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
