Download 2014 Spring Unit 1 Exam

College Algebra - Unit 1 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) 3i(9 - 8i)
A) 27i - 24i2
B) 27i - 24
C) 27i + 24i2
D) 24 + 27i
1)
Perform the indicated operation and express in lowest terms.
x
8
2)
x2 - 16 x2 + 5x + 4
2)
A)
x2 - 7
(x - 4)(x + 4)(x + 1)
B)
x2 - 7x + 32
(x - 4)(x + 4)
C)
x2 - 7x + 32
(x - 4)(x + 4)(x + 1)
D)
x2 + 7x + 32
(x - 4)(x + 4)(x + 1)
Perform the indicated operation and simplify.
5p - 5 8p - 8
3)
÷
p
9p2
3)
A)
45p3 - 45p2
8p2 - 8p
B)
8
45p
C)
45p
8
D)
40p2 + 80p + 40
9p3
Solve the equation.
4) 2(2z - 2) = 3(z + 3)
A) {7}
4)
B) {13}
C) {5}
1
D) {-5}
Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
1
5
-1
5)
5)
+
=
x+7 x+6
2
x + 13x + 42
A) Conditional, {6}
C) Inconsistent, ∅
Solve the absolute value equation.
6) 3m + 5 = 7
2
A) - , 4
3
B) Identity, {all real numbers}
D) Conditional, {-7}
6)
B)
2
12
,5
5
C) ∅
D)
2
,-4
3
Solve the problem.
7) One maid can clean the house in 7 hours. Another maid can do the job in 8 hours. How long will it
take them to do the job working together?
1
1
56
A)
hr
B) 56 hr
C)
hr
D)
hr
56
15
15
Find the distance between the points, and find the midpoint of the line segment joining them.
8) (4, -2) and (-8, 1)
1
1
A) 3 17; - 2, B) 3 17; - , - 2
C) 9; (-4, -1)
D) 9; (12, -3)
2
2
2
7)
8)
Write the standard equation for the circle.
9) Center at (-6, -1), passing through (-3, 3)
A) (x - 6)2 + (y - 1)2 = 25
9)
B) (x + 6)2 + (y + 1)2 = 25
D) (x + 1)2 + (y + 6)2 = 9
C) (x - 1)2 + (y - 6)2 = 9
Change the equation to slope-intercept form and identify the slope and y-intercept.
10) -6x + 4y = 13
3
13
3
13
3
13 3
13
A) y = - x +
, - , 0,
B) y = x , , 0, 2
4
2
4
2
4 2
4
C) y =
2
13 2
13
x+
, , 0,
3
4 3
4
D) y =
3
13 3
13
x+
, , 0,
2
4 2
4
Find the equation of the line through the given pair of points in standard form using only integers.
11) (5, 0) and (0, -3)
A) -3x + 5y = 15
B) 3x + 5y = -15
C) -3x - 5y = -15
D) -3x + 5y = -15
Find the perfect square trinomial whose first two terms are given.
12) x2 - 10x
A) 25
B) 100
C) 5
3
10)
11)
12)
D) -25
Use the method of your choice to find all real solutions of the equation.
13) 9k2 - 35k - 4 = 0
1
A) - , 4
9
1
B) - , 9
9
C) {-9, 4}
Solve the inequality. Write the solution set using interval notation and graph it.
14) -5 - 3x - 11 ≥ -4x - 14
13)
1
1
D)
,35
9
14)
A) (-3, ∞)
-10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
B) (-∞, 2]
-5
-4
C) (-∞, -3)
-10 -9
D) [2, ∞)
-5
-4
Solve the absolute value inequality. Write the solution set using interval notation.
15) 9x + 7 < 5
4
4
2
A) -∞, B) -∞, ∪ - ,∞
3
3
9
C) -∞, 9
D) -
4
4
2
,3
9
15)
Find the domain and range.
16) y = 2 + x
A) D = (-∞, ∞); R = [-2, ∞)
C) D = [-2, ∞); 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∣ + 1
D) y = ∣x + 2∣
Write the equation of the graph after the indicated transformation(s).
20) The graph of y = x is shifted 5 units to the left. Then the graph is shifted 9 units upward.
A) f(x) = 9 x + 5
B) f(x) = x + 9 + 5
C) f(x) = x + 5 + 9
D) f(x) = x - 5 + 9
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 - 6
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) = 3 - 2x, g(x) = -7x + 2
Find f + g.
A) -7x + 3
B) -4x
22)
C) -9x + 5
7
D) 5x + 5
23) f(x) = 3x - 5, g(x) = 6x - 3
Find f - g.
A) 3x + 2
23)
B) -3x - 8
C) -3x - 2
D) 9x - 8
Find the requested function value.
24) Find (g ∘ f)(32) when f(x) =
A)
193
6
x-2
and g(x) = 6x + 3.
6
24)
B) 45
C) 33
D) 975
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) = 56x - 0.3x2 and the total cost function is given by C(x) = 8x + 8, 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 + 40x + 8
B) P(x) = 0.3x2 + 48x - 16
C) P(x) = -0.3x2 + 48x - 8
D) P(x) = 0.3x2 + 40x - 24
8
25)