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MTH 120 Summer 2005 Bonus Questions Solution, Quizzes of Pre-Calculus

The solutions to the bonus questions of a mathematics course, mth 120, offered at essex county college during the summer of 2005. The solutions involve solving for x in a quadratic equation and identifying the term in a series that does not contain x.

Typology: Quizzes

Pre 2010

Uploaded on 08/08/2009

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MTH 120 Summer 2005
Essex County College Division of Mathematics and Physics
Bonus Question #1 1 Printed May 16, 2005
Name:
Signature:
The following questions are worth ten points total, and will be added to your quiz scores. Only
correct answers will be accepted. Due 05/19/2005.2
1. Solve3for x.4
X
k=0 4
k54kxk= 32
Solution: Rewrite as a binomial to a power.
(x+ 5)4= 32
x+ 5 = ±4
32
x=5±4
32
So x=5 + 4
32 or x=54
32 .
2. Find the term of
3x2
21
3x12
that does not contain x.
Solution: The general term has this form.
12
k3x2
2k1
3x12k
We’re looking for xto have a zero exponent.
x2k
x12k=x3k12 k= 4
1This document was prepared by Ron Bannon using L
A
T
E
X 2ε. Source and pdf are available by emailing a
request to rbannon@mac.com.
2Bonus questions are assigned on occasion, and have strict due dates that must be adhered to. If for some
reason you cannot physically make the due date, you can email either a pdf, plain text, or jpeg of your work.
Please do not send Microsoft Word files.
3Hint: It’s a binomial.
1
pf2

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MTH 120 — Summer — 2005 Essex County College — Division of Mathematics and Physics Bonus Question #1 1 — Printed May 16, 2005

Name:

Signature:

The following questions are worth ten points total, and will be added to your quiz scores. Only correct answers will be accepted. Due 05/19/2005.^2

  1. Solve^3 for x. ∑^4

k=

k

54 −kxk^ = 32

Solution: Rewrite as a binomial to a power.

(x + 5)^4 = 32 x + 5 = ± 4

x = − 5 ± 4

So x = −5 + 4

32 or x = − 5 − 4

  1. Find the term of (^) ( 3 x^2 2 −^

3 x

that does not contain x. Solution: The general term has this form. ( 12 k

3 x^2 2

)k ( − 1 3 x

) 12 −k

We’re looking for x to have a zero exponent.

x^2 k x^12 −k^

= x^3 k−^12 ⇒ k = 4 (^1) This document was prepared by Ron Bannon using LATEX 2ε. Source and pdf are available by emailing a request to 2 rbannon@mac.com. Bonus questions are assigned on occasion, and have strict due dates that must be adhered to. If for some reason you cannot physically make the due date, you can email either a pdf, plain text, or jpeg of your work. Please do not send Microsoft Word files. 3 Hint: It’s a binomial.

Substitute k = 4 in the general term and simplify.

( 12 4

3 x^2 2

3 x