Dimensional Analysis
Appendix E
Converting to different units of measure.
Convert 12 feet into yards.
12 ft = 4 yds
because
1 yd = 3 ft
so
1 yd
=
1
3 ft
and multiplying by 1 does not change the value
Permutations and Combinations
Section 2.4
The previous section covered selections of one item for each decision. Now choices include
more than one item selected with or without replacement.
With repla
Properties of Logarithms
Section 9.0B
Find x for
log332 = x
rewrite
3x = 32
therefore
x=2
Log525 = x
5x =25
x=2
Ln e3 = x
ex = e3
x=3
Log 10 = x
10x = 10
x=1
Inverse properties:
log10x = x
ln ex = x
D
Right Triangle Trigonometry
Section 6.5
A triangle has three sides measured in linear units and three angles measured in degrees or
radians whose sum is 180 degrees or (pi) radians, respectively.
This
Perimeter and Area
Section 6.1
Two dimensional figures are classified by the number of sides they have.
Polygon:
Many sides
Pentagon:
Five sides
Hexagon:
Six sides
Octagon:
Eight sides
Common figures:
Fundamental Principles of Counting, Combinations,
Permutations
Section 2.3
Collectively known as Combinatorics.
Fundamental Principle of Counting: Construct a tree diagram to keep track of all
possibi
Exponential Decay
Section 9.2
Our last Exponential model was for Growth. For radioactive decay, we also use an exponential
model. However, the rate is now negative to represent decay.
Example 1a:
If t
Exponential Growth
Section 9.1
The growth of a population depends on its initial size.
Delta Notation: Greek letter
Rate of Change =
=
Change in quantity
one change
Another change
Average growth rate
Exponentials and Logarithms
Section 9.0A
Applications involving population, radioactive decay, carbon-dating, earthquakes and the decibel
scale use exponential and logarithm properties.
Recall a Funct
Sets and Set Operations
Section 2.1
Set: a collection of objects
Elements: members belonging in a set
Sets can be well-defined (without ambiguity) or not well-defined.
Notations:
S = cfw_a, b, c
repr
Simple Interest
Section 5.1
Short term loans or investments use simple interest computed at percent-per-year of the
principal.
I = Prt
Future Value is Principal and Interest combined.
FV = P + I = P +
Compound Interest
Section 5.2
Bank and savings accounts pay compounded interest; interest that is periodically paid out on
existing accounts that include the principal and the previous interest paymen
Conditional Probability
Section 3.6
Public Opinion Polls may categorize respondents by sex, age, race and level of
education. Comparisons are made and trends observed by using conditional probability.
Deductive and Inductive Reasoning
Section 1.1
Logic is the science of correct reasoning.
In problem solving, we organize information, analyze it, compare it to previous problems and
come to some metho
Combinatorics and Probability
Section 3.4
Using rules of probability cuts work by not having to count the outcomes and sample
space. Using combinatorics from Chapter 2 is another alternative.
Recall C
Basic Terms of Probability
Section 3.2
(Read 3.1 to get acquainted with casino games.)
Definitions:
Experiment: a process by which an outcome is obtained, i.e., rolling a die.
Sample space: The set S
Amortized Loans
Section 5.4
Amortized Loan: A loan for which the loan amount plus interest owed is paid off in a series of
regular equal payments.
Previously, add-on interest loans were a type of amor
Basic Rules of Probability
Section 3.3
Probability Rules:
1. P(
)=0
*The smallest possible probability is of an impossible event (null set
).
2. P(S) = 1 *The largest possible probability is of a cert
Annuities
Section 5.3
Annuity: A sequence of equal regular payments into an account where each payment receives
compound interest.
Example of a Short-term annuity: Christmas club account.
Using our pr