# MATH 1111 Final Exam Rogers

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```					MATH 1111                                    Final Exam                                    Rogers
Directions: Do NOT write on test!!!!!!!!!!. Write test number and all answers on answer sheet.

0
 2 4  3 2 
1.   Evaluate  3 1  .
 5 2 
            
a. 32/125                      b. 0                       c. 4/125       d. 1

2.   Factor 4 - 81x2.
a. (4 - 9x)(1 + 9x)            b. (2 + 9x)(2 - 9x)        c. (2 - 9x)2   d.(9x + 2)(9x - 2)

3.   Factor x3 + 125.
a. (x + 5)(x2 - 5x + 25)       b. (x - 5)(x2 + 5x + 25)   c. (x - 5)3    d.(x - 5)(x2 - 5x + 25)

5        1
4.   Solve the equation                    .
2x  3 x  6
a. 11                           b. 3                      c. - 1         d. No solution

5.   Solve the equation x  2 = 5.
a. 3 and - 7             b. 7 and - 3                     c. 5 and -5    d. - 3

6.   Solve by factoring: 6z2 - 7z - 3 = 0.
2 1                      3 1                               3 1              2 6
a. - ,-                   b. ,-                           c.     ,       d. -     ,
3 3                      2 3                               2 3              3 7

7.   Write  50 in standard form.
a. 5i 2                b.5i 10                            c. 5i          d. 25i

8.   Simplify (9 + 4i)(-2 - 2i) and write in standard form.
a. 7 + 2i                   b. - 10 - 26i              c. - 12 + 8i      d. 17 - 12i

6  3i
9.   Write          as a complex number in standard form.
1 i
3 1
a. 1 - 3i                      b. 6 - 3i                  c. 3           d.    - i
2 3
57
10.   Simplify i .
a. 1                       b. – i                      c. i                    d. - 1

4   2
11.   Solve by factoring: x - 9x = 0.
a. 1, -1, 3, -3           b. 3, -3                     c.9, -9                 d.0, 3, -3

12.   Solve by factoring: 3x3 + 2x2 - 12x - 8 = 0.
2                             2                            2                     8
a. 2, -2,                    b. 0, 2, -                c. 2, -2, -             d. 0, 2,
3                             3                            3                     3

13.   Solve the equation     3x  x  2 = 4.
a. 9/2                     b. 4/3                      c. 3                    d. 2

14.   Find all real solutions of the equation x4 + 5x2 + 4 = 0.
a. 2, -2, 1, and -1         b. 2 and -2               c. 1 and -1              d. No real solutions

15.   Solve the inequality 9 ≤ 2x + 1 < 17. Write the solution using interval notation.
a. [5, 9]                 b. [4, 8)                   c. [4, 8]                d.[5, 9)

2x  5
16.   Solve the inequality        ≥ 1.
x4
a. (- ∞, 1] U (4, ∞)      b. (- ∞, 5/2] U (4, ∞)       c. [5/2, 4)             d. [1, 4)

17.   Solve the inequality x  3 > 5.
a. (- ∞, 2) U (8, ∞)      b. (-∞, -2) U (8, ∞)         c. (-2, 8)              d. (2, 8)

18.   A bank loaned out \$12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per
year. If the interest received totaled \$1,000, how much was loaned at 8%?
a. \$1, 250                  b. \$13,600                c. \$11,600               d. \$5, 680

19.   Determine the x and y-intercepts of the graph of 5x + 2y = 10.
a. (5, 0), (2, 0)        b. (2, 0), (0, 5)           c. (5, 0), (0, 2)         d. (0, 5), (0, 2)

20.   Suppose that the manufacturer of a gas clothes dryer had found that, when the unit price is p
dollars, the revenue R (in dollars) is R(p) = -4p2 + 4000p. What unit price should be established for
the dryer to maximize revenue?
a. \$500                    b. \$350                      c. \$ 620              d. \$ 275
7
21.   Determine the domain of the function f (x) =          .
x 5
a. (- ∞, 0) U (0, ∞)       b. [5, ∞)                      c. (- ∞, 5) U (5, ∞)   d. (- 5, ∞)

22.   Determine the domain of the function f (x) =       16  x 2 .
a. [- 4, 4]              b. (-∞, - 4] U [4, ∞)          c. (- 4, 4)              d. (- ∞, - 4) U (4, ∞)

23.   Find the slope of the line passing through the points (2, - 1) and (- 3, 5).
a. 6/5                     b. 5/6                      c. - 5/6                  d. - 6/5

24.   Find the equation of the line with slope 3/5 and y-intercept (0, - 5). Write your answer in the form
y = mx + b.
5                          5                           5                       5
a. y = x + 5               b. y = x - 5               c. y = x - 3             d. y = x - 5
3                          3                           3                       3

25.   Given f1(x) = - 3x + 5 and f2(x) = 3x - 2, find x such that f1(x) = f2(x).
6
a.                        b. 7                          c. None of these         d. 7
7

26.   Find the general form of the equation of the line that passes through (- 1, 5) and is perpendicular to
the graph of 5x + 2y - 11 = 0.
a. 2x - 5y - 32 = 0       b. 2x + 5y - 5 = 0           c. 5x + 2y - 46 = 0      d. 2x - 5y + 27 = 0

27.   Determine the vertex and axis of symmetry of the graph of the quadratic function
f(x) = x2 - 6x + 25.
a. (3, 16); x = 3        b.(-3, -16); x = -16       c. (3, 16); x = 16     d. (-3, 16); x = -3

28.   Which of the following functions are even functions?
I) f(x) = x  2                                   II) g(x) = - x2
a. I and II              b. II                       c. I                        d. Neither I nor II

29.   Given f(x) = x2 - 9 and g(x) = x - 7, find the domain of f/g.
a. {x| x ≤ 7}            b.{x| x ≥ 7}              c.{x| x > 7}                  d.{x| x ≠ 7}

30.   Let f(x) = x2 - 2x and g(x) = 3x. Find (fg)(-1).
a. (fg)(- 1) = 3        b. (fg)(- 1) = - 9                c.( fg)(-1) = 27       d.( fg)(- 1) = - 3

31.   If f(x) = 1 - x2 and g(x) = 2x + 1, find (g ◦ f)(x).
a. (g ◦ f)(x) = - 2x2 + 3 b. (g ◦ f)(x) = 2x2 - 4x + 3 c.( g ◦ f)(x) = - 4x2 - 4x    d.( g ◦ f)(x) = - 4x
32.    Divide the first polynomial by the second: 2x4 + 21x3 + 35x2 - 37x + 46, 2x + 7
4                                                     4
a. x3 + 7x2 - 7x + 6 -                           b. 2x3 + 14x2 - 14x + 12 +
2x  7                                               2x  7
4                                               4
c. x3 - 7x2 + 7x - 6 +                           d. x3 + 7x2 - 7x + 6 +
2x  7                                          2x  7

33.   Determine whether (x + 2) and (x - 2) are factors of P(x) = x4 + 3x3 - 9x2 - 12x + 20.
a. Both                 b. Only (x + 2)               c. Neither             d. Only (x - 2)

34.   Determine the far-left and far-right behavior of the graph of the polynomial function
P(x) = 3x4 - 5x2 + 7.
a. down to the left and down to the right              c. down to the left and up to the right
b. up to the left and up to the right                  d. up to the left and down to the right

35.   Find the real zeros of the polynomial function P(x) = x3 - 2x2 + 3x.
a. - 1, 3                  b. 0, 1, -3               c. 0, -1, 3               d. 1, -3

36.   Find the zeros of P(x) = x2(x - 5)(x2 - 49) and state the multiplicity of each zero.
a. 0 (multiplicity 2), 5 (multiplicity 1), 7 (multiplicity 1), -7 (multiplicity 1)
b. 0 (multiplicity 2), 5 (multiplicity 1), 49 (multiplicity 2)
c. 0 (multiplicity 1), -5 (multiplicity 1), 7 (multiplicity 1), -7 (multiplicity 1)
d. 0 (multiplicity 1), 5 (multiplicity 1), 49 (multiplicity 2)

37.   Use the Rational Zero Theorem to list the possible rational zeros of the polynomial 5x4 - 9x2 + 4.
a. ±1, ±2, ±4, ±5, ±10, ±20                          b. ±1, ±1/2, ±1/4, ±5, ±5/2, ±5/4
c. ±1, ±1/4, ±5, ±5/4                                d. ±1, ±1/5, ±2, ±2/5, ±4, ±4/5

38.   Find all the zeros of x4 + 3x3 - 2x2 - 2x + 12 given that 1 + i is a zero.
a. 1 + i, 1 - i            b. 1 + i, 1 - i, 5, 6      c. 1 + i, 1 - i, 2, 3    d. 1 + i, 1 - i, -2, -3

39.   Find a polynomial of degree 3 that has zeros 3, -2, and -1.
a. x3 + 4x2 + x - 6      b. x3 - 7x - 6               c. x3 - 4x2 + x + 6      d. x3 - 6x2 - x + 6

3x 1
40.   Find the vertical asymptotes of F(x) =             .
x 2  3x
a. x = 3                   b. x = 1/3                   c. x = 0, x = 3        d. None

 x 2 1
41.   Find the horizontal asymptotes of F(x) =                 .
x 2  2x 1
a. y = - 1                 b. y = 5                      c. y = 0              d. None
42.   Find the inverse of the function f(x) = x2 + 1, for 0 ≤ x ≤ 2. State the domain and range of f-1(x).
a. f-1(x) = x 1 ; domain [0, 2]; range [1, 5]        b. f-1(x) = x 1 ; domain [1, 5]; range [0, 2]
c. f-1(x) = 1 - x2; domain [1, 5]; range [0, 2]       d. f-1(x) = 1 - x2; domain [0, 2]; range [1, 5]

43.   Lead shielding is used to contain radiation. The percent of a certain radiation that can penetrate x
millimeters of lead shielding is given by r(x) = 100e-1.5x. What percent of radiation, to the nearest
tenth of a percent, will penetrate a lead shield that is 3 millimeters thick?
a. 90.0%                   b. 111.1%                      c. 63.8%             d. 1.1%

44.   Evaluate log7 49.
a. 2                       b. 1/7                     c. 7                    d. -2

45.   Write logb x3yz4 in terms of logarithms of x, y, and z.
a. 12 logb xyz                                        c. 3 logb x - logb y - 4 logb z
b. (3 logb x)(logb y)(4 logb z)                       d. 3 logb x + logb y + 4 logb z

46.   Use the change-of-base formula and a calculator to approximate log3 8,
accurate to five significant digits.
a. 0.90309                 b. 0.52832               c. 1.8928                 d. 2.6667

47.   Solve: 22x+1 = 32.
a. – 2                     b. – 3                     c. 2                    d. 3

48.   Solve: 173x = 4.
a. 3.7670                  b. 0.2690                  c. - 3.7670             d. 3.7173

49.   Solve: log 2x - log(x - 2) = 1.
a. 2.5                     b. – 1                     c. 8                    d. No solution

50.   \$6000 is invested at an annual interest rate of 7% and compounded annually. Find the balance after
5 years.
a. \$13,299.17             b. \$6640.90                 c. \$8415.31          d. \$8514.41
1.    d
2.    b
3.    a
4.    a
5.    a
6.    b
7.    a
8.    b
9.    d
10.   c
11.   d
12.   c
13.   c
14.   d
15.   b
16.   a
17.   b
18.   c
19.   b
20.   a
21.   c
22.   a
23.   d
24.   b
25.   d
26.   d
27.   a
28.   b
29.   d
30.   b
31.   a
32.   d
33.   a
34.   b
35.   c
36.   a
37.   d
38.   d
39.   b
40.   c
41.   a
42.   b
43.   d
44.   a
45.   d
46.   c
47.   c
48.   b
49.   a
50.   c

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