  210 e.  300 8 34. Express the angle in terms of degrees. Round if necessary. 3 a. 480 b. 310 c. 60 d. 120 e. 150 35. Express the angle 3.5 in terms of degrees. Round if necessary. a. 620 b. 363.5 c. 200.5 d. 210 e. 312.5 36. Express the angle -1.7 in terms of degrees. Round if necessary. a.  306 b.  97.4 c.  0.03 d. 102 e.  138.3 37. Find the arc length given r  5 and   180. a. 10 b. 15.71 c. 36 d. 900 e. 7.86 38. Find the arc length given r  3 and   72. a. 216 b. 24 c. 7.54 d. 10.15 e. 3.77  39. Find the arc length given r  4 and  . 4 a. 4 b. 45 c. 180 d. 3.14 e. 5.18 3 40. Find the arc length given r  7 and  . 5 a. 13.19 b. 15.43 c. 756 d. 151.61 e. 4.24 41. An airplane flying at 520 mph has a bearing of S 58W. After flying for 1.5 hours, how far south and how far west has the plane traveled? a. 661.5 mi. S, b. 275.6 mi. S, c. 441.0 mi. S, d. 413.3 mi. S e. 388.5 mi. S, 413.3 mi. W 441.0 mi. W 275.6 mi. W 661.5 mi. W 511.9 mi. W 42. At a point 175 feet from the base of a building, the angle of elevation to the top of the building is 29 , and the angle of elevation to the top of a flag pole that sits atop the building is 35. Find the height of the flag pole. a. 12.4 feet b. 25.5 feet c. 97.0 feet d. 122.5 feet e. 84.8 feet 43. At a point 150 feet from the base of a building, the angle of elevation to the top of the building is 35 , and the angle of elevation to the top of the flag pole that sits atop the building is 40. Find the height of the flag pole. a. 105.0 feet b. 86.0 feet c. 125.9 feet d. 16.4 feet e. 20.8 feet 44. Given y  5 sin2 x     10 state the period. 2 a. 2 b. 5 c. d. 2 e.   45. Given y  5 sin2 x     10 state the phase shift. 2   2 a. -2 b. c. d.  e.   2 2  46. Given y  5 sin2 x     10 state the vertical shift. a. 10 b. 5 c. -5 d. 2 e.  47. Given y  5 sin2 x     10 state the amplitude. a. -5 b. 10 c. 5 d. 2 e.   x 48. Given y  tan  state the period. 3  2 a. b. 2 c. d. 3 e. 6 3 3 49. Given y  3 tan(2 x) state the period.  a. 2 b.  c. 3 d. e. 4 2   50. Given y  3 cos x     6 state the amplitude. 4  a. 6 b. 3 c. -6 d. -3 e.    51. Given y  3 cos x     6 state the period. 4   1 a. 4 b. 8 c. d. e. 8 4 8    52. Given y  3 cos x     6 state the phase shift. 4  1 a.  b. 4 c.   d.  e. -4 4   53. Given y  3 cos x     6 state the vertical shift. 4  a. 6 b. -3 c. -6 d. 3 e.   3 54. Simplify sec arcsin .  5 4 5 3 4 5 a. b. c. d. e. 5 3 5 3 4  5 55. Simplify cot  arccos .  13  5 12 13 12 5 a. b. c. d. e. 12 13 12 5 13   3  56. Simplify cot  arcsin       8  55 3 55 3 73 a.  b.  c. d. e.  3 8 3 55 3   3  57. Simplify sin arctan       7  7 58  3 58  3 10 7 10 40 a. b. c. d. e.  58 58 20 20 3 58. State the exact value of the sine and cosine functions of the angle  given in the figure. 3 1 2 3 3 1 1 3 a. 2 , 2 3 b. 2 , c. , d. , e. , 2 2 3 2 2 2 2 Pre-Calculus Honors Final Exam Review Chapter 6 & 7 Multiple Choice Questions 1. A value of  that satisfies the equation sin  2sin  10 is: 5 7  3 a. b. c. d. e. none of these 6 6 2 2 2. The graph represented by the equation y  3 sin(4 )  5 has a maximum value of: a. 2 b. 3 c. 5 d. 8 e. -3 sec 3. The expression is equivalent to: tan  cot  1 1 a. b. c. sin  d. cot  e. cos  sin  cos  3 4. If  is measured in radians and cos   , then we know that cos(  2 ) is: 5 3 4 3 4 a.  b.  c. d. e. 1 5 5 5 5 sin  tan  csc 2  5. Which of the following equals ? sec a. cos  b. csc c. sin  d. 1 e. none of these  5  6. Determine g   given that g ( x)  sin(4 x).  16  1 1 1 1 3 a. b.  c. d.  e. 2 2 2 2 2 7. 1 cos 2  = 1 a. sin 2  b. 1 c. d. tan 2  e. sec 2  2 8. Find the exact value of the cos 75. 6 2  6 2 6 2  6 2 a. b. c. d. e. not possible 4 4 4 4  tan 80   tan 20  9. Which of the following is equivalent to. 1  tan 80  tan 20  a. tan 60  b. tan100  c. sin 60  d. sin 100  e. cot 100  3 A 10. Given sin A  , A in quadrant II, find cos. 5 2 10 3 3 10 3 a. b. c. d. 3 e.  10 10 10 10 11. Solve: cos 2 A  cos A, 0 , 360  ,   ,  ,   ,  ,   a. 0 ,90 ,180 b. 0 ,120 ,240 c. 90 ,270 d. 0 ,180 e. 22.5 ,112.5 ,202.5 ,292.5 12. 2 sin a cos a is equivalent to which of the following? a a a. cos 2a b. sin 2a c. tan 2a d. sin e. cos 2 2 13. Solve: tan x sin 2 x  2 tan x, 0,2   3  3  5 a. 0,  b. 0,  ,2 c. 0, , d. , e. 0, , , 4 4 4 4 4 4 cos  cot  csc 2  14. Which of the following equals ? csc  a. cos 2  cot 2  b. csc 2    c. 1  sin 2  1  cot 2   d. cot 2  e. none of these 55 15. Use the period of the function to select an expression that has the same value as cos , 0  . 9   5 2 5 a. cos b. cos c. cos d. cos e. cos 9 6 9 9 6 Pre-Calculus Honors Final Exam Review Chapter 7 & 8Multiple Choice Questions 1. Two homes are located on opposite sides of a small hill at points P and Q. To measure the distance between them, a surveyor walks the distance of 50 feet from house P to point R, uses a transit to measure PRQ , which is found to be 80  , and then walks to house Q, a distance of 60 feet. How far apart are the houses? a. 71.12 ft b. 72.11 ft c. 81.12 ft d. 82.11 ft e. 83.21 ft 2. Suppose we know that a = 5 cm., b = 3 cm., and A = 53 , in a certain triangle. According to the Law of Sines, a. B  48 b. B is obtuse c. two triangles exist d. one triangle exists e. no triangle exists 3. In a triangle, suppose we know that b = 3 feet, c = 2 feet, and angle A = 140. According to the Law of Cosines, the length of side a is approximately a. 3.9 ft b. 4.2 ft c. 3.6ft d. 17.6 ft e. 4.7 ft sin 52  sin 30  4. Find b such that . b 12 a. 0.05 b. 4.73 c. 5.78 d. 20.8 e. 18.91 5. Find the area of the given triangle: a. 10 b. 13.2 c. 18.4 d. 23.5 e. 28 6. Find the area of the triangle whose sides are 6, 6, and 8. a. 15 b. 17.9 c. 20 d. 23.5 e. 28.6 7. In triangle ABC , c = 2, B = 45o and a = 6. Find the area of triangle ABC. a. 3.6 b. 4.8 c. 7.5 d. 4.2 e. 10.1 8. Find the value of x. a. 3.4 b. 7.4 c. 8.4 d. 10.7 e. 12.6 9. Find the value of x. a. 16.3 b. 16.8 c. 17.9 d. 23.5 e. 35.3 10. Given P(4,8) and Q(12,7) , find the component form of the vector  . PQ a.  16,1 b.  8,1 c. 8,1 d.  8,1 e. 16,1 11. Given P(4,8) and Q(12,7) , find the magnitude of the vector  . PQ a. 257 b. 65 c. 65 d. -65 e. 257 12. Let u   7,1 and v  8,3. Find v  u. a. 10,7 b. 15,2 c. 1,4 d. 8,5 e.  15,2 13. Let u   7,1 and v  8,3. Find u  v. a. -53 b. 53 c. 17 d. 4 e. -59 14. Let u  1,3 and find the unit vector in the direction of u. 1 3 1 3 1 3 a. 1,1 b.  1,1 c. , d. , e. , 10 10 4 4 10 10 15. Find the angle between the vectors 6,3 and  5,3 to the nearest tenth of a degree. a. 77.8° b. 175.6° c. 87.8° d. 185.6° e. 126.5 16. Given P(3,5) and Q(8,7) , find the component form of the vector  PQ. a.  11,2 b.  8,1 c. 11,2 d.  11,2 e. 8,1 17. Given P(12,4) and Q(4,6) , find the magnitude of the vector  PQ. a. 2 17 b. 2 65 c. 258 d.  2 17 e. 260 18. Let u  8,5 and v   10,3. Find v  u. a.  18,2 b. 18,2 c.  2,2 d. 2,8 e.  8,2 19. Let u  3,5 and v  4,8. Find u  v. a. 52 b.  2 17 c. 2 7 d. 28 e. -28 20. Let u  5,5 and find the unit vector in the direction of u. 1 1 1 1 1 1 a. , b.  5,5 c. , d. 5 2 ,5 2 e. , 5 2 5 2 2 2 2 2 21. Find the angle between the vectors 4,3 and 3,5 to the nearest tenth of a degree. a. 157.8° b. -157.8° c. 22.2° d. -22.2° e. 112.2  Pre-Calculus Honors Final Exam Review Chapter 11 Multiple Choice Questions 1 1 1 1. Given the infinite geometric series 2    ... the value of the common ratio is: 2 8 32 1 1 A. B. C. There isn’t a common ratio D. 2 E. 4 4 2 (n  2)! 2. Choose the expression equivalent to. (n)! (n  2) 1 A. 2! B. cannot be simplified. C. D. (n  2)(n  1) E. (n  1) (n  2)(n  1) 3   1  2k k 3. Evaluate k 1 A. -14 B. -8 C. -6 D. 6 E. 8 2 4. Find the first term in the arithmetic sequence for which a19  42 and d  . 3 2 164 A. 19 B. 54 C.  D. -12 E. 3 3 5. Find the 60th partial sum for the arithmetic series 9  14  19 ...  304. A. 346 B. 304 C. 9390 D. 1256 E. 687 1 1 6. Find the fifth term in the geometric sequence 1,  , ,... 2 4 1 1 1 1 1 A.  B. C.  D. E.  2 2 16 16 32 7. Find the 4th term of the recursive sequence an  3an1  2 where a1 4 A. 50 B. 152 C. 458 D. 14 E. none of these 8. Find the nth term of the sequence 1, −8, 27,−64,.... B. an   1 n 3 C. an   1 D. an   1 n 2 E. an   1 n 1 n 1 A. a n  n 3 n n n3 n2 9. Find the 4th term of the sequence an  nx n1. A. 5x 4 B. 4x 4 C. 4x 3 D. 5x 5 E. 4x 2 10. Find the two-hundredth term, a 200 , of the sequence 1, 5, 9, 13,.... A. 797 B. 801 C. 805 D. 809 E. none of these 11. What type of series is 32 + 16 + 8 + 4 + 2 + 1? A. Finite arithmetic series B. Finite geometric series C. Infinite arithmetic series D. Infinite geometric series E. None of these   i 4 12. Find the sum of the infinite series.  4  i 1  5  4 A. 4 B. 16 C. D. 64 E. 256 5 13. Use sigma notation to write the sum. 12 + 15 + 18 + 21 + 24 5 5 5 4 4 A.  (12  n) B.  (3n  9) C.  (12  n) D.  (3n  9) E.  (3n  9) i 0 i 0 i 1 i 0 i 0 15 45 135 405 14. Write the nth term of the sequence as a function of n. , , , ,...... 8 32 128 512 n 1 n 1 n 1 n 1 n 1 15  3  15  3  54 54 53 A. a n    B. a n    C. a n    D. a n    E. a n    8 4 8 4 23 23 24 42 15. Find the partial sum.  (5n  6) n 1 A. 4263 B. 204 C. 216 C. 4269 E. 256 16. Find a formula for a n for the arithmetic sequence. a1  4, a11  24 A. an  4n  2 B. an  4n  2 C. an  2n  2 D. an  2n  2 E. an  4n  11 Pre-Calculus Honors Final Exam Review Chapter 9 & 10 Multiple Choice Questions 1. Which of the following would be the corresponding rectangular equation by eliminating the parameter given x  t  4 and y  t 2. a. y  ( x  4) 2 b. x  y 2  4 c. y  ( x  4) 2 d. y  x  4 e. x  y  4 2. Which of the following would be the corresponding rectangular equation by eliminating the parameter given 1 x  and y  2t  3. t 1 1 2 1 a. y  b. x  c. y   3 d. y  2 x  3 e. x  2x  3 2y  3 x 2y  3 3. Convert the polar equation r  4 sin  into a rectangular equation. a. x 2  y 2  16 b. x 2  y 2  4 x  0 c. x 2  y 2  4 y  0 d. y  4 x e. y  4 5 4. Convert the polar equation   into a rectangular equation. 3 3 a. x 2  y 2   3 b. y   3x c. x 2  y 2  3 d. y   x e. y  x  3 3 3 5. Convert the polar equation   into a rectangular equation. 4 1 a. x 2  y 2  1 b. y  x c. y   x d. y  x  1 e. y   x 6. Convert the polar equation r  10 into a rectangular equation. a. x 2  10 x  100 b. x 2  y 2  10 c. x 2  y 2  10 y  100 d. y  10 x e. x 2  y 2  100 7. Convert the polar equation r  7 into a rectangular equation. a. x 2  y 2  49 b. x 2  7 y  7 c. x 2  y 2  7 d. 7 y 2  x e. y  7x 2 8. Find the zeros of r  2 cos 3.  3 5  3 5 7   5  2 a. , , b. 0 ,  , 2 , 3 c. , , , d. , , e. 0 , , , 2 2 2 4 4 4 4 6 2 6 3 3 9. Find the zeros of r  3 cos 2.  3  3   5 7 11 2 4 a. 0 , , b. , c. 0 , d. , , , e. , 2 2 4 4 3 6 6 6 6 3 3 10. Classify the type of curve r 2  9 sin 2. a. limacon b. cardiod c. rose curve d. circle e. lemniscate 11. Classify the type of curve r 2  16 cos 2. a. limacon b. cardiod c. rose curve d. circle e. lemniscates 12. Classify the type of curve r  3 cos 5. a. limacon b. cardiod c. rose curve d. circle e. lemniscate 13. Classify the type of curve r  8 sin 2. a. limacon b. cardiod c. rose curve d. circle e. lemniscate 14. Classify the type of curve r  7 cos . a. limacon b. cardiod c. rose curve d. circle e. lemniscate 15. Classify the type of curve r  5 sin . a. limacon b. cardiod c. rose curve d. circle e. lemniscate 16. Classify the type of curve r  6  6 cos . a. limacon b. cardiod c. rose curve d. circle e. lemniscate 17. Classify the type of curve r  3  3 sin . a. limacon b. cardiod c. rose curve d. circle e. lemniscate   18. Convert  3 ,  to rectangular coordinates.  6  3 3  6 6 3 3  1 a.  ,  b. 1.73 , 30 c.  ,   d.  ,   e.  3 ,   2 2   2 2   2 2   2 19. Convert 2,   to rectangular coordinates. a. 2 , 0 b.  2 , 0 c. 0 , 2 d. 0 ,  2 e. 2 , 180  2  20. Convert   4,  to rectangular coordinates.  3   a. 2 ,  2 3  b. 4 , 120  c.  2 , 2 3   d.  2 3 , 2   e. 2 3 , 2    21. Convert   3,   to rectangular coordinates.  3  3 3 3  3 3 3 3 3 3  3 3 3 a.   ,   b.   ,    c.  ,  d.   ,  e. 3 , 60  2 2   2 2   2 2  2 2    22. Convert  2,   to rectangular coordinates.  4  a. 2 , 2  b.  2 , 2 c.  2, 2   d. 2 , 45 e.   2, 2  23. Convert the rectangular coordinate 3,  2 to polar coordinates. a.   5 ,  0.588 b.  5 , 3.730  c.  13 , 0.588 d.  13 , 3.730 e.  13 ,  0.588 24. Convert the rectangular coordinate  4, 5 to polar coordinates. a. 3 ,  0.675 b.  41 ,  0.896  c. 3 , 0.675 d.  3 ,  0.896 e.  41 , 0.675    25. Convert the rectangular coordinate  6,  6 3 to polar coordinates.    2     2    a. 12 ,  b.  3 6 ,  c.   12 ,  d.   3 6 ,  e.   3 6 ,   3  3   3  3   3 26. Convert the rectangular coordinate 2, 2 to polar coordinates.        3   5  a.  8 ,  b.  2 2 ,   c.   2 2 ,  d.  8 ,  e.   2 2 ,   4  4  4  4   4  27. Convert the rectangular equation y  5 to a polar equation. a. r  5 sec b. r  5 sin  c. r  5 cos  d. r  5 csc e. r  5 28. Convert the rectangular equation x  10 to a polar equation. a. r  10 sec b. r  10 sin  c. r  10 cos  d. r  10 csc e. r  10 29. Convert the rectangular equation x 2  y 2  6 x  0 to a polar equation. a. r  6 sin  b. r  6 cos  c. r  6 cos  d. r  6 sin  e. r  6 csc 30. Convert the rectangular equation x 2  y 2  8 y  0 to a polar equation. a. r  8 cos  b. r  8 sin  c. r  8 sin  d. r  8 cos  e. r  8 sec 31. The graph r  16 cos 3 has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 4 32. The graph r  has symmetry to: 1  cos   a.   b. polar axis c. pole d. a, b & c e. none of the above 2 33. The graph r  4  sin  has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 34. The graph r  2 csc cos  has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 35. The graph r 2  25 cos 4 has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 36. The graph r  10  4 cos  has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 6 37. The graph r  has symmetry to: 1  sin   a.   b. polar axis c. pole d. a, b & c e. none of the above 2 38. The graph r  4 sec csc has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 39. The graph r 2  25 sin 2 has symmetry to:  a.   b. polar axis c. pole d. a, b & c e. none of the above 2 Pre-Calculus Honors Final Exam Review Chapter 12 Multiple Choice Questions x 1. lim x 0 x 1 1 a. 0 b. -1 c. 1 d. 2 e. does not exist x 2. lim x 0 x a. 1 b. -1 c. 0 d.  e. does not exist x 1 3. lim x 1 x  2x  3 2 1 1 1 a. b. c. d. 3 e. does not exist 3 4 2 7 4. lim x 3 x3 7 a. 7 b. 3 c. 0 d.  e. does not exist 3 3x 2  12 5. lim x 2 x2 a. 3 b. 12 c. 6 d. 0 e. does not exist 1 1  6. lim x  2 4 x 2 x2 1 1 1 a. b. 0 c. d. e. does not exist 16 4 2 x 2 7. lim x  2 x 4 x4 1 1 1 a. 0 b. c. d. e. does not exist 4 2 16 x 3  27 8. lim x 3 x3 a. 27 b. 9 c. -9 d. 0 e. does not exist  4  18  x 9. lim x 2 x2 1 1 a. -2 b. 0 c. d. e. does not exist 2 8 x  1 , x  2 10. lim f ( x)   x 2 2 x  3 , x  2 a. 2 b. 1 c. 3 d. -2 e. does not exist 4  x 2 , x  1 11. lim f ( x)   x 1 3  x , x  1 a. 3 b. 2 c. 2.5 d. 1 e. does not exist sin 3x 12. lim  x x 6 3  6 9 a. b. c. d. e. does not exist  6   1  cos 2 x 13. lim 5 x x 3 9 3 63 3 9 a. b. c. d. e. does not exist 10 10  10 10 5 x 14. lim x 5 x 2  25 1 1 1 a.  b. -5 c.  d. e. does not exist 5 10 5 4 x 15. lim x 16 x  16 1 1 1 a. b. - c. 4 d.  e. does not exist 4 8 4 16. Find the slope of the tangent line to f ( x)  3x  1 at (2 , 5). a. 6 b. 14 c. 2 d. 5 e. 3 17. Find the slope of the tangent line to f ( x)  2 x  5 at (2 , 1). a. 2 b. -2 c. 1 d. 5 e. -1 18. Find the slope of the tangent line to f ( x)  5x 2  3x at (-1 , 8). a. -13 b. -8 c. -10 d. -7 e. 8 19. Find the slope of the tangent line to f ( x)  3x 2  5x at (2 , 2). a. -5 b. 7 c. 2 d. 3 e. –2 20. Find the derivative of f ( x)  x 2  5x  7. a. x 2  5 b.  5x  7 c. 2 x  5 d. 2 x  7 e. -5 21. Find the derivative of f ( x)  6 x 2  2 x  5. a. 12 x  5 b.  2 x c. 6 x  2 d. 12 x  2 e. 6 x  5 22. Find the derivative of f ( x)  3x 4  10 x 2  9. a. 12 x 3  10 x b. 12 x 3  20 x  9 c. 12 x 3  9 d. 4 x 3  2 x e. 12 x 3  20 x 23. Find the derivative of f ( x)  5x 3  12 x 2  3x. a. 15x 2  24 x  3 b. 15x 2  24 x c. 3x 2  2 x  3 d. 5x 2  12 x  3 e. 15x 2  3 24. Find the difference quotient for f ( x)  5x 2  3x  2. a. 10 x  3 b. 10 x  5h  3 c. 10 x  3h d. 5xh  3xh  2h e. 5xh  3h 25. Find the difference quotient for f ( x)  2 x 2  4 x  7. a. 4 x  4 b. 4 x  2h  4 c. 2 x  4h d. 4 x  6h  7 e. 2 x  h  4x  1 26. lim x  3x 2  1 4 a. does not exist b. 0 c. 1 d.  e. -4 3 8x  4 27. lim x  10 x 2  3 4 a. does not exist b. 0 c. 1 d. e. 8 5   4x 2  5 28. lim x  8x 2  1 1 a. does not exist b. 0 c. 1 d. -4 e.  2 5x 2  1 29. lim x  2x 2  4 5 a. does not exist b. 0 c. 1 d. 5 e. 2  5x 3  2 30. lim x  2x 2  1 5 a. does not exist b. 0 c. 1 d.  e. -5 2 8x 3  1 31. lim x  4x  5 a. does not exist b. 0 c. 1 d. 2 e. 8 4 32. lim 5  x  x2 a. does not exist b. 0 c. -4 d. 5 e. 1 3 33. lim 8  x  x a. does not exist b. 0 c. 11 d. 8 e. 3 1 5n 34. lim  n  3n 2 n2 a. does not exist b. 0 c. -5 d. -4 e. 5 6n 2n 2 35. lim  n  3n  1 n  22 a. does not exist b. 0 c. 4 d. 2 e. 8 n2 36. Find the limit of the sequence a n  5n 3  1 1 a. does not exist b. 0 c. d. 1 e. 5 5  n2 37. Find the limit of the sequence a n  3n  2 1 a. does not exist b. 0 c. d. 1 e. 3 3 x5 38. lim x 5 x  5 a. 1 b. -1 c. 0 d.  e. does not exist