Review

1
Review

• Fall 2007
• Math 302B
• Section 4

2
Outline

• Algebraic Reasoning
• Statistics
• Interpreting data
• Representing data
• Probability
• Geometry
• Characteristics and Classifications
• Transformations
• Properties

3
Algebraic reasoning

• Determine how many small squares in the nth figure

n2 (n-4)2 for all n gt 3, and n2 for n1,2,3
4
Algebraic Reasoning

• A prime is any integer, not equal to one, and is
  divisible only by one and itself.
• Marta starts plugging in 1, 2, 3, and 4 into the
  function n2 n 17, and notices they are all
  primes. She says that every time you plug in an
  integer you get a prime.
• Prove Martas claim is not true and find the
  first instance where it is not true.

If n17, then everything in sight is divisible by
17, so it can not be a prime. The first instance
where it fails is n16 (plug and chug is simplest
way To verify this).
5
Statistics

• Two types batteries are tested to see how long
  they last. Below is the data set after ten tests
  (units are in hours)

Explain which battery you would choose based on
the tests above. Be sure to support your
decision based on what we have learned about
statistics.
It is important to compute the statistics, and
then be able to translate why Those numbers are
important in your comparision.
6
Statistics

• Devise a data set with 15 elements that has a
  mean less than 5 and median greater than 10.

Whoever said negative numbers are not allowed?
7
Probability

• Given a normal deck of playing cards
• How many different 5 card combinations are there?
• How many ways are there to get at least one pair
  out of 5 cards?
• What is the probability of getting at least one
  pair out of five cards?

8
Probability

• Given a normal deck of playing cards
• How many ways are there to get a 5 card flush?
• What is the probability of getting a flush?
• There are 4 suits times 13 cards for the 1st card
  times 12 cards for the 2nd and so on. So there
  are 4(13x12x11x10x9) ways to get a flush.

9
Probability

• Given a normal deck of playing cards
• How many ways are there to get a 5 card straight?
• What is the probability of getting a straight?
• There are 10 different straights (Ace low through
  10 low), and there are 4 of the low, 4 of the
  next, and so on. So there are 10(4x4x4x4x4)
  10280 ways to get a straight.

10
Geometry
B cm
A cm
Find the area of this parallelogram.
11
Geometry

• How faces does a prism have where the base is an
  n sided polygon?

12
Geometry

• If a cell phone box measures 1 in. by 2 in. by 5
  in., how many can be placed into a box that
  measures 12 in. by 24 in. by 10 in.?
• How do you know your placement of boxes is
  optimal?
• What if the box was 12 in. by 24 in. by 9 in.?