Questions for Honors Precalculus, PreAB Precalculus, and PreBC Precalculus

Do all questions without a calculator unless asked to use one.

1.  Solve for x:                                

2.  Solve for x:     4      -     3        =   1
                         x + 1       x + 2

3.  Solve for x:  |2x - 1| = 5                                                  

4.  Solve for x:  

5.

    (a)  f(-1) =       (b)  f(0) =       (c)  f(2) =        (d)  Graph f(x)

6.  Find the domain for   
                          
7.  Find the domain for 

8.  Find the domain for                                   

9.   Graph y = x²(x - 1)(x + 3)³                                   

10.  f(x) = 3x⁴ - 6x²  
                                                                           
        (a)  increasing intervals      (b)  decreasing intervals     
                                      
        (c)  even, odd, or neither    (d)  relative minimum
                                                              
        (e)  relative maximum:                                                               

11. 
       This is a graph of f(x).

       Graph:  (a)  f (x + 1)        (b)  f (x) - 1       (c)  f ( |x| )           (d)  f (2x)     (e)  -f (x)              (f)  |f(x)|

                    (g)  3 f(x)            (h)  f(-x)

12.  f(x) = x² + 1   and   g(x) = 2x + 3
                              
        (a)  (f + g)(x) =        (b)  (f /g)(x) =               (c)  f (g(x)) =            (d)  g (f (x)) = 
                                 
        (e)  f ^-1(x) =              (f)  g^-1(x) =                  (g)  f ^-1(g(x)) =

13.  Solve for t:  t³ - 4t² + 4t = 0                                     

14.  Find a polynomial whose zeros are  -2, -1, 0, 1, 2

15.  Divide  6x³ - 16x²+ 17x - 6 by 3x - 2                       

16.  Solve for x:  -2x⁴ + 13x³ - 21x² + 2x + 8 = 0

17.  Graph:                                                                                        

18.  Graph:                                                     

19.  Graph:  

20.  Graph:              
                                      

21.  Graph:                                                    

22.  Graph y = 2x² - 4x + 1

23.  Solve for x:  x³ - 8 = 0    

24.  Find the equation of the circle whose center is (-1,5) and is tangent to the x-axis.                                        

25.  One root of x³ - 3x² + x + 5 = 0 is 2 + i.       Find the other roots.

26.  Is y = x³ + 3x even, odd, or neither?                        

27.  Find the equation of the line through (1, -4) with slope 2.

28.  For what x-values is     discontinuous?

29.  Find the quadratic function that has a minimum at (-1,-2) and passes through (0,4).

30.  Find the points of intersection of the graphs of   y = 2x + 3 and y = x² - 6x - 6.  

31.  How many points of intersection do y = x³ - 1 and -x² + 2x - 1 have?  You may use your calculator.

32.  Find the point(s) of intersection for y = 3x - 1 and y = 2x² + 5.

33.  Graph  -2 < x - y < 6

34.  Graph  y < 2(x - 1)(x + 2)(x + 1)

36.  A rectangle has a perimeter of 10.  Find the length and width that would maximize the area of the rectangle.

37.  Determine whether the graph of has infinite discontinuity, jump discontinuity, point discontinuity,  or is continuous..

38. Use a graphing calculator to find an equation for the line of regression and the correlation value (r)
      for the data in the chart.  The table below shows the blood pressure of members of a fitness class. 

      If the correlation value (r) for the regression equation shows a moderate or strong relationship,
      use the equation to predict the missing value and explain whether the prediction is reliable.

39.  (2 + 3i)2 + (4 - i)(5 + 2i) - 1 =  ?   Complex Numbers  

40.  Simplify:  

Questions for PreAB Precalculus and PreBC Precalculus

41.  Solve for x:

       (a)  log₂16 = x                                   (b)  9^x = 27

       (c)  log_a(1/a) = x                                (d)  log (4/5) = x (use calculator)

       (e)  ln .75 = x  (use calculator)           

42.  Graph:  (a)  y = 2^x          (b)  y = -2^x

                          (c)  y = 2^x - 4    (d)  y = 2 ^x-2

                          (e)  y = 2 ^|x|        (f)  y = 2 ^x/3

43.  Graph:  (a)  y = log ₂ x         (b)  y = ln x

                    (c)  y = ln (x - 1)     (d)  y = | ln x |

                    (e)  y = ln |x|            (f)  y = -ln (-x)

44.   Solve for x:  log₃5 = x  (use calculator)                                             
45.   Expand: 

46.  Write as one logarithm:  ln x - 2[ ln (x + 2) + ln (x - 2)]      

Questions for Honors Precalculus, PreAB Precalculus, and PreBC Precalculus

47.  Graph:  y > -x² + 3x + 4

48.  Graph  y > |x - 1|.

49.  Solve the inequality:  |x + 3| > 9

50.  Graph the function. Determine the interval(s) for which the function is increasing and the interval(s)
       for which the function is decreasing.  (Use your calculator)

                           y = x³ - 0.5x² - 10x + 2
51.  Find the vertical, horizontal, and slant asymptotes, if any, for 

      (a)  4^{2x - 7} = 64       (b)  ln (x -1) = 3.8     (c)  e^x = 10

      (d)  10^x = 570         (e)  3^x = 7

53.  Solve for x:  x² - ln x = 24 (it is necessary to use your calculator) 
                                    
54.  Solve for x:   (a)  ln (x + 1) - ln (x - 2) = ln x²

                             (b)  ln x + ln (x - 2) = 1        

                             (c)  2 ln x = 7

Questions for Honors Precalculus, PreAB Precalculus, and PreBC Precalculus

55.  Simplify: 

56.   2 + i   =      Complex Numbers
        1 - 3i

Questions for PreAB Precalculus and PreBC Precalculus

57.  Know the definition of e

58.  Find the domain for log₂(x² - 1)

60.  Write the equation of the parabola y = x² - 5x + 1 in standard form.

       (a)  Find the domain for f(g(x)).
       (b)  Find the domain for g(f(x)).

63.  Write a rational function that has:
       (a)  vertical asymptote: x = 2,
             slant asymptote: y = x + 1,
             zero: x = -2
       (b)  vertical asymptote:  x = -2,
              horizontal asymptote: y = 3,
              zero: x = 1
64.  Find two coterminal angles to  (a)  p/3    (b)  112^o

65.  Change 2p/3 to degrees

66.  Change 260^o to radians                                           

67.  Find trigonometric function values for all the special angles

68.  sin A = 2/7;   A is in quadrant II             Find the other trigonometric functions.                              

69.  Solve the right triangles:
       (a)  C = 90^o, a = 2, c = 4
       (b)  A = 30^o, b = 75, C = 90^o
       (c)  C = 90^o, B = 45^o, b = 20

70.  Find the exact values of the trigonometric functions for an angle A whose terminal side passes through (-1,-10).

71.  sin A = -1/2,  tan A > 0;  Find all  trigonometric function values.

72.  Find:  (a)  tan 225^o    (b)  cos 2p/3    (c)  sin 5p/4    (d)  sec 17p/3   (e)  csc -p/6    (f)  cot - 405^o       

73.  Use your calculator to find:  (a)  sin 40^o (b)  cot 142^o    (c)  sec 67^o    (d)  csc 215^o

Questions for PreBC Precalculus

74.  Graph:  (a)  y = 2 sin [3(x -p/4)] + 1     (b)  y = - cos (x - p/3)    (c)  y = 2 sec x      (d)  y = cot x - 1

Questions for PreAB Precalculus and PreBC Precalculus

75.  Change 303.22°  to degrees, minutes, and seconds.

76.  Write 114° 26´ 11´´ as a decimal to the nearest thousandth.

78.  A pulley of radius 15 cm turns at 8 revolutions per second. What is the linear velocity of the belt
       driving the pulley in meters per second?

79.  Find a logistic equation   y =     500
                                                   1 + Ae^-kt
       when (3, 200) and (10, 410) satisfy it.

80.  y =        200        
                1 + 50e^-.12t
      What is t when y = 100?

81.  The data below give the number of bacteria found in a certain culture.

83.  Graph:  (a)  y = arctan x    (b)  y = arctan x - 3         (c)  y = 2 arctan x             (d)  y = | arctan x |

                    (e)  y = arctan |x|                                          (f)  y = arctan (x - 3)

84.  sin (Arctan 3/4)

85.  cot (Arctan 5/8)                                                      

86.  sec [Arcsin (x - 1)]

87.  sin (Arccos x)                                                          

88.  Arccos (-1/2)

89.  csc (Arctan (-5/12)                                                  

90.
        
91. Write the equation for the inverse of the function 

92.  Jane observes a raft floating on the water bobbing up and down with an amplitude of 8 feet. Beginning at the top of the wave, if the raft completes a full cycle every 5 seconds, what is the height of the raft relative to the lowest point after 25 seconds?

93.  Find the value of 

94.  Find the value of 

95.  Find the value of 

Questions for PreBC Precalculus

96.  The hourly temperature at Portland, Oregon, on a particular day is recorded below.

Answers