Download DMAT 0310 - Richland College

Final Exam Review for DMAT 0310
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the polynomial completely. What is one of the factors?
1) 3x2 + 2x - 8
A) (3x - 2)
2) 15z 2 + 14z - 8
A) prime
B) (3x - 4)
C) (3x + 4)
D) (3x + 2)
B) (3z - 4)
C) (z - 2)
D) (5z - 2)
B) (11 - w)
C) 11 - w2
3) 121 - w2
A) prime
4) t3 + 1000
Solve the equation.
5) x(4x + 18) = 10
A) 2, 5
6) 49x3 - x = 0
1
A) 7
D) 121 - w
4)
9
B) 0,
2
1
C) , -5
2
9
D) 0, 2
1
B)
7
1
C) , 0
7
1
1
D) , - , 0
7
7
Simplify the expression.
a 2 - ab + 8a - 8b
7)
a+8
A)
2)
3)
B) (t2 + 100)
D) (t2 - 10t + 100)
A) (t - 10)
C) (t2 + 10t + 100)
1)
5)
6)
7)
a 2 - ab + 8a - 8b
a+8
B) a - 2b + 1
C) a - b
D)
1
a+8
Solve the problem.
8) If f(x) =
A) -
x2 - 8
, find f(-5).
x3 - 8x
5
17
8)
B) -
1
5
C) -
17
133
D) -
17
125
Find the quotient and simplify.
z 2 + 10z + 16
z 2 + 2z
÷
9)
z 2 + 11z + 24 z2 + 13z + 30
A) z + 10
B)
9)
z + 10
z 2 + 3z
C)
z
2
z + 11z + 24
D)
z + 10
z
Find the product and simplify.
x3 + 1
7x
·
10)
3
2
-56x
- 56
x -x +x
A) -
x3 + 1
8(x + 1)
10)
B) -
x2 + 1
8
C) -
1
8
D)
x+1
8(-x - 1)
Find the least common denominator (LCD).
7
7
,
11)
2
2
x - 6x + 5 x + 3x - 4
11)
A) (x + 5)(x + 1)(x + 4)
C) (x - 5)(x - 1)(x + 4)
B) (x - 1)(x + 4)
D) (x - 5)(x - 1)
Perform the indicated operation. Simplify if possible.
10x - 2
9x - 6
12)
2
2
x + 12x + 32 x + 12x + 32
A)
13)
B)
1
x+4
C)
x-4
2
x + 12x + 32
D)
1
2
x + 12x + 32
-6x + 8 7x - 7
+
x
6x
A)
14)
1
x+8
12)
-43x + 41
6x
13)
B)
-29x + 41
6x2
C)
-29x + 41
6x
D)
-29x - 55
6x
3
7
+
2
2
x - 3x + 2 x - 1
14)
A)
42x - 11
(x - 1)(x + 1)(x - 2)
B)
10x - 11
(x - 1)(x - 2)
C)
10x - 11
(x - 1)(x + 1)(x - 2)
D)
11x - 10
(x - 1)(x + 1)(x - 2)
Solve the equation.
x
2x - 3
-2x
=
+
15)
2x + 2 4x + 4
x+1
A) no solution
16)
15)
B) -3
C)
3
2
D) 3
x+8
12
2
+
=
x+2 x2 +2x x
A) -2
16)
B) -4
C) -2,-4
D) 2
Solve the equation for the indicated variable.
x y 1
for a
17) + =
a b a
A) a =
y
b-x
B) a =
17)
1
-y
by
C) a = by -
2
1
y
D) a =
b - bx
y
Solve.
18) There are 0.5 milligrams of iron in a 3.5 ounce serving of cod. How much iron is in 5 ounces of cod?
Round the answer to one decimal place.
A) 1.4 mg
B) 0.7 mg
C) 1.7 mg
D) 0.4 mg
18)
19) A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job.
How long would it take for them to complete the job if they were working together?
16
15
hr
hr
A)
B) 3
C) 8 hr
D) 6 hr
63
16
19)
20) A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on
mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level
ground, find its rate in the mountains.
A) 80 mph
B) 20 mph
C) 50 mph
D) 40 mph
20)
Determine whether the graph is the graph of a function and find the domain.
21)
A) yes; Domain = [-6,2]
C) yes; Domain = [2,4]
21)
B) no; Domain = [-6,2]
D) no; Domain = [2,4]
Find the domain and range of the function graphed.
22)
22)
A) domain: (- , ); range: (- , 3]
B) domain: (- , ); range: (- , )
C) domain: (- , -2) (-2, ); range: (- , 3) (3, )
D) domain: (-5, 1]; range: (- , 3]
3
Find an equation of the line. Write the equation using function notation.
23) Through (-2, -2); perpendicular to 4x + 7y = -14
7
3
7
3
4
A) f(x) = - x +
B) f(x) = x +
C) f(x) = - x - 2
4
2
4
2
7
24) (6, -16), (8, -22)
A) f(x) = -3x + 2
B) y = -
4
D) f(x) = - x - 14
7
24)
1
x - 14
3
Write an equation of the line using function notation.
25) Horizontal; through (-6, -3)
A) x = -3
B) x = -6
C) y = -3x + 2
D) f(x) = 3x - 34
C) f(x) = -3
D) f(x) = -6
Use the given graph of the function.
26) Find f(-3).
A) 3
25)
26)
B) 4
C) 5
D) -4
27) If f(x) = 1, what is the value of x?
A) x = 6
23)
27)
B) x= -5
C) x =-5
4
D) x = -2
Graph the function.
28) h(x) = 4x - 3
28)
A)
B)
C)
D)
Solve the compound inequality. Graph the solution set.
29) x 1 and x -3
A) (-3, 1)
B) (- , -3]
29)
C)
[1, )
D) [-3, 1]
Solve the compound inequality. Write the solution set in interval notation.
30) -17 -3c + 1 < -8
A) [-6, -3)
31) 6x - 4 < 2x or -2x
A) [1, 3]
B) [3, 6)
30)
C) (3, 6]
D) (-6, -3]
31)
-6
B)
C) (- , 1)
5
[3, )
D) (1, 3)
Solve the absolute value equation.
3x + 1
=3
32)
9
A)
32)
B) -
26
3
33) |-3x + 9| = |8 - 4x|
B) - 1, -
A)
C)
17
7
28
3
C) - 1,
D)
33)
17
7
D) - 1
Solve the inequality. Write the solution set in interval notation.
34) |8k - 2| < -3
34)
A) -
5 1
,
8 8
B)
C) -
1 5
,
8 8
D) - , -
1
8
5
,
8
35) |3k - 2| + 8 > 17
A) -
C)
26
28
,3
3
35)
7 11
,
3 3
11
,
3
6
B) - , -
7
3
11
,
3
D) - , -
7
3
11
,
3
Graph the solution of the system of linear inequalities.
36) y < 2x + 7
y x-8
36)
A)
B)
C)
D)
7
37)
x
3x + 2y
3
-4
37)
A)
B)
C)
D)
Find the cube root.
3
38) - -8x30y24
A) 2x10y8
B) 4x10y8
C) 2x10y12
D) -2x30y8
Simplify the radical expression. Assume that all variables represent positive real numbers.
3
39) 16x4 y11
3
A) 4x2 y5 y
B) 2xy3
3
3
C) 4xy xy
2xy2
8
D) 2xy2
38)
39)
3
2xy5
Identify the domain and then graph the function.
40) f(x) = x + 5;
40)
A) [0, )
B) [0, )
C) [-5, )
D) [5, )
Write with positive exponents. Simplify if possible.
41) 36-3/2
1
A) 216
B) -216
C) 216
1
D)
216
Use the properties of exponents to simplify the expression. Write with positive exponents.
2
(5x3/2 )
42)
x1/6
A) 25x19/6
B) 5x19/6
Use rational exponents to simplify the following.
25
y10z 25
43)
A) y2/5 z
B) y5/5 z 5/2
41)
42)
C) 25x17/6
D) 5x17/6
C) y5/2 z
D) y2/5
43)
Simplify the radical expression. Assume that all variables represent positive real numbers.
44)
3
128
A) 8
44)
C) 4
B) 4
9
3
2
D) 4
3
8
45)
100
5
45)
A) 5
B)
100
5
500
5
C)
Find the midpoint of the line segment whose endpoints are given.
46) (6, -8), (-2, 7)
15
A) 4, B) (4, -1)
C) (8, -15)
2
D) 2 5
1
D) 2, 2
Add or subtract. Assume all variables represent positive real numbers.
47) 2x2 + 7 50x2 - 3 50x2
A) 4x 73
B) 4x 2
C) 21x 73
47)
D) 21x 2
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
48) 7( 3 + 5)
A) 8 7
B) 21 + 35
C) 7 3 + 7 5
D) 56
49) ( x - 1 + 4)2
A) x + 8 x - 1 + 16
51)
6
B) x + 8 x - 1 + 25
C) x + 8 x - 1 + 15
D) x + 8 x - 1 + 17
B) 1
6
6
C)
D)
50)
6
36
11
17 + 4
A) 11 17 + 44
48)
49)
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
1
50)
6
A)
46)
51)
11 17 + 44
34
B) 11 17 - 44
C)
B) 9
36
C)
5
D) 11 17 - 4
Solve.
52)
10x - 9 - 9 = 0
A) 81
52)
D)
53)
4x - 4 = 4 - x
A)
B) 10
C) 2
D) 2, 10
54)
5x + 4 = 3x + 1 + 3
A) 0, 33
B) 0, 5
C)
D) 33
Perform the indicated operation. Write the result in the form a + bi.
55) (3 + 8i) - (-2 + i)
A) -5 - 7i
B) 5 + 7i
C) 1 + 9i
10
D) 5 - 7i
53)
54)
55)
56)
8 - 6i
6 + 4i
A)
56)
3
17
i
10 20
B)
18 17
i
5
20
C)
6
17
i
13 13
D)
57) (9 - 6i)2
A) 45 + 0i
B) 45 - 108i
72
4
i
+
13 13
D) 81 - 108i + 36i2
C) 117 - 108i
Represent each given condition using a single variable, x.
58) Three consecutive odd integers
A) x, x + 2, and x + 4, if x is an odd integer
B) x, x + 1, and x + 2, if x is an odd integer
C) x + 2, x + 4, and x + 6, if x is an odd integer
D) x and x + 2, if x is an odd integer
Solve.
57)
58)
59) An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet
per second. The height h of the object after t seconds is given by the quadratic equation
h = -16t2 + 48t + 160. When will the object hit the ground?
59)
60) Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse
is 6 more than twice the shorter leg.
A) 18 m
B) 17 m
C) 10 m
D) 9 m
60)
A) 2 sec
B) 160 sec
C) -2 sec
Use the square root property to solve the equation.
61) x2 + 36 = 0
A) 1296
B) -6i, 6i
C) 6
62) (x + 5)2 = 20
A) -5 - 2 5, -5 + 2 5
C) -2 5, 2 5
1
3
,2
2
D) -6, 6
B) 2 5 - 5, 2 5 + 5
D) -5 - 2 10, -5 + 2 10
B)
1 3
,
2 2
C) -
3 3
,
2 2
D) -
Use the quadratic formula to solve the equation.
64) x2 + 14x + 35 = 0
A) 7 - 35, 7 +
C) -14 + 35
61)
62)
Solve the equation by completing the square.
63) 4x2 + 8x + 3 = 0
A) -
D) 5 sec
1
3
,4
4
63)
64)
35
B) -7 - 14, -7 +
D) 7 + 14
65) (x - 9)(x - 1) = 20
A) -11, 1
C) -1, 11
14
65)
B) -5 - 14, -5 + 14
D) 5 - 14, 5 + 14
11
66)
x2
11
+x+
=0
10
10
66)
A) -10 + 11
C) 5 + 14
Solve.
B) 5 - 11, 5 + 11
D) -5 - 14, -5 + 14
67) The product of a number and 8 less than the number is 33. Find the number.
A) -2 or 12
B) -11 or 3
C) -3 or 11
67)
D) -12 or 2
Solve the inequality. Write the solution set in interval notation.
68) x2 - 7x + 10 > 0
A) (- , 2)
69) x2 + 4x
B) (5, )
C) (2, 5)
D) (- , 2)
B) (- , -3]
[-1, )
C) [-1, )
(x - 1)(3 - x)
(x - 2)2
(5, )
69)
-3
A) (- , -3]
70)
68)
D) [-3, -1]
0
A) (- , -3]
(-2, -1)
C) (- , -3)
(-1, )
70)
[1, )
12
B) (- , 1)
(3, )
D) (- , 1]
[3, )
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
71) f(x) = x2 - 5
A) vertex (0, -5); axis x = 0
B) vertex (0, 5); axis x = 0
C) vertex (5, 0); axis x = 5
D) vertex (-5, 0); axis x = -5
13
71)
72) f(x) = (x - 5)2 + 2
72)
A) vertex (2, 5); axis x = 2
B) vertex (-5, 2); axis x = -5
C) vertex (-2, -5 ); axis x = -2
D) vertex (5, 2); axis x = 5
Provide an appropriate response.
73) Given a parabola opens upward and the vertex is located in quadrant III, determine the number of
x-intercept(s).
A) cannot be determined
B) 0
C) 1
D) 2
Find the vertex of the graph of the quadratic function.
74) f(x) = x2 - 12x + 9
A) (-12, 297)
B) (6, -99)
C) (6, -27)
D) (-6, 117)
Fine the x-intercepts and y-intercept:
75) f(x) = x2 + 8x +7
73)
74)
75)
A) x-intercepts: (-7,0),(-1,0)
y-intercept (0,7)
B) x-intercepts: (7,0,(1,0)
y-intercept (0,7)
C)
D)
x-intercepts: (-7,0),(-1,0)
y-intercept (0,-7)
14
x-intercepts: (-8,0),(-1,0)
y-intercept (0,-7)
310 Final Exam Review
1
B
26
B
51
B
2
D
27
A
52
B
3
B
28
D
53
C
4
D
29
D
54
D
5
C
30
C
55
B
6
D
31
C
56
C
7
C
32
D
57
B
8
B
33
C
58
A
9
D
34
B
59
D
10
C
35
D
60
C
11
C
36
B
61
B
12
A
37
C
62
A
13
C
38
A
63
A
14
C
39
B
64
B
15
D
40
C
65
C
16
B
41
D
66
D
17
D
42
C
67
C
18
B
43
A
68
D
19
B
44
C
69
A
20
B
45
D
70
D
21
B
46
D
71
A
22
A
47
D
72
D
23
B
48
B
73
D
24
A
49
C
74
C
25
C
50
C
75
A
15
76)
A)
B)
C)
16
76)