MMW MIDTERM Flashcards
set of ordered pairs.
relation
may have more than 1 output for any given input.
relation
The set whose elements are the first coordinates in the ordered pairs is the
domain
The set whose elements are the second coordinates is the
range
what are the 3 correspondence?
one is to many correspondence
one is to one correspondence
many is to one correspondence
can have no more than 1 output for any given input.
function
notion f(x)
The letter x
The letter y is replaced by f(x)
defines a function named f
represents the input value, or independent variable.
represents the output value, or dependent variable.
It involves only one value or accepts one value or operand.
unary operation
It can act on two operands “+” and “ – ”
binary operations
It takes two values and include the operations of addition, subtraction, multiplication, division and exponentiation.
binary operations
properties of two binary operations.
Closure of binary operations
commutativity of binary operations
Associativity of binary operations
Distributivity of binary operations
Identity elements of binary operations
Inverse of binary operations
the product and the sum of any two real numbers is also a real number
5+3 =8. 5x3=15
Closure of binary operations
Addition and multiplication of any two real numbers is commutative as seen in their mathematical symbols
x + y = y + x and x ● y = y ● x
Commutativity of Binary Operations
three real numbers you may take any two and perform addition or multiplication as the case maybe and you will end with the same answer.
(x+y)+z= x+ (y+z)
(4+5)+7=4+(5+7)
9+7=4+12
16=16
Associativity of Binary Operations
applies when multiplication is performed on a group of two numbers added or subtracted together.
z(x ± y) = zx ± zy
Distributivity of Binary Operations
set of real numbers is an identity element for addition/multiplication. this means that the identity is the number that you add to any real numbers and the result will be the same real number.
5+0=0+5=5 50x1=1x50=50
e- zero for addition, one for multiplication
Identity Elements of binary operations
x+(-x)=-x+x=0
4+(-4)=-4+4=0
inverse of binary operation
additive inverse/ reciprocal
4 operation of functions
sum of function
difference of function
product of function
quotient of function
father of problem
George polya(1887- 1985)
who strongly believed that the skill problem can be taught
George polya(1887-1985)
Polya’s Four-Step Problem Solving Strategy
Step 1 : Understand the problem.
Step 2 : Devise a plan.
Step 3: Carry out the plan.
Step 4: Review the solution
it is the process of translating a problem scenario into a drawing
strategy 1: draw a diagram, picture or model
data or information are organized by listing them or recording them systematically in tables.
The data are then analyzed to discover relationships and patterns and to draw out generalizations or solutions to the problem.
strategy 2: make a table or an organized list
Making a logical guess at the answer. The student learns more about the problem.
strategy: guess and check
Checking the guess.
strategy 3: guess and check
It is important that computation is accurate to avoid wastage of time and effort by making more guesses when in fact, the solution might have found some guesses before.st
strategy 3: guess and check
a strategy in which people physically act out what is taking place in a word problem.
strategy 4: act it out/ acting out a problem
One may use people or objects exactly as described in the problem, or you might use items that represent the people or objects.
strategy 4: act it out
people visualize and simulate the actions described in the problem.
strategy 4: act it out
method works well for problems where a series of operations is done on an unknown number and you’re only given the result.
strategy 5:word backwards
start with the result and apply the operations in reverse order until you find the starting number.
strategy 5:word backwards
Without mathematics, there’s nothing you can do.Everything around you is mathematics.Everything around you is numbers.”
shakuntala devi
It is a type of reasoning that uses specific examples to reach a general conclusion.
inductive reasoning
The conclusion formed by using inductive reasoning is called a
CONJECTURE
is an idea that may or may not be correct.
CONJECTURE
to a conjecture is an example for which the conjecture is incorrect
counterexample
a special kind of example that disproves a statement or proposition.
COUNTEREXAMPLE
It is a type of reasoning that uses general procedures and principles to reach a conclusion.
deductive reasoning
It is the process of reaching a general conclusion by applying general assumptions, procedures, or principles.
deductive reasoning
8 properties of equality
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
reflexive property of equality
symmetric property of equality
transitive property of equality
substitution property of equality
a+c=b+c
addition property of equality
a-c=b-c
subtraction property of equality
ac=bc
multiplication property of equality
a/c=b/c
division property of equality
a=a
reflexive property of equality
if a=b, then b =a
symmetric property of equality]]]
if a=b and b=c, then a=c
transitive property of equality
if a=b, then b can be substituted for a in any expression
substitution property of equality
ax=b
closure property
can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner.
Logic puzzles
Reaching conclusions based on a series of observations.
Inductive
Conjecture may or may not be valid or uncertain.
Inductive
Reaching conclusions based on previously known facts.
Deductive
Conjecture are correct and valid or certain.
Deductive
Forms of Deductive Reasoning
Hypothetical syllogism
Categorical Syllogism
if a statement p implies another statement q and p is true, then q must also be true
modus ponens
opposite of modus ponens
modus tollens
It is a type of deductive reasoning consisting of a conditional major premise, an unconditional minor premise, and an unconditional conclusion.
Hypothetical syllogism
Premise 1-If p then q,
Premise 2-and p,(true)-This is called
Premise 3-Therefore, q.( True). This is called the
- ( Conditional statement)
- antecedent
- consequent.
valid argument form, meaning if the premises are true, then the conclusion must be true
modus ponens
It is a form of deductive reasoning wherein a categorical conclusion is based on two categorical premises.
Categorical Syllogism
There are four types of propositions that are used in the syllogism:
Positive Universal: “All A are B” Ex.All dogs are mammals.
Negative Universal: “No A are B” Ex. No dogs are fish.
Positive Existential: “Some A are B” Ex. Some dogs are brown.
Negative Existential: “Some A are not B”. Ex.Some dogs are not brown.
three types of propositions will be used to create an argument
Major premise (universal quantifier)
Minor premise (existential quantifier)
Conclusion (universal or existential)
-a general statement about a category of things.
Major premise (universal quantifier)
a statement about a specific member or subset of that category.
Minor premise (existential quantifier)-
A statement that logically follows from the major and minor premises.
Conclusion (universal or existential)-
It is also denoted by
All p are q.
r is p.
Therefore, r is q.
Categorical Syllogism
it is development, execution, and supervision of plans
data management
the word statistics originated from the word
“status” meaning “state”
it is the science that deals with the collection, classification, analysis, and interpretation of numerical
statistics
are used to organize and summarize the information so that the researcher can see what happened in the research study
statistics
help to researcher to answer the questioning that initiated the researcher by determining exactly what general conclusions are justified
statistics
5 methods of data gathering
direct or interview method
indirect or questionnaire method
registration method
observation method
experimental method
it is a person to person encounter between the source of information, the interviewee
direct or interview method
it is the technique in which questionnaire is used to elicit the information
indirect or questionnaire method
It obtains data from the records of government agency authorized by law to keep such data or information and made these available to researchers.
registration
It is the technique in which data particularly those pertaining to the behaviors of individuals or group of individuals during the given situation.
observation
To notice using a full range of appropriate senses. To see, hear, feel, taste, and smell.
observation
This is also used when the respondents cannot read nor write.
observation
used to gather data from the result of performed series
experimental
systematically manipulated by the investigator
Independent variable
(IV)
Investigator measures to determine the effect of the independent variable
dependent variable(DV)
THE CAUSE
THE EFFECT
Independent variable
Dependent variable
experiment force a conclusion consonant with reality.
scientific method
It involves the collection and classification of data
descriptive statistics
It involves the analysis and interpretation of data.
inferential statistics
exampple: average and percentage
descriptive statistics
example: predict and estimate
inferential statistics
set of measurement corresponding to the entire collection of units
population
is a set of individuals selected from a population, usually intended to represent the population in a research study.
sample
sample formula
sample size= population size divide 1+ population size multiply by margin of error then squared
are measurements or observations.
Data
is a single measurement or observation and is commonly called a score or raw score.
datum
The measurements that are made on the subjects of an experiment are also called
data
The data as originally measured are often referred to as
raw or original scores.
2 types of data
Qualitative Data
Quantitative Data
Data that deal with categories or attributes
ex.Color of skin
Courses in Computer Engineering
Qualitative Data
Data that deal with numerical values
ex.Number of units in one semester
Grade point average
Quantitative Data
Data that are obtained by counting
ex. number of students in the classroom
number of cars in the parking lot
Discrete Data
Data that are obtained by measuring
ex. area of a mango farm in Pampanga
volume of water in a pool in Pansol, Laguna
Continuous Data
It can assume any of an infinite number of values and can be
associated with points on a continuous line interval.
Example: Height, weight, volume
Continuous Data
It results from either a finite number of possible values or a countable number of possible values.
Example: number of students, number of books, and number of patients
Discrete Data
is a value, usually a numerical value that describes a population.
Parameter
is usually derived from measurements of the individuals in the population
Parameter
is a value, usually a numerical value that describes a sample.
statistic
usually derived from measurements of the individuals in the sample.
statistic
occurring discrepancy, or error, that exists between a sample statistic
sampling error
characteristics of some events, object, or person that may have different values
variable
isa variable describing a characteristic.
qualitative variable
are also sometimes referred to as categorical variables because they can be separated into categories.
Qualitative variables
are often descriptive but can sometimes be given a numeric value.
Quantitative variables
has a value or numerical measurement for which operation can be applied.
For example: age, height, and weight are quantitative.
quantitative variable
Interval and ratio are sometimes called
continuous or scale
the hierarchy of levels
absolute zero
distance is meaningful
attributes can be ordered
attributes are only named; weakest
ratio
interval
ordinal
nominal
4 LEVELS OF MEASUREMENT
Nominal
Ordinal
Interval
Ratio
- labels qualitative data into mutually exclusive categories
Nominal
ranks qualitative data according to its degree
Ordinal
numerical data that has order and its differences can be determined;
do not have a “true” zero
Interval
numerical data that has order, differences can be determined and has a “true” zero
ratio
example: what is your civil status :
single, married, separated, annulled
Nominal
example: how satisfied are you with our food? extremely satisfied, very satisfied , satisfied
Ordinal
example: temperature
Interval
example: Speed, Height, Weight
ratio
data is the precious thing that last together
Tim berners lee
A single value that describes the center of a distribution:
mean, median,mode
also known as the “average” or “arithmetic mean”
mean
the middlemost score
median
the most frequent score
mode
the sum of all values in a dataset divided by the total number of observations
mean
in excel when computing the mean
type?
average (A1:A8) then enter
in excel when computing the meadian you’‘ll type?
median (A1:A8) then enter
in excel when computing the mode you’‘ll type?
mode(A1:A8) then entero
