Converting to different units of measure.
Convert 12 feet into yards.
12 ft = 4 yds
1 yd = 3 ft
and multiplying by 1 does not change the value (property of real numbers).
x 1 yd = 4 yds
Permutations and Combinations
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
Find x for
log332 = x
3x = 32
Log525 = x
Ln e3 = x
ex = e3
Log 10 = x
10x = 10
log10x = x
ln ex = x
Do not confuse log with ln.
Right Triangle Trigonometry
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.
Perimeter and Area
Two dimensional figures are classified by the number of sides they have.
Three angles, three sides.
Fundamental Principles of Counting, Combinations,
Collectively known as Combinatorics.
Fundamental Principle of Counting: Construct a tree diagram to keep track of all
possibilities. Each decision made produces new branches.
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.
If there were 20 grams of Iodine-131 8 days ago and now the
The growth of a population depends on its initial size.
Delta Notation: Greek letter
Rate of Change =
Change in quantity
Average growth rate:
In 1980, Anytown USA had a population of 2
Exponentials and Logarithms
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
Set: a collection of objects
Elements: members belonging in a set
Sets can be well-defined (without ambiguity) or not well-defined.
S = cfw_a, b, c
represents a list, roster.
The set S is equal to the set of
Short term loans or investments use simple interest computed at percent-per-year of the
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
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
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
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
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
(Read 3.1 to get acquainted with casino games.)
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 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
*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
Annuity: A sequence of equal regular payments into an account where each payment receives
Example of a Short-term annuity: Christmas club account.
Using our previous formulas for FV, we would need to compute a new