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QUIZ 1A  SOLUTIONS
(CHAPTER 0)
MATH 141 – SPRING 2011 – KUNIYUKI
90 POINTS TOTAL
No notes or books allowed. A scientific calculator is allowed.
You may assume that twodimensional graphs are in the usual Cartesian
xy
plane.
Give exact answers, unless you are told to approximate.
SHORTER PROBLEMS
(30 POINTS TOTAL:
2 POINTS EACH, UNLESS OTHERWISE SPECIFIED)
1)
The symbol
±
means which of the following? (Box in one.)
For all
There exists
Is a member of
2)
(6 points total).
a)
Write the
converse
of this statement:
“If John is good, then I buy John the Harry Potter book.”
“If I buy John the Harry Potter book, then John is good.”
b)
Write the
contrapositive
of this statement:
“If John is good, then I buy John the Harry Potter book.”
“If I do not buy John the Harry Potter book, then John is not good.”
Note
: Just because a person is “not good” does not necessarily mean that
s/he is “bad.”
c)
Which of the following is logically equivalent to the given statement?
(Box in one.)
Its converse
Its inverse
Its contrapositive
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Use absolute value notation to mathematically express the distance between
x
and 4 on the real number line.
x
±
4
or
4
±
x
4)
(5 points). Factor completely over
±
, the integers:
4
x
7
+
32
x
4
.
First, factor out the GCF, 4
x
4
.
4
x
7
+
32
x
4
=
4
x
4
x
3
+
8
()
We must now factor
x
3
+
8
.
Template for factoring a Sum of Two Cubes:
A
3
+
B
3
=
A
+
B
A
2
±
AB
+
B
2
.
Here,
A
=
x
and
B
=
2 .
4
x
4
x
3
+
8
=
4
x
4
x
+
2
x
2
±
2
x
+
4
Note
: The last factor,
x
2
±
2
x
+
4
, is irreducible over the integers by the Test for
Factorability.
5)
Is
a
2
+
b
2
equivalent to
a
+
b
? Box in one:
Y
e
s
N
o
A counterexample is provided by the case
a
=
3 and
b
=
4 , for example.
The square root of a sum does not typically equal the sum of the square roots.
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 Fall '11
 staff
 Math, Calculus

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