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Algebra II / Mr. Hansen |
Name:
_________F period_________ |
Test on Chapter 11: Sequences, Series, Binomial
Theorem
Time limit: 26 minutes. A calculator is
required.
Each problem is worth 3 points. There is no partial credit. Write the capital letter of the
best choice, or fill in the word or phrase that best fits each blank.
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For problems 1-5, identify each numbered item as one
of the following: |
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1. ____ |
2 – 1 + .5 – .25 + .125 –
.0625 + . . . |
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2. ____ |
0 + 1 + 3 + 7 + 15 + 31 +
63 + . . . |
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3. ____ |
555 + 666 + 777 + 888 + 999 |
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4. ____ |
2/3, 1, 1.5, 2.25 |
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5. ____ |
5, –5, –15, –25 |
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6. ____ |
A series converges if and
only if |
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(A) the terms become fairly small (B) the terms approach zero (C) the sequence of partial sums has a limit |
(D) the sequence of partial sums is arithmetic (E) the sequence of partial sums is geometric |
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7. ____ |
In the phrase “arithmetic sequence,”
how is the word “arithmetic” pronounced? |
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(A) with stress on the first and third syllables (B) with stress on the second syllable only (C) with stress on the fourth syllable only |
(D) with stress on the second and fourth syllables (E) with no stress whatsoever |
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8. |
Standard notation for a
common ratio is r, and standard
notation for a common difference is ______ . |
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9. |
An infinite geometric
series converges if and only if ________________________ . |
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10, 11. |
Compute the numeric value
for #1 and #2. If the value does not exist as a number, write “DNE.” |
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1. Answer:
________________________________ |
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2. Answer:
________________________________ |
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12. ____ |
In #1, S3 equals |
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(A) .5 |
(D) 3.5 |
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13. ____ |
Compute the sum of the
first 3500 counting numbers (1 through 3500). |
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(A) 6,126,700 |
(D) 7,126,800 |
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14, 15. |
“Full work” generally
consists of three components: formula (equation), _______________ , and circled result. The circled result should include proper
_______________ in word problems. |
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16-18. |
Find the 481st term of this
sequence: 55, 44, 33, 22, 11, 0, –11, –22, . . .
Show all three components of your proper work. |
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19-21. |
In the series 5 + 2.5 +
1.25 + .625 + .3125 + . . . , at least how many terms must we sum in order to
make the partial sum exceed 9.99995? Show a relevant formula (equation or inequality);
then either solve or use “brute force” to find the answer. |
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22. ____ |
Bridge is a game played
with a standard 52-card deck. Each player receives a hand consisting of 13
cards, randomly drawn. How many different bridge hands are possible? |
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(A) approximately 6.35
billion |
(D) approximately 6.35
trillion |
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23. ____ |
The 4th term in the
expansion of (q + w)9 equals |
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(A) q6w6 |
(D) 126q6w3 |
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24. ____ |
How many terms are in the
expansion of (a + b)n, where n is a positive integer? |
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(A) n – 1 |
(D) 2ab |
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25. ____ |
Give a real-world example
of a geometric sequence. |
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(A) the phase-out schedule of a government program
that is being cut to 75%, 50%, 25%, and finally 0% of its original funding (B) the pitches (in cycles per second) of the notes
on a grand piano (C) the interest payable at the end of each year
that a bond is in effect (simple interest, not compound interest) (D) the side lengths of an isosceles triangle (E) all of the above |
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26. ____ |
The even-numbered terms in
the expansion of (q – w)n all have what
general form? |
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(A) + |
(D) – |
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27-30. |
Write out the first 3 terms
of |
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