Precalculus
Take Home Test 1
Expectations
You may get help from other sources. Although cooperative learning is encouraged, the turned in product MUST
remain the work of the individual student. Each student is responsible for communicating his or her
understanding of the mathematics involved in this test.
This is a test! You are to create a final product that could stand on its own – Offer a statement of each problem,
show and explain organized work, explain final answers. We are looking for SOLUTIONS not answers. Since this
is the case, I do not want this sheet turned in with your responses.
Due Date: MON 9/10/07 at the start of class. There will be absolutely no extensions. Late work will earn 0
points. You are expected to turn the test in early if you will be gone on the due date.
Rubric
6
5
4
0
Mathematics
The response exceeds the prompted purpose of
the task. The student's strategy and execution
meet the content (including concepts, technique,
representations, and connections), thinking
processes and mathematical demands of the
task. Minor omissions may exist, but do not
detract from the correctness of the response.
Communication
The response demonstrates adequate
evidence of the learning and strategic tools
necessary to complete the prompted purpose. It
may contain overlooked issues, misleading
assumptions, and/or errors in execution.
Evidence in the response demonstrates that the
student can revise the work to accomplish the
task with the help of written feedback or
dialogue.
The response adequately communicates the
student's mathematical understanding, meets
the qualitative demands of the task, and
describes the strategies and processes used.
It may contain overlooked issues or
misleading assumptions. The response
demonstrates that the student can revise the
work to more effectively communicate their
ideas with the help of written feedback or
dialogue.
The response demonstrates some evidence of
mathematical knowledge that is appropriate to
the intent of the prompted purpose. An effort
was made to accomplish the task, but with little
success. Evidence in the response demonstrates
that with instruction the student can revise the
work to accomplish the task.
The response does not effectively
communicate the student's mathematical
understanding or meet the qualitative
demands of the task. Strategies and processes
are not described. It may contain overlooked
issues or misleading assumptions. An effort
was made to communicate ideas, but with
little success. The response demonstrates
that the student can revise the work to more
effectively communicate their ideas with
further instruction.
The response lacks any evidence of
mathematical knowledge that is appropriate to
the intent of the task.
The response lacks any clear
communication of mathematical knowledge
that is appropriate for the intent of the task.
The response effectively communicates the
student's mathematical understanding, meets
the qualitative demands of the task, and
describes the strategies and processes used.
Minor omissions may exist, but do not detract
from the quality of the response.
Please put all responses on separate paper with a statement of the problem.
(1)
It all adds up!
Express the following sum as a fraction
a
and verify your answer with a proof.
b
1
1
1
1


 ... 
1 2 2  3 3  4
99  100
(2)
You've got to fight for your right to party!
You are having a party. The first time the doorbell rings, one guest enters. If on each successive ring
a group enters that has 2 more guests than the group that entered on the previous ring, how many total
guests will have arrived after the 20th ring?
(3)
Escalating Excitement!
Determine the number of positive integers whose digits are in strictly increasing order. (Single digit
numbers automatically satisfy this condition)
(4)
Domino Effect
Prove by mathematical induction:
n
k
k 1
(5)
2

n(n  1)( 2n  1)
6
An Avalanche of Possibilities
The Colorado Avalanche are heading into a best-of -7 series versus the Detroit Red Wings. Assuming
the chances that the Avs win any one single game versus Detroit is
Avalanche win the series.
2
, find the probability that the
3