Download Math 0310 Final Exam-Review

Math 0310 Final Exam-Review
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Graph the linear equation by finding and plotting its
intercepts.
1) 6x - 30y = 30
Determine whether the pair of lines is parallel,
perpendicular, or neither.
6) y = -5x + 3
y = 5x - 3
Answer: neither
Find an equation of the line. Write the equation using
function notation.
7) Through (-4, 13); perpendicular to 3x + 4y =
43
Answer: f(x) =
4
55
x+
3
3
8) Through (5, 8); parallel to f(x) = 3x - 8
Answer: f(x) = 3x - 7
Answer:
Write an equation of the line with the given slope, m, and
y-intercept (0, b).
1
9) m = , b = 4
2
Answer: y =
1
x+4
2
Find an equation of the line described. Write the equation
in slope-intercept form if possible.
10) Through (4, 14) and (7, 20)
Answer: y = 2x + 6
Find the slope of the line that passes through the given
points.
2) (-8, 2) and (-3, 4)
Answer:
2
5
Complete the following:
(a) Write the equation in slope-intercept form.
(b) Give the slope and y-intercept of the line.
11) 2x + 3y = 16
Answer: (a) y = Find the slope of the line.
3) 8x - 3y = 24
Answer: m =
8
3
4) y = 3
Answer: m = 0
5) x = -2
Answer: undefined slope
(b) -
2
16
x+
3
3
2 16
;
3 3
Find the domain and the range of the relation.
12) {(8, 1), (-10, 0), (-2, -2), (12, -10)}
Answer: domain: {-10, -2, 8, 12} ; range: {-10, -2,
0, 1}
Determine whether the relation is also a function.
13) {(-7, -1), (-7, -5), (2, 9), (3, 1), (8, 6)}
Answer: no
Determine whether the graph is the graph of a function.
14)
19) 18x2 - 12xy - 15xy + 10y2
Answer: (6x - 5y)(3x - 2y)
20) x2 - 5x - 24
Answer: (x - 8)(x + 3)
21) x2 - x - 40
Answer: prime
22) x4 - 4x 3 - 45x2
Answer: x2 (x - 9)(x + 5)
23) 8y2 - 18y + 9
Answer: (4y - 3)(2y - 3)
24) x2 + 8xy + 16y2
Answer: no
Use the graph of the function to find the value.
Answer: (x + 4y)2
25) 6x2 + 17x + 12
Answer: (3x + 4)(2x + 3)
26) 9x2 - 4
Answer: (3x + 2)(3x - 2)
Solve the equation.
27) x2 + 4x - 12 = 0
Answer: -6, 2
28) x(3x + 16) = 12
Answer:
15) Find f(-2)
Answer: 0
Evaluate the function.
16) Find f(-4) when f(x) = 5x2 + 4x - 1.
Answer: 63
Factor completely. If the polynomial cannot be factored,
write "prime."
17) 54x8y9 + 18x6 y6 + 24x3y4
Answer: 6x3 y4(9x5 y5 + 3x 3 y2 + 4)
18) -8x4 + 12x3 - 4x2
Answer: -4x2 (2x2 - 3x + 1)
2
, -6
3
29) 13x2 - 3x = 0
Answer:
3
,0
13
30) 25x2 - 81 = 0
Answer:
9
9
,5
5
Find the domain of the rational expression.
x2 - 64
31) f(x) =
x2 + 11x + 30
Answer: {x|x is a real number and x -6, x
-5}
Simplify the rational expression.
5-x
32)
4x - 20
40)
Answer: -
1
Answer: 4
Find the product and simplify.
4p - 4
9p2
·
33)
7
p2 - p
Answer:
36p
7
41)
42)
35)
6
25y2
z+6
z
Perform the indicated operation. Simplify if possible.
x2 - 11x
30
+
36)
x-5
x-5
Answer: x - 6
Find the least common denominator (LCD).
4
8
,
37)
12x 15x2
Answer: 60x2
38)
9
3
,
2
2
x + 4x x + 9x + 20
Answer: x(x + 4)(x + 5)
Perform the indicated operation. Simplify if possible.
7
9
39) +
x x-2
16x - 14
Answer:
x(x - 2)
x2 - 2x + 12
(x - 4)(x + 4)(x + 1)
2
7
+
5x 10x
Answer:
11
10x
Solve the equation.
7x
1
+4=
43)
5
4
z2 + 5z + 6
z2 + 3z
÷
z 2 + 10z + 16 z2 + 14z + 48
Answer:
9
x-4
x
3
2
2
x - 16 x + 5x + 4
Answer:
Find the quotient and simplify.
2z 2y 10z2 y2
÷
34)
6zy
5zy2
Answer:
7
16
+
x-4 4-x
Answer: -
44)
75
28
2
t
=
t
5t - 12
Answer: 4, 6
45)
8
2
12
=
y + 3 y - 3 y2 - 9
Answer: 7
Solve the equation for the indicated variable.
Bh
for h
46) V =
3
Answer: h =
47) T =
V
Q
3V
B
for Q
Answer: Q =
Solve the proportion.
x+6 x+8
=
48)
5
7
Answer: -1
V
T
Solve.
49) The ratio of a quarterback's completed passes
to attempted passes is 2 to 9. If he attempted
45 passes, find how many passes he completed.
Round to the nearest whole number if
necessary.
Answer: 10 passes
50) A painter can finish painting a house in 4
hours. Her assistant takes 6 hours to finish the
same job. How long would it take for them to
complete the job if they were working
together?
Answer: 2
Simplify.
51)
2
hr
5
2
x
57) (5x)3/7
Answer:
Answer:
Answer: 7
59)
7
x2
8 2/3
27
Answer:
12
x
4
9
1
x+8
Find the square root. Assume that all variables represent
positive real numbers.
53) - 81
Answer: -9
-576
Answer: not a real number
Find the cube root.
3
55) -729
Answer: -9
1
81
61) x-4/5
Answer:
64
x
Answer:
125x3
58) 7x2/7
8
1x
x-
7
Write with positive exponents. Simplify if possible.
60) 243-4/5
x 1
+
3 6
54)
Answer: 7x3
Answer:
4+
52)
Use radical notation to write the expression. Simplify if
possible.
56) (49x6)1/2
1
x4/5
Use the properties of exponents to simplify the
expression. Write with positive exponents.
(-2x2/7 )3
62)
x1/5
Answer: -8x23/35
63)
x2/3 · x1/2
x-1/7
Answer: x55/42
Use rational exponents to simplify the following.
8
64) y12z 14
Answer: y3/2 z 7/4
Simplify the radical expression. Assume that all variables
represent positive real numbers.
65) 45k7 q8
Answer: 3k3 q4
5k
Find the distance between the pair of points.
66) (2, -1) and (6, -7)
Answer: 2 13 units
Add or subtract. Assume all variables represent positive
real numbers.
67) 108 + 10 75 - 6 48
Answer: 32 3
Multiply, and then simplify if possible. Assume all
variables represent positive real numbers.
68) ( 13 + 3)( 13 - 3)
Answer: 4
69) 2 7( 11 +
7)
Answer: 2 77 + 14
Rationalize the denominator and simplify. Assume that all
variables represent positive real numbers.
5
70)
11
55
11
Answer:
15 + 3 6
19
4x + 9 - 2 = 0
Answer: -
73)
3
5
4
3x + 1 + 4 = 0
Answer: 74)
77) (6 - 9i)2
Answer: -45 - 108i
78) 4i(8 - 6i)
Answer: 24 + 32i
79)
2
9 - 4i
Answer:
18
8
+
i
97 97
Use the square root property to solve the equation.
80) x2 = 140
Answer: -2 35, 2 35
81) (2x - 3)2 = 49
Answer: 5, -2
Answer: 11 - 2i, 11 + 2i
Solve.
72)
Answer: 13 + 7i
82) (x - 11)2 = -4
3
71)
5- 6
Answer:
Perform the indicated operation. Write the result in the
form a + bi.
76) (5 + 8i) - (-8 + i)
65
3
Add the proper constant to each binomial so that the
resulting trinomial is a perfect square trinomial. Then
factor the trinomial.
83) x2 + 14x + _______
Answer: x2 + 14x + 49 = (x + 7)2
Solve the equation by completing the square.
84) x2 + 16x + 53 = 0
Answer: -8 -
Write in terms of i.
75) -225
Answer: 15i
11
85) 9x2 + 18x + 8 = 0
Answer: -
43 - x = x - 1
Answer: 7
11, -8 +
2
4
,3
3
Use the quadratic formula to solve the equation.
86) 3x2 = -6x - 1
Answer:
-3 - 6 -3 + 6
,
3
3
87) 7x2 - 3x + 5 = 0
Answer:
90) x + y < -4
3 - i 131 3 + i 131
,
14
14
88) x2 + 8x + 52 = 0
Answer: -4 - 6i, -4 + 6i
Graph the linear inequality.
89) -3x - 5y 15
Answer:
Answer:
Solve the absolute value equation.
91) |2x + 8| + 10 = 4
Answer:
92) |5x - 9| = |x + 2|
Answer:
11 7
,
4 6
Solve the equation or inequality.
93) |3k + 1| > -9
Answer: (- , )
94) |x + 5| - 4 2
Answer: [-11, 1]