Download 2014 Spring Unit 2 Exam

College Algebra - Unit 2 Exam - Spring 2014
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.
1) 2i(9 - 2i)
A) 18i - 4i2
B) 18i - 4
C) 18i + 4i2
D) 4 + 18i
1)
Perform the indicated operation and express in lowest terms.
x
3
2)
x2 - 16 x2 + 5x + 4
2)
A)
x2 - 2
(x - 4)(x + 4)(x + 1)
B)
x2 - 2x + 12
(x - 4)(x + 4)
C)
x2 - 2x + 12
(x - 4)(x + 4)(x + 1)
D)
x2 + 2x + 12
(x - 4)(x + 4)(x + 1)
Perform the indicated operation and simplify.
4p - 4 5p - 5
3)
÷
p
8p2
3)
A)
32p3 - 32p2
5p2 - 5p
B)
5
32p
C)
32p
5
D)
20p2 + 40p + 20
8p3
Solve the equation.
4) 4(2z - 3) = 7(z + 2)
A) {6}
4)
B) {26}
C) {2}
1
D) {-2}
Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
1
4
-1
5)
5)
+
=
x+6 x+5
2
x + 11x + 30
A) Conditional, {5}
C) Inconsistent, ∅
Solve the absolute value equation.
6) 3m + 4 = 8
4
A) - , 4
3
B) Identity, {all real numbers}
D) Conditional, {-6}
6)
B) 1, - 3
C) ∅
D)
4
,-4
3
Solve the problem.
7) One maid can clean the house in 5 hours. Another maid can do the job in 8 hours. How long will it
take them to do the job working together?
1
40
1
40
A)
hr
B)
hr
C)
hr
D)
hr
40
3
13
13
Find the distance between the points, and find the midpoint of the line segment joining them.
8) (5, -1) and (6, -8)
11
9
9 11
A) 5 2;
,B) 5 2; - ,
C) 6; (11, -9)
D) 6; (-1, 7)
2
2
2 2
2
7)
8)
Write the standard equation for the circle.
9) Center at (-3, -10), passing through (0, -6)
A) (x - 3)2 + (y - 10)2 = 25
9)
B) (x + 3)2 + (y + 10)2 = 25
D) (x + 10)2 + (y + 3)2 = 9
C) (x - 10)2 + (y - 3)2 = 9
Change the equation to slope-intercept form and identify the slope and y-intercept.
10) -3x + 5y = 19
3
19
3
19
3
19 3
19
A) y = - x +
, - , 0,
B) y = x , , 0, 5
5
5
5
5
5 5
5
C) y =
5
19 5
19
x+
, , 0,
3
5 3
5
D) y =
3
19 3
19
x+
, , 0,
5
5 5
5
Find the equation of the line through the given pair of points in standard form using only integers.
11) (-4, 0) and (0, 3)
A) 3x - 4y = 12
B) -3x - 4y = -12
C) 3x + 4y = -12
D) 3x - 4y = -12
Find the perfect square trinomial whose first two terms are given.
12) x2 - 16x
A) 64
B) 256
C) 8
3
10)
11)
12)
D) -64
Use the method of your choice to find all real solutions of the equation.
13) 7k2 - 41k - 6 = 0
1
A) - , 6
7
1
B) - , 7
7
C) {-7, 6}
Solve the inequality. Write the solution set using interval notation and graph it.
14) 6 - 4z + 3 ≥ -5z + 21
13)
1
1
D)
,41
7
14)
A) (-4, ∞)
-11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
7
8
9
10 11 12 13 14 15 16 17 18 19
-11 -10 -9
-8
-7
-6
8
9
10 11 12 13 14 15 16 17 18 19
B) (-∞, 12]
5
6
C) (-∞, -4)
-5
-4
-3
-2
-1
0
1
2
3
D) [12, ∞)
5
6
7
Solve the absolute value inequality. Write the solution set using interval notation.
15) 6x + 4 < 16
10
10
A) -∞, B) -∞, ∪ 2, ∞
3
3
C) -∞, 6
D) -
4
10
,2
3
15)
Find the domain and range.
16) y = 8 + x
A) D = (-∞, ∞); R = [-8, ∞)
C) D = [-8, ∞); R = [0, ∞)
16)
B) D = (-∞, ∞); R = (-∞, ∞)
D) D = [0, ∞); R = (-∞, ∞)
Use the vertical line test to determine whether y is a function of x.
17)
17)
y
10
5
-10
-5
5
10
x
-5
-10
A) Yes
B) No
Determine the intervals on which the function is increasing, decreasing, and constant.
18)
y
10
10 x
-10
-10
A) Increasing on (-∞, 0); Decreasing on (0, ∞)
B) Increasing on (0, ∞); Decreasing on (-∞, 0)
C) Increasing on (∞, 0); Decreasing on (0, -∞)
D) Increasing on (-∞, 0); Decreasing on (-∞, 0)
5
18)
Match the function with the graph.
19)
19)
y
10
-10
10
x
-10
A) y = ∣x∣ - 2
B) y = ∣x - 2∣
C) y = ∣x - 2∣ + 3
D) y = ∣x + 2∣
Write the equation of the graph after the indicated transformation(s).
20) The graph of y = x is shifted 9 units to the left. Then the graph is shifted 2 units upward.
A) f(x) = 2 x + 9
B) f(x) = x + 2 + 9
C) f(x) = x + 9 + 2
D) f(x) = x - 9 + 2
6
20)
Graph the pair of functions on the same plane. Use a dashed line for g(x).
21) f(x) = x2 , g(x) = x2 - 2
21)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
For the pair of functions, perform the indicated operation.
22) f(x) = 4 - 7x, g(x) = -2x + 7
Find f + g.
A) -2x + 4
B) 2x
22)
C) -9x + 11
7
D) -5x + 11
23) f(x) = 5x - 2, g(x) = 8x - 8
Find f - g.
A) 3x - 6
23)
B) -3x - 10
C) -3x + 6
D) 13x - 10
Find the requested function value.
24) Find (g ∘ f)(21) when f(x) =
A) 31
x-1
and g(x) = 7x + 9.
5
24)
B) 64
C) 37
D) 624
Solve the problem.
25) At Allied Electronics, production has begun on the X-15 Computer Chip. The total revenue
function is given by R(x) = 48x - 0.3x2 and the total cost function is given by C(x) = 3x + 15, where x
represents the number of boxes of computer chips produced. The total profit function, P(x), is such
that P(x) = R(x) - C(x). Find P(x).
A) P(x) = -0.3x2 + 42x + 15
B) P(x) = 0.3x2 + 45x - 30
C) P(x) = -0.3x2 + 45x - 15
D) P(x) = 0.3x2 + 42x - 45
8
25)