BRIEF QUIZ ANSWERS FOR PRECALCULUS STUDENTS

In this document you will find brief answers to quiz questions. If the quiz question is a homework problem, and the answer is in the back of the book, then the brief answer that you will see below may be only ``See the back of the book.''

QUIZ

Quiz 1

  1. [-4,-1)
  2. y = (-1/3)x + 1/3
  3. Domain = (-infinity,-3] union [3,+infinity), Range = [0,infinity)
  4. Domain = [-2,3) union (3,+infinity)

Quiz 2

  1. D = 25t.
  2. See the back of the book for this graph.
  3. h(x) = -(x+1/2)^2 + 5/4, MAX = 5/4.
  4. Dimensions are: length = 1200 ft, width = 600 ft.

Quiz 3

  1. Domain(f o g) = (-infinity,-1) union [1,infinity).
  2. f^(-1)(x) = (x^2-2)/5, defined for x in [0,infinity).
    • f(-2) = -3, f(1) = 3.
    • See graph in back of book.
  4. See graph in back of book.

Quiz 4

  1. True or False.
    1. False. To see that h(x) = 2^x is not even it is enough to notice that h(1) = 2 is not equal to h(-1) = 1/2.
    2. True. Since 4^(1/2) = 2 we have log_4(2) = 1/2.
  2. Domain = (-infinity,infinity), Range = (-infinity,5), asymptote is y = 5.
  3. Componded weekly: Balance = 3000*(1 + (.09)/52)^(5*52) = $4703.11. Compounded continuously: Balance = 3000*e^(.09*5) = $4704.94.
  4. An investment that doubles every 5 years increases by a factor of 2^(1/5) per year, and an investment that triples every 8 years increases by a factor of 3^(1/8) per year. Since 2^(1/5) > 3^(1/8) the first investment earns more money per year.

Quiz 5

  1. Domain = (-infinity,0), Range = (-infinity,infinity), asymptote is x = 0.
  2. Rewrite log_a(b) = ln(b)/ln(a) and log_b(a) = ln(a)/ln(b). Then it is clear that (log_a(b))(log_b(a)) = 1.
  3. If we set u = e^x, then this equation reduces to u^2 - u - 12 = 0. The solutions of this equation are u = 4, -3, so we must have e^x = 4 or -3. Since e^x is positive, we must have e^x = 4, or x = ln(4).
  4. If log(x + 3) = log(x) + log(3) = log(3x), then x + 3 = 3x. The only solution to this equation is x = 3/2.
  5. 1 + APY = (1 + (.08)/12)^12, so APY =~ 8.3%.

Quiz 6

  1. 20 degrees/180 degrees = x radians/Pi radians, so x = Pi/9 radians corresponds to 20 degrees. A similar computation shows that y = 3600/Pi degrees corresponds to 20 radians.
  2. sin(x) = 3/5.
    1. cos(x) = -4/5
    2. tan(x) = -3/4
    3. sec(x) = -5/4
    4. csc(x) = 5/3
    5. cot(x) = -4/3
    1. sin(11*Pi/4) = sin(3*Pi/4) = sin(Pi/4) = square_root(2)/2.
    2. cos(-Pi/6) = cos(Pi/6) = square_root(3)/2
    3. tan(4*Pi/3) = tan(Pi/3) = square_root(3)
  4. amplitude = 1, k = 3 so period = 2*Pi/k = 2*Pi/3, phase shift = -Pi/3.

Quiz 7

  1. Let angle A be the 52 degree angle. The opposite angle is 38 degrees. The length of the unknown leg is 35tan(52) and the length of the hypotenuse is 35sec(52).
    1. sin(150) = sin(30) = 1/2.
    2. sec(17*Pi/3) = sec(-Pi/3) = 2.
  3. Area = (1/2)(7)(9)sin(72)
  4. By the Law of Sines a = 200*sin(52)/sin(46).

Quiz 8

    1. Pi/6
    2. Pi/3
    3. undefined
  2. 12/13
  3. Want all x such that sin(x) = -1. The values are x = 3*Pi/2 + multiples of 2*Pi.
  4. Want all x between 0 and 2*Pi such that cos(x) = 1/2 or -1. The values are x = Pi/3, x = Pi, x = 5*Pi/3.

Quiz 9

  1. True or False?
    1. False. Points, lines and pairs of crossed lines are also conics.
    2. False. The eccentricity of an ellipse is less than 1 while the eccentricity of a hyperbola is greater than 1.
  2. y = (1/7)*x^2.
  3. x^2/4 + y^2/3 = 1.
  4. x^2/9 - y^2/16 = 1.

Quiz 10

Quiz 11

Quiz 12

Last modified on Jan 20, 1999.