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 (property of real numbers).
12 ft
x 1 yd = 4 yds
3 ft
t
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 replacement means the same item can be chosen more than once
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
Do not confuse log with ln.
log ex
x
ln 10x
x,
and
More
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 book only uses degrees for angle measurement.
Recall a
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:
Triangle:
Three angles, three sides.
Quadrilateral: Fo
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
possibilities. Each decision made produces new branches.
Examp
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 there were 20 grams of Iodine-131 8 days ago and now the
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:
Example 1:
In 1980, Anytown USA had a population of 2
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 Function is a correspondence between two sets; the first set
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
represents a list, roster.
The set S is equal to the set of
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 + Prt = P(1 + rt)
Businesses use this type of loan for s
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 payments. (Interest is not
taken out so that the balance incr
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.
The conditional probability of event A given event B i
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 method for solving it.
Deductive reasoning is the process of
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 Combinatorics are the Fundamenatal Counting Principle (F
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 of all possible outcomes of an experiment.
i.e. the sam
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 amortized loans.
The difference is the amount of interest p
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 certain event (event equal to S, the sample
space
3. 0
P(E)
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 previous formulas for FV, we would need to compute a new