Download Math 102 Course Review Review #`s 1

Math 102 Course Review
Review #'s 1-43 for the Midterm Exam. Review all questions for the Final Exam.
Decide whether or not the ordered pair is a solution of the system.
1) (-5, 3)
4x + y = -23
2x + 4y = -22
Solve the system by graphing.
2) y = x + 3
y = 3x - 1
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state.
3) y = 2x + 5
4x + y = 23
4) 2x + y = 11
8x + 4y = 44
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state.
5) x + 3y = 18
2x + 4y = 24
6) 6x - 2y = 6
-18x + 6y = -12
Solve the problem.
7) One number is four more than a second number. Two times the first number is 4 more than four times the
second number.
8) A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 5 bags of potato chips for
$7.75. Another customer buys 4 hot dogs and 2 bags of potato chips for $9.50. Find the cost of each item.
9) A college student earned $8100 during summer vacation working as a waiter in a popular restaurant. The
student invested part of the money at 8% and the rest at 6%. If the student received a total of $564 in interest
at the end of the year, how much was invested at 8%?
Course Review
10) A chemist needs 140 milliliters of a 35% solution but has only 23% and 65% solutions available. Find how
many milliliters of each that should be mixed to get the desired solution.
Find all values that make the rational expression undefined.
11) 16
19x
12)
x2 - 16
2
x - 10x + 16
Simplify the rational expression.
7x5
13)
21x9
14) 16x - 10
5 - 8x
15)
x + 10
x2 + 8x - 20
Simplify the rational expression.
(x - 2)2
16)
x2 - 4
2
17) y + 12y + 27
y2 + 18y + 81
Multiply. Simplify if possible.
3
18) 4z · 10
5
z2
2
19) 2p - 2 · 4p
p
6p - 6
2
20) k + 12k + 27 ·
k2 + 13k + 36
k2 + 4k
k2 - 3k - 18
Divide. Simplify if possible.
2
3
21) 2x ÷ x
3
18
Course Review
Revised 201220
2
22) (y - 4) ÷ 11y - 44
11
121
Find the least common denominator of the rational expressions.
23) 7 and 5
8x3
6x7
24)
1
x2 + 10x + 25
and
1
x2 + 5x
Simplify the complex rational expression.
1
+8
7
25)
26)
5+
1
4
5
7
+
x x2
25 49
x
x2
Solve the rational equation.
27) 4 - 1 = 7
x 6 x
28) 7 + x = 16
x
x
29) x - 3 = x + 2
9
3
30) 7 - 6 = 7x
x
31)
Solve.
x+6
x
-2x
2x - 3
=
+
2x + 2 4x + 4
x+1
32) Young's rule, C = DA , can be used to approximate the dosage of a drug prescribed for children. In this
A + 12
formula, A = child's age in years, D = an adult dosage, and C = the proper child's dosage. When the adult
dosage is 120 milligrams and the child's dosage is 40 milligrams, what is the child's age?
Course Review
Revised 201220
Find the domain and range.
33) {(41, -2), (5, -1), (5, 0), (6, 1), (14, 3)}
Decide whether the relation is a function.
34) {(-6, -5), (-6, -2), (-1, -2), (5, -4), (9, 4)}
Find the indicated function value.
35) Find f(-1) when f(x) = x2 - 3x - 1.
Use the vertical line test to determine whether or not the graph is a graph of a function.
36)
37)
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Use the graph to find the indicated function value.
38) y = f(x). Find f(-4)
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
39) If f(x) = 9%, what year is represented by x?
Course Review
Revised 201220
Use the graph to identify domain and range.
40)
41)
Find the domain of the function.
42) f(x) = 5x
x-1
43) f(x) = -7x + 4
**STOP HERE FOR MIDTERM EXAM**
Find the square root if it is a real number, or state that the expression is not a real number.
44) 289
81
Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a
real number and does not exist, state so.
45) Evaluate f(x) =
x - 16 for f(9)
Determine the domain of the function.
46) f(x) = x + 6
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Answer the question.
47) The formula v = 20L can be used to estimate the speed of a car, v, in miles per hour, based on the length, L,
in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident and its
skid marks measure 405 feet, at what estimated speed was the car traveling when it applied its brakes just
prior to the accident?
Simplify the expression.
48) 36x4
Find the indicated function value for the function.
3
49) Evaluate f(x) = x + 5 for f(-13)
Use radical notation to rewrite the expression. Simplify, if possible.
50) (xy)1/6
Rewrite the expression with a rational exponent.
51) ( 23xy)3
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
52) (144x6y8 )1/2
1/2 3
53) (5x )
x1/8
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
9
54) x · x
Simplify by factoring.
55) 80
56) 20x2y
Simplify by factoring.
3
57) 54x8
Multiply and simplify.
58) 12xy ·
6xy2
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
59) 45 + 320
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3
3
60) 14 2 - 3 54
Use the quotient rule to simplify. Assume all variables represent positive real numbers.
12x2 y
61)
49
Divide and, if possible, simplify.
150x11
62)
63)
6x
3
108x6
3
4x2
Multiply and simplify. Assume that all variables represent positive real numbers.
64) (2 + 5)(4 + 2 5)
Rationalize the denominator and simplify.
65) 2
5x
66) 3 7
9x2
Rationalize the denominator.
67) 3
5- 5
Solve the equation.
68) 7x + 9 = 5
69) x2 - 5x + 9 = x - 2
70) ( 4x + 2 )1/3 - 5 = -3
71) 4y + 9 = 3y + 2
72) x2 - 8 - x + 4 = 0
Write in terms of i.
73) -36
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74) -224
Perform the indicated operation. Write the result in the form a + bi.
75) (4 + 7i) - (-2 + i)
Find each product. Write the result in the form a + bi.
76) 2i(2 - 4i)
77) (8 + 8i)(7 - 2i)
Divide and simplify to the form a + bi.
78) 9 + 7i
8 - 3i
Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express
imaginary solutions in the form a + bi.
79) 144x2 = 25
80) (x + 2)2 = 12
Complete the square for the binomial. Then factor the resulting perfect square trinomial.
81) x2 - 18x
Solve the quadratic equation by completing the square.
82) x2 - 8x = 7
Use the quadratic formula to solve the equation.
83) 2x2 = -8x - 1
Use the discriminant to determine the number and type of solutions for the given equation.
84) x2 + 2x + 8 = 0
Use the quadratic formula to solve the equation.
85) x2 - 6x + 45 = 0
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The graph of a quadratic function is given. Determine the function's equation. Assume a = 1.
86)
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
87) f(x) = 11(x - 2)2 + 9
Find the axis of symmetry of the parabola defined by the given quadratic function.
88) f(x) = -7(x - 2)2 - 6
Find the range of the quadratic function.
89) f(x) = (x + 6)2 - 2
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
90) f(x) = (x - 1)2 - 5
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Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.
91) f(x) = 8 - x2 - 2x
Determine whether the given quadratic function has a minimum value or maximum value. Then find the minimum or
maximum value and determine where it occurs.
92) f(x) = x2 - 2x - 5
Solve the problem.
93) You have 296 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that
maximize the enclosed area.
94) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function
C(x) = 3x2 - 30x + 225. Find the number of automobiles that must be produced to minimize the cost.
95) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -4p2 + 1210p, when the
unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum
revenue to the nearest whole dollar?
Course Review
Revised 201220